Traffic Optimization with Trace¶
Introduction¶
This tutorial will guide you through the process of using trace to optimize parameters in a traffic simulation. The goal is to find the optimal green light durations for an intersection to minimize overall traffic delay.
Setup and Installation¶
First, ensure you have the required packages installed in addition to trace. You can install them using pip.
!pip install numpy uxsimImport Necessary Libraries¶
Let's start by importing the necessary libraries.
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%pip install trace-opt ipywidgets uxsim numpy
%pip install trace-opt ipywidgets uxsim numpy
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import numpy as np
import uxsim as ux
import itertools
import opto.trace as trace
from opto.optimizers import OptoPrime
from opto.trace.bundle import ExceptionNode
import numpy as np
import uxsim as ux
import itertools
import opto.trace as trace
from opto.optimizers import OptoPrime
from opto.trace.bundle import ExceptionNode
/home/aswaminathan/miniconda3/envs/trace/lib/python3.10/site-packages/tqdm/auto.py:21: TqdmWarning: IProgress not found. Please update jupyter and ipywidgets. See https://ipywidgets.readthedocs.io/en/stable/user_install.html from .autonotebook import tqdm as notebook_tqdm
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import os
import ipywidgets as widgets
from IPython.display import display
# Function to save the environment variable and API key
def save_env_variable(env_name, api_key):
# Validate inputs
if not env_name.strip():
print("⚠️ Environment variable name cannot be empty.")
return
if not api_key.strip():
print("⚠️ API key cannot be empty.")
return
# Store the API key as an environment variable
os.environ[env_name] = api_key
globals()[env_name] = api_key # Set it as a global variable
print(f"✅ API key has been set for environment variable: {env_name}")
# Create the input widgets
env_name_input = widgets.Text(
value="OPENAI_API_KEY", # Default value
description="Env Name:",
placeholder="Enter env variable name (e.g., MY_API_KEY)",
)
api_key_input = widgets.Password(
description="API Key:",
placeholder="Enter your API key",
)
# Create the button to submit the inputs
submit_button = widgets.Button(description="Set API Key")
# Display the widgets
display(env_name_input, api_key_input, submit_button)
# Callback function for the button click
def on_button_click(b):
env_name = env_name_input.value
api_key = api_key_input.value
save_env_variable(env_name, api_key)
# Attach the callback to the button
submit_button.on_click(on_button_click)
import os
import ipywidgets as widgets
from IPython.display import display
# Function to save the environment variable and API key
def save_env_variable(env_name, api_key):
# Validate inputs
if not env_name.strip():
print("⚠️ Environment variable name cannot be empty.")
return
if not api_key.strip():
print("⚠️ API key cannot be empty.")
return
# Store the API key as an environment variable
os.environ[env_name] = api_key
globals()[env_name] = api_key # Set it as a global variable
print(f"✅ API key has been set for environment variable: {env_name}")
# Create the input widgets
env_name_input = widgets.Text(
value="OPENAI_API_KEY", # Default value
description="Env Name:",
placeholder="Enter env variable name (e.g., MY_API_KEY)",
)
api_key_input = widgets.Password(
description="API Key:",
placeholder="Enter your API key",
)
# Create the button to submit the inputs
submit_button = widgets.Button(description="Set API Key")
# Display the widgets
display(env_name_input, api_key_input, submit_button)
# Callback function for the button click
def on_button_click(b):
env_name = env_name_input.value
api_key = api_key_input.value
save_env_variable(env_name, api_key)
# Attach the callback to the button
submit_button.on_click(on_button_click)
Define Constants and Functions¶
We define the constants and helper functions needed for the simulation.
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# Define minimum and maximum values for green light durations (parameter space)
MIN_GREEN_TIME = 15
MAX_GREEN_TIME = 90
# Define the simulation parameters (in seconds)
MAX_DURATION = 1800
SIMULATION_STEP = 6
# Define the demands
def create_demand(demand=0.25):
np.random.seed(42)
demandDict = {}
for n1, n2 in itertools.permutations(["W1", "E1", "N1", "S1"], 2):
for t in range(0, MAX_DURATION, SIMULATION_STEP):
demandDict[(n1, n2, t)] = np.random.uniform(0, demand)
# Add extra demand for E-W direction
for t in range(0, MAX_DURATION // 3, SIMULATION_STEP):
demandDict[("W1", "E1", t)] += demand
for t in range(2 * MAX_DURATION // 3, MAX_DURATION, SIMULATION_STEP):
demandDict[("E1", "W1", t)] += demand
return demandDict
# Define minimum and maximum values for green light durations (parameter space)
MIN_GREEN_TIME = 15
MAX_GREEN_TIME = 90
# Define the simulation parameters (in seconds)
MAX_DURATION = 1800
SIMULATION_STEP = 6
# Define the demands
def create_demand(demand=0.25):
np.random.seed(42)
demandDict = {}
for n1, n2 in itertools.permutations(["W1", "E1", "N1", "S1"], 2):
for t in range(0, MAX_DURATION, SIMULATION_STEP):
demandDict[(n1, n2, t)] = np.random.uniform(0, demand)
# Add extra demand for E-W direction
for t in range(0, MAX_DURATION // 3, SIMULATION_STEP):
demandDict[("W1", "E1", t)] += demand
for t in range(2 * MAX_DURATION // 3, MAX_DURATION, SIMULATION_STEP):
demandDict[("E1", "W1", t)] += demand
return demandDict
Using bundle to wrap the Create World Function¶
The create_world function sets up the traffic intersection with given green light durations.
Let us wrap the function with trace.bundle to let the optimizer view the entire function as a node in the traced graph.
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@trace.bundle(trainable=False, allow_external_dependencies=True)
def create_world(EW_time, NS_time):
global demand_dict
assert EW_time >= MIN_GREEN_TIME and EW_time <= MAX_GREEN_TIME, "EW_time out of bounds."
assert NS_time >= MIN_GREEN_TIME and NS_time <= MAX_GREEN_TIME, "NS_time out of bounds."
W = ux.World(
name="Grid World",
deltan=1,
reaction_time=1,
tmax=MAX_DURATION,
print_mode=0,
save_mode=0,
show_mode=0,
random_seed=0,
duo_update_time=120,
show_progress=0,
vehicle_logging_timestep_interval=-1,
)
W1 = W.addNode("W1", -1, 0)
E1 = W.addNode("E1", 1, 0)
N1 = W.addNode("N1", 0, 1)
S1 = W.addNode("S1", 0, -1)
for k, v in demand_dict.items():
n1, n2, t = k
node1 = eval(n1)
node2 = eval(n2)
W.adddemand(node1, node2, t, t + SIMULATION_STEP, v)
I1 = W.addNode("I1", 0, 0, signal=[EW_time, NS_time])
for n1, n2 in [[W1, I1], [I1, E1]]:
W.addLink(n1.name + n2.name, n1, n2, length=500, free_flow_speed=10, jam_density=0.2, signal_group=0)
W.addLink(n2.name + n1.name, n2, n1, length=500, free_flow_speed=10, jam_density=0.2, signal_group=0)
for n1, n2 in [[N1, I1], [I1, S1]]:
W.addLink(n1.name + n2.name, n1, n2, length=500, free_flow_speed=10, jam_density=0.2, signal_group=1)
W.addLink(n2.name + n1.name, n2, n1, length=500, free_flow_speed=10, jam_density=0.2, signal_group=1)
return W
@trace.bundle(trainable=False, allow_external_dependencies=True)
def create_world(EW_time, NS_time):
global demand_dict
assert EW_time >= MIN_GREEN_TIME and EW_time <= MAX_GREEN_TIME, "EW_time out of bounds."
assert NS_time >= MIN_GREEN_TIME and NS_time <= MAX_GREEN_TIME, "NS_time out of bounds."
W = ux.World(
name="Grid World",
deltan=1,
reaction_time=1,
tmax=MAX_DURATION,
print_mode=0,
save_mode=0,
show_mode=0,
random_seed=0,
duo_update_time=120,
show_progress=0,
vehicle_logging_timestep_interval=-1,
)
W1 = W.addNode("W1", -1, 0)
E1 = W.addNode("E1", 1, 0)
N1 = W.addNode("N1", 0, 1)
S1 = W.addNode("S1", 0, -1)
for k, v in demand_dict.items():
n1, n2, t = k
node1 = eval(n1)
node2 = eval(n2)
W.adddemand(node1, node2, t, t + SIMULATION_STEP, v)
I1 = W.addNode("I1", 0, 0, signal=[EW_time, NS_time])
for n1, n2 in [[W1, I1], [I1, E1]]:
W.addLink(n1.name + n2.name, n1, n2, length=500, free_flow_speed=10, jam_density=0.2, signal_group=0)
W.addLink(n2.name + n1.name, n2, n1, length=500, free_flow_speed=10, jam_density=0.2, signal_group=0)
for n1, n2 in [[N1, I1], [I1, S1]]:
W.addLink(n1.name + n2.name, n1, n2, length=500, free_flow_speed=10, jam_density=0.2, signal_group=1)
W.addLink(n2.name + n1.name, n2, n1, length=500, free_flow_speed=10, jam_density=0.2, signal_group=1)
return W
Analyze World Function¶
Similar to the create_world function, the analyze_world function analyzes the traffic data after the simulation runs.
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@trace.bundle(trainable=False, allow_external_dependencies=True)
def analyze_world(W):
assert not W.check_simulation_ongoing(), "Simulation has not completed."
outputDict = {"Avg. Delay": W.analyzer.average_delay}
time_lost = 0
num_vehicles = 0
for k, v in W.analyzer.od_trips.items():
outputDict[k] = {"Trips attempted": v}
num_vehicles += v
outputDict[k]["Trips completed"] = W.analyzer.od_trips_comp[k]
theoretical_minimum = W.analyzer.od_tt_free[k]
observed_delay = np.sum(W.analyzer.od_tt[k] - theoretical_minimum)
imputed_delay = (np.max(W.analyzer.od_tt[k]) + 1 - theoretical_minimum) * (v - len(W.analyzer.od_tt))
time_lost += observed_delay + imputed_delay
outputDict[k]["Time lost per vehicle"] = (observed_delay + imputed_delay) / v
outputDict["Best-Case Estimated Delay"] = time_lost / num_vehicles
variance = 0
for k, v in W.analyzer.od_trips.items():
variance += ((outputDict[k]["Time lost per vehicle"] - outputDict["Best-Case Estimated Delay"]) ** 2) * v
score = outputDict["Best-Case Estimated Delay"] + np.sqrt(variance / num_vehicles)
outputDict["OVERALL SCORE"] = score
return outputDict
@trace.bundle(trainable=False, allow_external_dependencies=True)
def analyze_world(W):
assert not W.check_simulation_ongoing(), "Simulation has not completed."
outputDict = {"Avg. Delay": W.analyzer.average_delay}
time_lost = 0
num_vehicles = 0
for k, v in W.analyzer.od_trips.items():
outputDict[k] = {"Trips attempted": v}
num_vehicles += v
outputDict[k]["Trips completed"] = W.analyzer.od_trips_comp[k]
theoretical_minimum = W.analyzer.od_tt_free[k]
observed_delay = np.sum(W.analyzer.od_tt[k] - theoretical_minimum)
imputed_delay = (np.max(W.analyzer.od_tt[k]) + 1 - theoretical_minimum) * (v - len(W.analyzer.od_tt))
time_lost += observed_delay + imputed_delay
outputDict[k]["Time lost per vehicle"] = (observed_delay + imputed_delay) / v
outputDict["Best-Case Estimated Delay"] = time_lost / num_vehicles
variance = 0
for k, v in W.analyzer.od_trips.items():
variance += ((outputDict[k]["Time lost per vehicle"] - outputDict["Best-Case Estimated Delay"]) ** 2) * v
score = outputDict["Best-Case Estimated Delay"] + np.sqrt(variance / num_vehicles)
outputDict["OVERALL SCORE"] = score
return outputDict
Run Approach Function¶
This helper function runs the optimization approach, catching exceptions thrown if any as feedback to the trace optimizer.
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def run_approach(num_iter, trace_memory=0):
W = None
return_val = np.zeros((num_iter, 3))
def traffic_simulation(EW_green_time, NS_green_time):
W = None
try:
W = create_world(EW_green_time, NS_green_time)
except Exception as e:
e_node = ExceptionNode(
e,
inputs={"EW_green_time": EW_green_time, "NS_green_time": NS_green_time},
description="[exception] Simulation raises an exception with these inputs.",
name="exception_step",
)
return e_node
W.data.exec_simulation()
return_dict = analyze_world(W)
return return_dict
EW_x = trace.node(MIN_GREEN_TIME, trainable=True, description=f"Value constrained to be within [{MIN_GREEN_TIME},{MAX_GREEN_TIME}]")
NS_x = trace.node(MIN_GREEN_TIME, trainable=True, description=f"Value constrained to be within [{MIN_GREEN_TIME},{MAX_GREEN_TIME}]")
optimizer = OptoPrime(
[EW_x, NS_x], memory_size=trace_memory
)
optimizer.objective = (
"You should suggest values for the variables so that the OVERALL SCORE is as small as possible.\n"
+ "There is a trade-off in setting the green light durations.\n"
+ "If the green light duration for a given direction is set too low, then vehicles will queue up over time and experience delays, thereby lowering the score for the intersection.\n"
+ "If the green light duration for a given direction is set too high, vehicles in the other direction will queue up and experience delays, thereby lowering the score for the intersection.\n"
+ "The goal is to find a balance for each direction (East-West and North-South) that minimizes the overall score of the intersection.\n"
+ optimizer.default_objective
)
for i in range(num_iter):
result = traffic_simulation(EW_x, NS_x)
feedback = None
if isinstance(result, ExceptionNode):
return_val[i] = (EW_x.data, NS_x.data, np.inf)
feedback = result.data
else:
return_val[i] = (EW_x.data, NS_x.data, result.data["OVERALL SCORE"])
feedback = (
"OVERALL SCORE: "
+ str(result.data["OVERALL SCORE"])
+ "\nPlease try to optimize the intersection further. If you are certain that you have found the optimal solution, please suggest it again."
)
optimizer.zero_feedback()
optimizer.backward(result, feedback, visualize=False)
optimizer.step(verbose=True)
return return_val
def run_approach(num_iter, trace_memory=0):
W = None
return_val = np.zeros((num_iter, 3))
def traffic_simulation(EW_green_time, NS_green_time):
W = None
try:
W = create_world(EW_green_time, NS_green_time)
except Exception as e:
e_node = ExceptionNode(
e,
inputs={"EW_green_time": EW_green_time, "NS_green_time": NS_green_time},
description="[exception] Simulation raises an exception with these inputs.",
name="exception_step",
)
return e_node
W.data.exec_simulation()
return_dict = analyze_world(W)
return return_dict
EW_x = trace.node(MIN_GREEN_TIME, trainable=True, description=f"Value constrained to be within [{MIN_GREEN_TIME},{MAX_GREEN_TIME}]")
NS_x = trace.node(MIN_GREEN_TIME, trainable=True, description=f"Value constrained to be within [{MIN_GREEN_TIME},{MAX_GREEN_TIME}]")
optimizer = OptoPrime(
[EW_x, NS_x], memory_size=trace_memory
)
optimizer.objective = (
"You should suggest values for the variables so that the OVERALL SCORE is as small as possible.\n"
+ "There is a trade-off in setting the green light durations.\n"
+ "If the green light duration for a given direction is set too low, then vehicles will queue up over time and experience delays, thereby lowering the score for the intersection.\n"
+ "If the green light duration for a given direction is set too high, vehicles in the other direction will queue up and experience delays, thereby lowering the score for the intersection.\n"
+ "The goal is to find a balance for each direction (East-West and North-South) that minimizes the overall score of the intersection.\n"
+ optimizer.default_objective
)
for i in range(num_iter):
result = traffic_simulation(EW_x, NS_x)
feedback = None
if isinstance(result, ExceptionNode):
return_val[i] = (EW_x.data, NS_x.data, np.inf)
feedback = result.data
else:
return_val[i] = (EW_x.data, NS_x.data, result.data["OVERALL SCORE"])
feedback = (
"OVERALL SCORE: "
+ str(result.data["OVERALL SCORE"])
+ "\nPlease try to optimize the intersection further. If you are certain that you have found the optimal solution, please suggest it again."
)
optimizer.zero_feedback()
optimizer.backward(result, feedback, visualize=False)
optimizer.step(verbose=True)
return return_val
Running the Notebook¶
Now, you can run each cell of the notebook step-by-step to see how the simulation and optimization are performed. You can modify the parameters and observe the effects on the optimization process.
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demand_dict = create_demand(0.25)
returned_val = run_approach(10, trace_memory=0)
print(returned_val)
demand_dict = create_demand(0.25)
returned_val = run_approach(10, trace_memory=0)
print(returned_val)
Prompt
You're tasked to solve a coding/algorithm problem. You will see the instruction, the code, the documentation of each function used in the code, and the feedback about the execution result.
Specifically, a problem will be composed of the following parts:
- #Instruction: the instruction which describes the things you need to do or the question you should answer.
- #Code: the code defined in the problem.
- #Documentation: the documentation of each function used in #Code. The explanation might be incomplete and just contain high-level description. You can use the values in #Others to help infer how those functions work.
- #Variables: the input variables that you can change.
- #Constraints: the constraints or descriptions of the variables in #Variables.
- #Inputs: the values of other inputs to the code, which are not changeable.
- #Others: the intermediate values created through the code execution.
- #Outputs: the result of the code output.
- #Feedback: the feedback about the code's execution result.
In #Variables, #Inputs, #Outputs, and #Others, the format is:
<data_type> <variable_name> = <value>
If <type> is (code), it means <value> is the source code of a python code, which may include docstring and definitions.
Output_format: Your output should be in the following json format, satisfying the json syntax:
{{
"reasoning": <Your reasoning>,
"answer": <Your answer>,
"suggestion": {{
<variable_1>: <suggested_value_1>,
<variable_2>: <suggested_value_2>,
}}
}}
In "reasoning", explain the problem: 1. what the #Instruction means 2. what the #Feedback on #Output means to #Variables considering how #Variables are used in #Code and other values in #Documentation, #Inputs, #Others. 3. Reasoning about the suggested changes in #Variables (if needed) and the expected result.
If #Instruction asks for an answer, write it down in "answer".
If you need to suggest a change in the values of #Variables, write down the suggested values in "suggestion". Remember you can change only the values in #Variables, not others. When <type> of a variable is (code), you should write the new definition in the format of python code without syntax errors, and you should not change the function name or the function signature.
If no changes or answer are needed, just output TERMINATE.
Now you see problem instance:
================================
#Instruction
You should suggest values for the variables so that the OVERALL SCORE is as small as possible.
There is a trade-off in setting the green light durations.
If the green light duration for a given direction is set too low, then vehicles will queue up over time and experience delays, thereby lowering the score for the intersection.
If the green light duration for a given direction is set too high, vehicles in the other direction will queue up and experience delays, thereby lowering the score for the intersection.
The goal is to find a balance for each direction (East-West and North-South) that minimizes the overall score of the intersection.
You need to change the <value> of the variables in #Variables to improve the output in accordance to #Feedback.
#Code
create_world0 = create_world(EW_time=int0, NS_time=int1)
analyze_world0 = analyze_world(W=create_world0)
#Documentation
[create_world] .
[analyze_world] .
#Variables
(int) int0=15
(int) int1=15
#Constraints
(int) int0: [15,90]
(int) int1: [15,90]
#Inputs
#Others
(World) create_world0=<uxsim.uxsim.World object at 0x7fe8b2a94100>
#Outputs
(dict) analyze_world0={'Avg. Delay': 11.060312732688013, (<Node W1>, <Node E1>): {'Trips attempted': 226, 'Trips completed': 224, 'Time lost per vehicle': 52.769911504424776}, (<Node W1>, <Node N1>): {'Trips attempted': 105, 'Trips completed': 103, 'Time lost per vehicle': 47.89523809523809}, (<Node W1>, <Node S1>): {'Trips attempted': 86, 'Trips completed': 80, 'Time lost per vehicle': 33.91860465116279}, (<Node E1>, <Node W1>): {'Trips attempted': 238, 'Trips completed': 188, 'Time lost per vehicle': 93.33613445378151}, (<Node E1>, <Node N1>): {'Trips attempted': 104, 'Trips completed': 94, 'Time lost per vehicle': 84.75961538461539}, (<Node E1>, <Node S1>): {'Trips attempted': 93, 'Trips completed': 82, 'Time lost per vehicle': 79.72043010752688}, (<Node N1>, <Node W1>): {'Trips attempted': 98, 'Trips completed': 92, 'Time lost per vehicle': 21.387755102040817}, (<Node N1>, <Node E1>): {'Trips attempted': 100, 'Trips completed': 96, 'Time lost per vehicle': 21.62}, (<Node N1>, <Node S1>): {'Trips attempted': 98, 'Trips completed': 94, 'Time lost per vehicle': 22.56122448979592}, (<Node S1>, <Node W1>): {'Trips attempted': 111, 'Trips completed': 103, 'Time lost per vehicle': 21.153153153153152}, (<Node S1>, <Node E1>): {'Trips attempted': 93, 'Trips completed': 86, 'Time lost per vehicle': 21.956989247311828}, (<Node S1>, <Node N1>): {'Trips attempted': 104, 'Trips completed': 101, 'Time lost per vehicle': 20.509615384615383}, 'Best-Case Estimated Delay': 48.97458791208791, 'OVERALL SCORE': 77.2999365054568}
#Feedback
OVERALL SCORE: 77.2999365054568
Please try to optimize the intersection further. If you are certain that you have found the optimal solution, please suggest it again.
================================
Your response:
LLM response:
{
"reasoning": "The OVERALL SCORE represents an aggregated measure based on the time vehicles require to traverse through different nodes or intersections in the simulation. The goal is to minimize this OVERALL SCORE, which entails adjusting both East-West (EW_time) and North-South (NS_time) green light durations. Currently, both durations are set identically at 15 seconds. Given that increasing the duration for one direction will likely cause increased waiting for the opposing direction, changing these values could provide better balancing, thereby optimizing traffic flow across the intersection. By looking at the 'Time lost per vehicle' statistics from the outputs, we can see certain patterns. Generally, there are significant delays for vehicles traveling from east to west and north to south. This suggests that the current durations might be causing less optimal flow in those directions. To mitigate this, we may consider adjusting the durations slightly up for these directions. Changing both values within the given constraints might provide a solution that will help reduce the overall score.",
"suggestion": {
"int0": 25,
"int1": 25
}
}
Prompt
You're tasked to solve a coding/algorithm problem. You will see the instruction, the code, the documentation of each function used in the code, and the feedback about the execution result.
Specifically, a problem will be composed of the following parts:
- #Instruction: the instruction which describes the things you need to do or the question you should answer.
- #Code: the code defined in the problem.
- #Documentation: the documentation of each function used in #Code. The explanation might be incomplete and just contain high-level description. You can use the values in #Others to help infer how those functions work.
- #Variables: the input variables that you can change.
- #Constraints: the constraints or descriptions of the variables in #Variables.
- #Inputs: the values of other inputs to the code, which are not changeable.
- #Others: the intermediate values created through the code execution.
- #Outputs: the result of the code output.
- #Feedback: the feedback about the code's execution result.
In #Variables, #Inputs, #Outputs, and #Others, the format is:
<data_type> <variable_name> = <value>
If <type> is (code), it means <value> is the source code of a python code, which may include docstring and definitions.
Output_format: Your output should be in the following json format, satisfying the json syntax:
{{
"reasoning": <Your reasoning>,
"answer": <Your answer>,
"suggestion": {{
<variable_1>: <suggested_value_1>,
<variable_2>: <suggested_value_2>,
}}
}}
In "reasoning", explain the problem: 1. what the #Instruction means 2. what the #Feedback on #Output means to #Variables considering how #Variables are used in #Code and other values in #Documentation, #Inputs, #Others. 3. Reasoning about the suggested changes in #Variables (if needed) and the expected result.
If #Instruction asks for an answer, write it down in "answer".
If you need to suggest a change in the values of #Variables, write down the suggested values in "suggestion". Remember you can change only the values in #Variables, not others. When <type> of a variable is (code), you should write the new definition in the format of python code without syntax errors, and you should not change the function name or the function signature.
If no changes or answer are needed, just output TERMINATE.
Now you see problem instance:
================================
#Instruction
You should suggest values for the variables so that the OVERALL SCORE is as small as possible.
There is a trade-off in setting the green light durations.
If the green light duration for a given direction is set too low, then vehicles will queue up over time and experience delays, thereby lowering the score for the intersection.
If the green light duration for a given direction is set too high, vehicles in the other direction will queue up and experience delays, thereby lowering the score for the intersection.
The goal is to find a balance for each direction (East-West and North-South) that minimizes the overall score of the intersection.
You need to change the <value> of the variables in #Variables to improve the output in accordance to #Feedback.
#Code
create_world1 = create_world(EW_time=int0, NS_time=int1)
analyze_world1 = analyze_world(W=create_world1)
#Documentation
[create_world] .
[analyze_world] .
#Variables
(int) int0=25
(int) int1=25
#Constraints
(int) int0: [15,90]
(int) int1: [15,90]
#Inputs
#Others
(World) create_world1=<uxsim.uxsim.World object at 0x7fe8b250ff40>
#Outputs
(dict) analyze_world1={'Avg. Delay': 15.03579418344519, (<Node W1>, <Node E1>): {'Trips attempted': 226, 'Trips completed': 224, 'Time lost per vehicle': 67.02212389380531}, (<Node W1>, <Node N1>): {'Trips attempted': 105, 'Trips completed': 103, 'Time lost per vehicle': 62.78095238095238}, (<Node W1>, <Node S1>): {'Trips attempted': 86, 'Trips completed': 79, 'Time lost per vehicle': 50.23255813953488}, (<Node E1>, <Node W1>): {'Trips attempted': 238, 'Trips completed': 188, 'Time lost per vehicle': 103.01680672268908}, (<Node E1>, <Node N1>): {'Trips attempted': 104, 'Trips completed': 94, 'Time lost per vehicle': 90.48076923076923}, (<Node E1>, <Node S1>): {'Trips attempted': 93, 'Trips completed': 82, 'Time lost per vehicle': 84.95698924731182}, (<Node N1>, <Node W1>): {'Trips attempted': 98, 'Trips completed': 92, 'Time lost per vehicle': 31.642857142857142}, (<Node N1>, <Node E1>): {'Trips attempted': 100, 'Trips completed': 96, 'Time lost per vehicle': 34.09}, (<Node N1>, <Node S1>): {'Trips attempted': 98, 'Trips completed': 93, 'Time lost per vehicle': 32.56122448979592}, (<Node S1>, <Node W1>): {'Trips attempted': 111, 'Trips completed': 103, 'Time lost per vehicle': 32.810810810810814}, (<Node S1>, <Node E1>): {'Trips attempted': 93, 'Trips completed': 86, 'Time lost per vehicle': 32.86021505376344}, (<Node S1>, <Node N1>): {'Trips attempted': 104, 'Trips completed': 101, 'Time lost per vehicle': 36.29807692307692}, 'Best-Case Estimated Delay': 60.482142857142854, 'OVERALL SCORE': 87.25295510124234}
#Feedback
OVERALL SCORE: 87.25295510124234
Please try to optimize the intersection further. If you are certain that you have found the optimal solution, please suggest it again.
================================
Your response:
LLM response:
{
"reasoning": "According to the #Instruction, the goal is to minimize the 'OVERALL SCORE' at the intersection by finding a balanced setting for the green light durations in both the East-West (EW) and North-South (NS) directions. The two variables int0 and int1 represent these durations. Given the performance feedback that entails a relatively high 'OVERALL SCORE' of 87.25295510124234, it indicates that the current settings of 25 seconds each for EW and NS might not be optimal and could potentially lead to prolonged delays. Analyzing the 'Output' where we see significant delays, especially between (Node E1, Node W1) with the highest time lost per vehicle, suggests that the distribution of green light durations might be uneven, causing excessive delays for one direction over the other. Changing the values of int0 and int1 within the specified constraints of [15, 90] seconds might help in achieving a better trade-off between minimizing delays and balancing traffic flow across all directions.",
"suggestion": {
"int0": 35,
"int1": 30
}
}
Prompt
You're tasked to solve a coding/algorithm problem. You will see the instruction, the code, the documentation of each function used in the code, and the feedback about the execution result.
Specifically, a problem will be composed of the following parts:
- #Instruction: the instruction which describes the things you need to do or the question you should answer.
- #Code: the code defined in the problem.
- #Documentation: the documentation of each function used in #Code. The explanation might be incomplete and just contain high-level description. You can use the values in #Others to help infer how those functions work.
- #Variables: the input variables that you can change.
- #Constraints: the constraints or descriptions of the variables in #Variables.
- #Inputs: the values of other inputs to the code, which are not changeable.
- #Others: the intermediate values created through the code execution.
- #Outputs: the result of the code output.
- #Feedback: the feedback about the code's execution result.
In #Variables, #Inputs, #Outputs, and #Others, the format is:
<data_type> <variable_name> = <value>
If <type> is (code), it means <value> is the source code of a python code, which may include docstring and definitions.
Output_format: Your output should be in the following json format, satisfying the json syntax:
{{
"reasoning": <Your reasoning>,
"answer": <Your answer>,
"suggestion": {{
<variable_1>: <suggested_value_1>,
<variable_2>: <suggested_value_2>,
}}
}}
In "reasoning", explain the problem: 1. what the #Instruction means 2. what the #Feedback on #Output means to #Variables considering how #Variables are used in #Code and other values in #Documentation, #Inputs, #Others. 3. Reasoning about the suggested changes in #Variables (if needed) and the expected result.
If #Instruction asks for an answer, write it down in "answer".
If you need to suggest a change in the values of #Variables, write down the suggested values in "suggestion". Remember you can change only the values in #Variables, not others. When <type> of a variable is (code), you should write the new definition in the format of python code without syntax errors, and you should not change the function name or the function signature.
If no changes or answer are needed, just output TERMINATE.
Now you see problem instance:
================================
#Instruction
You should suggest values for the variables so that the OVERALL SCORE is as small as possible.
There is a trade-off in setting the green light durations.
If the green light duration for a given direction is set too low, then vehicles will queue up over time and experience delays, thereby lowering the score for the intersection.
If the green light duration for a given direction is set too high, vehicles in the other direction will queue up and experience delays, thereby lowering the score for the intersection.
The goal is to find a balance for each direction (East-West and North-South) that minimizes the overall score of the intersection.
You need to change the <value> of the variables in #Variables to improve the output in accordance to #Feedback.
#Code
create_world2 = create_world(EW_time=int0, NS_time=int1)
analyze_world2 = analyze_world(W=create_world2)
#Documentation
[create_world] .
[analyze_world] .
#Variables
(int) int0=35
(int) int1=30
#Constraints
(int) int0: [15,90]
(int) int1: [15,90]
#Inputs
#Others
(World) create_world2=<uxsim.uxsim.World object at 0x7fe8b15c74f0>
#Outputs
(dict) analyze_world2={'Avg. Delay': 14.975537435137138, (<Node W1>, <Node E1>): {'Trips attempted': 226, 'Trips completed': 224, 'Time lost per vehicle': 60.243362831858406}, (<Node W1>, <Node N1>): {'Trips attempted': 105, 'Trips completed': 103, 'Time lost per vehicle': 55.59047619047619}, (<Node W1>, <Node S1>): {'Trips attempted': 86, 'Trips completed': 79, 'Time lost per vehicle': 41.151162790697676}, (<Node E1>, <Node W1>): {'Trips attempted': 238, 'Trips completed': 192, 'Time lost per vehicle': 74.18067226890756}, (<Node E1>, <Node N1>): {'Trips attempted': 104, 'Trips completed': 96, 'Time lost per vehicle': 69.64423076923077}, (<Node E1>, <Node S1>): {'Trips attempted': 93, 'Trips completed': 84, 'Time lost per vehicle': 68.06451612903226}, (<Node N1>, <Node W1>): {'Trips attempted': 98, 'Trips completed': 92, 'Time lost per vehicle': 44.66326530612245}, (<Node N1>, <Node E1>): {'Trips attempted': 100, 'Trips completed': 96, 'Time lost per vehicle': 41.79}, (<Node N1>, <Node S1>): {'Trips attempted': 98, 'Trips completed': 93, 'Time lost per vehicle': 45.54081632653061}, (<Node S1>, <Node W1>): {'Trips attempted': 111, 'Trips completed': 103, 'Time lost per vehicle': 46.585585585585584}, (<Node S1>, <Node E1>): {'Trips attempted': 93, 'Trips completed': 86, 'Time lost per vehicle': 48.82795698924731}, (<Node S1>, <Node N1>): {'Trips attempted': 104, 'Trips completed': 101, 'Time lost per vehicle': 50.28846153846154}, 'Best-Case Estimated Delay': 56.44230769230769, 'OVERALL SCORE': 68.0403160003715}
#Feedback
OVERALL SCORE: 68.0403160003715
Please try to optimize the intersection further. If you are certain that you have found the optimal solution, please suggest it again.
================================
Your response:
LLM response:
{
"reasoning": "The OVERALL SCORE of 68.0403160003715 indicates that the current settings for the East-West and North-South green light durations (int0 = 35 and int1 = 30 respectively) are not optimally balanced. According to the instruction, the objective is to minimize the OVERALL SCORE by finding an optimal balance for the green light durations that minimizes the average delay caused by queuing vehicles. Lowering the OVERALL SCORE implies reducing the 'Time lost per vehicle' for each direction at the intersection. In the available 'Output', specific 'Time lost per vehicle' values like 74.18067226890756 (East to West) suggest that certain directions might have disproportionately long or short green light spans. The feedback asks for further optimization, implying the potential for better balancing of int0 and int1 within the constraints given (15 to 90). Adjusting int0 and int1 to trial values that are closer to the midpoint or slightly shifting them might provide a better distribution of green times, thereby lowering the overall score.",
"suggestion": {
"int0": 40,
"int1": 35
}
}
Prompt
You're tasked to solve a coding/algorithm problem. You will see the instruction, the code, the documentation of each function used in the code, and the feedback about the execution result.
Specifically, a problem will be composed of the following parts:
- #Instruction: the instruction which describes the things you need to do or the question you should answer.
- #Code: the code defined in the problem.
- #Documentation: the documentation of each function used in #Code. The explanation might be incomplete and just contain high-level description. You can use the values in #Others to help infer how those functions work.
- #Variables: the input variables that you can change.
- #Constraints: the constraints or descriptions of the variables in #Variables.
- #Inputs: the values of other inputs to the code, which are not changeable.
- #Others: the intermediate values created through the code execution.
- #Outputs: the result of the code output.
- #Feedback: the feedback about the code's execution result.
In #Variables, #Inputs, #Outputs, and #Others, the format is:
<data_type> <variable_name> = <value>
If <type> is (code), it means <value> is the source code of a python code, which may include docstring and definitions.
Output_format: Your output should be in the following json format, satisfying the json syntax:
{{
"reasoning": <Your reasoning>,
"answer": <Your answer>,
"suggestion": {{
<variable_1>: <suggested_value_1>,
<variable_2>: <suggested_value_2>,
}}
}}
In "reasoning", explain the problem: 1. what the #Instruction means 2. what the #Feedback on #Output means to #Variables considering how #Variables are used in #Code and other values in #Documentation, #Inputs, #Others. 3. Reasoning about the suggested changes in #Variables (if needed) and the expected result.
If #Instruction asks for an answer, write it down in "answer".
If you need to suggest a change in the values of #Variables, write down the suggested values in "suggestion". Remember you can change only the values in #Variables, not others. When <type> of a variable is (code), you should write the new definition in the format of python code without syntax errors, and you should not change the function name or the function signature.
If no changes or answer are needed, just output TERMINATE.
Now you see problem instance:
================================
#Instruction
You should suggest values for the variables so that the OVERALL SCORE is as small as possible.
There is a trade-off in setting the green light durations.
If the green light duration for a given direction is set too low, then vehicles will queue up over time and experience delays, thereby lowering the score for the intersection.
If the green light duration for a given direction is set too high, vehicles in the other direction will queue up and experience delays, thereby lowering the score for the intersection.
The goal is to find a balance for each direction (East-West and North-South) that minimizes the overall score of the intersection.
You need to change the <value> of the variables in #Variables to improve the output in accordance to #Feedback.
#Code
create_world3 = create_world(EW_time=int0, NS_time=int1)
analyze_world3 = analyze_world(W=create_world3)
#Documentation
[create_world] .
[analyze_world] .
#Variables
(int) int0=40
(int) int1=35
#Constraints
(int) int0: [15,90]
(int) int1: [15,90]
#Inputs
#Others
(World) create_world3=<uxsim.uxsim.World object at 0x7fe8b080ae00>
#Outputs
(dict) analyze_world3={'Avg. Delay': 17.071375464684014, (<Node W1>, <Node E1>): {'Trips attempted': 226, 'Trips completed': 223, 'Time lost per vehicle': 72.51769911504425}, (<Node W1>, <Node N1>): {'Trips attempted': 105, 'Trips completed': 102, 'Time lost per vehicle': 63.523809523809526}, (<Node W1>, <Node S1>): {'Trips attempted': 86, 'Trips completed': 79, 'Time lost per vehicle': 48.98837209302326}, (<Node E1>, <Node W1>): {'Trips attempted': 238, 'Trips completed': 192, 'Time lost per vehicle': 87.08403361344538}, (<Node E1>, <Node N1>): {'Trips attempted': 104, 'Trips completed': 96, 'Time lost per vehicle': 72.70192307692308}, (<Node E1>, <Node S1>): {'Trips attempted': 93, 'Trips completed': 83, 'Time lost per vehicle': 78.03225806451613}, (<Node N1>, <Node W1>): {'Trips attempted': 98, 'Trips completed': 92, 'Time lost per vehicle': 50.36734693877551}, (<Node N1>, <Node E1>): {'Trips attempted': 100, 'Trips completed': 95, 'Time lost per vehicle': 51.32}, (<Node N1>, <Node S1>): {'Trips attempted': 98, 'Trips completed': 93, 'Time lost per vehicle': 52.52040816326531}, (<Node S1>, <Node W1>): {'Trips attempted': 111, 'Trips completed': 103, 'Time lost per vehicle': 53.414414414414416}, (<Node S1>, <Node E1>): {'Trips attempted': 93, 'Trips completed': 86, 'Time lost per vehicle': 51.774193548387096}, (<Node S1>, <Node N1>): {'Trips attempted': 104, 'Trips completed': 101, 'Time lost per vehicle': 52.06730769230769}, 'Best-Case Estimated Delay': 64.69093406593407, 'OVERALL SCORE': 78.47073722046562}
#Feedback
OVERALL SCORE: 78.47073722046562
Please try to optimize the intersection further. If you are certain that you have found the optimal solution, please suggest it again.
================================
Your response:
LLM response:
{
"reasoning": "From the problem statement, the goal is to adjust the green light durations for the East-West (EW) and North-South (NS) directions to achieve the smallest possible OVERALL SCORE, which measures intersection performance. The `create_world` function seems to simulate the intersection based on the EW and NS green light durations (int0 and int1). The `analyze_world` function then evaluates this simulation, providing outputs such as average delays, trips completed, and the overall score. Adjusting int0 and int1 within their constraints (15 to 90) changes the dynamics of the intersection. Considering the feedback, the current settings of int0=40 and int1=35 result in an OVERALL SCORE of 78.47073722046562, which has been suggested for optimization. Since the delays are significantly different across directions (e.g., East to West has a higher time lost per vehicle than North to West), a possible path to optimization is to adjust the durations to equalize these delays, suggesting that the network load is unevenly distributed. Given the constraints, a balanced decrease might be needed to help reduce the higher delays observed in East-West trips, which currently have longer lost times. A suggested change could be to reduce East-West time slightly and increase North-South time to see if this balances out the network load better.",
"suggestion": {
"int0": 35,
"int1": 40
}
}
Prompt
You're tasked to solve a coding/algorithm problem. You will see the instruction, the code, the documentation of each function used in the code, and the feedback about the execution result.
Specifically, a problem will be composed of the following parts:
- #Instruction: the instruction which describes the things you need to do or the question you should answer.
- #Code: the code defined in the problem.
- #Documentation: the documentation of each function used in #Code. The explanation might be incomplete and just contain high-level description. You can use the values in #Others to help infer how those functions work.
- #Variables: the input variables that you can change.
- #Constraints: the constraints or descriptions of the variables in #Variables.
- #Inputs: the values of other inputs to the code, which are not changeable.
- #Others: the intermediate values created through the code execution.
- #Outputs: the result of the code output.
- #Feedback: the feedback about the code's execution result.
In #Variables, #Inputs, #Outputs, and #Others, the format is:
<data_type> <variable_name> = <value>
If <type> is (code), it means <value> is the source code of a python code, which may include docstring and definitions.
Output_format: Your output should be in the following json format, satisfying the json syntax:
{{
"reasoning": <Your reasoning>,
"answer": <Your answer>,
"suggestion": {{
<variable_1>: <suggested_value_1>,
<variable_2>: <suggested_value_2>,
}}
}}
In "reasoning", explain the problem: 1. what the #Instruction means 2. what the #Feedback on #Output means to #Variables considering how #Variables are used in #Code and other values in #Documentation, #Inputs, #Others. 3. Reasoning about the suggested changes in #Variables (if needed) and the expected result.
If #Instruction asks for an answer, write it down in "answer".
If you need to suggest a change in the values of #Variables, write down the suggested values in "suggestion". Remember you can change only the values in #Variables, not others. When <type> of a variable is (code), you should write the new definition in the format of python code without syntax errors, and you should not change the function name or the function signature.
If no changes or answer are needed, just output TERMINATE.
Now you see problem instance:
================================
#Instruction
You should suggest values for the variables so that the OVERALL SCORE is as small as possible.
There is a trade-off in setting the green light durations.
If the green light duration for a given direction is set too low, then vehicles will queue up over time and experience delays, thereby lowering the score for the intersection.
If the green light duration for a given direction is set too high, vehicles in the other direction will queue up and experience delays, thereby lowering the score for the intersection.
The goal is to find a balance for each direction (East-West and North-South) that minimizes the overall score of the intersection.
You need to change the <value> of the variables in #Variables to improve the output in accordance to #Feedback.
#Code
create_world4 = create_world(EW_time=int0, NS_time=int1)
analyze_world4 = analyze_world(W=create_world4)
#Documentation
[create_world] .
[analyze_world] .
#Variables
(int) int0=35
(int) int1=40
#Constraints
(int) int0: [15,90]
(int) int1: [15,90]
#Inputs
#Others
(World) create_world4=<uxsim.uxsim.World object at 0x7fe8af8661a0>
#Outputs
(dict) analyze_world4={'Avg. Delay': 23.384036144578317, (<Node W1>, <Node E1>): {'Trips attempted': 226, 'Trips completed': 222, 'Time lost per vehicle': 127.6858407079646}, (<Node W1>, <Node N1>): {'Trips attempted': 105, 'Trips completed': 102, 'Time lost per vehicle': 117.43809523809524}, (<Node W1>, <Node S1>): {'Trips attempted': 86, 'Trips completed': 79, 'Time lost per vehicle': 100.53488372093024}, (<Node E1>, <Node W1>): {'Trips attempted': 238, 'Trips completed': 178, 'Time lost per vehicle': 139.38235294117646}, (<Node E1>, <Node N1>): {'Trips attempted': 104, 'Trips completed': 91, 'Time lost per vehicle': 125.40384615384616}, (<Node E1>, <Node S1>): {'Trips attempted': 93, 'Trips completed': 81, 'Time lost per vehicle': 122.27956989247312}, (<Node N1>, <Node W1>): {'Trips attempted': 98, 'Trips completed': 92, 'Time lost per vehicle': 42.142857142857146}, (<Node N1>, <Node E1>): {'Trips attempted': 100, 'Trips completed': 97, 'Time lost per vehicle': 42.17}, (<Node N1>, <Node S1>): {'Trips attempted': 98, 'Trips completed': 94, 'Time lost per vehicle': 44.92857142857143}, (<Node S1>, <Node W1>): {'Trips attempted': 111, 'Trips completed': 104, 'Time lost per vehicle': 46.31531531531532}, (<Node S1>, <Node E1>): {'Trips attempted': 93, 'Trips completed': 87, 'Time lost per vehicle': 44.526881720430104}, (<Node S1>, <Node N1>): {'Trips attempted': 104, 'Trips completed': 101, 'Time lost per vehicle': 46.125}, 'Best-Case Estimated Delay': 92.20467032967034, 'OVERALL SCORE': 133.36548770347846}
#Feedback
OVERALL SCORE: 133.36548770347846
Please try to optimize the intersection further. If you are certain that you have found the optimal solution, please suggest it again.
================================
Your response:
LLM response:
{
"reasoning": "Given the current inputs, the green light durations for East-West (int0=35) and North-South (int1=40) return an OVERALL SCORE of 133.36548770347846 as noted in the output. The instruction requires this score to be minimized. To optimize this, a balance needs to be achieved between the two durations, considering that too high or too low values could exacerbate traffic delays in one direction or the other, impacting the OVERALL SCORE negatively.\n\nFrom the current performance metrics, it is evident that specific intersections turning from and to various directions (like from E1 to W1 and W1 to S1) are experiencing significant delays in terms of 'Time lost per vehicle'. Since 'analyze_world' function evaluates the performance based largely on delays and completed trips, a readjustment of the traffic light durations may distribute delays more uniformly and possibly reduce them. To achieve a smaller OVERALL SCORE, slight adjustments can be made within the allowable range to find a better balance.\n\nGiven the current scoring and configuration, slightly reducing the time for the East-West (int0) and increasing the time for North-South (int1) might create a more balanced distribution of delays, as the time lost for movements from node E1 is consistently higher, suggesting potential over-capacity or insufficient time allocation for other routes.",
"suggestion": {
"int0": 30,
"int1": 45
}
}
Prompt
You're tasked to solve a coding/algorithm problem. You will see the instruction, the code, the documentation of each function used in the code, and the feedback about the execution result.
Specifically, a problem will be composed of the following parts:
- #Instruction: the instruction which describes the things you need to do or the question you should answer.
- #Code: the code defined in the problem.
- #Documentation: the documentation of each function used in #Code. The explanation might be incomplete and just contain high-level description. You can use the values in #Others to help infer how those functions work.
- #Variables: the input variables that you can change.
- #Constraints: the constraints or descriptions of the variables in #Variables.
- #Inputs: the values of other inputs to the code, which are not changeable.
- #Others: the intermediate values created through the code execution.
- #Outputs: the result of the code output.
- #Feedback: the feedback about the code's execution result.
In #Variables, #Inputs, #Outputs, and #Others, the format is:
<data_type> <variable_name> = <value>
If <type> is (code), it means <value> is the source code of a python code, which may include docstring and definitions.
Output_format: Your output should be in the following json format, satisfying the json syntax:
{{
"reasoning": <Your reasoning>,
"answer": <Your answer>,
"suggestion": {{
<variable_1>: <suggested_value_1>,
<variable_2>: <suggested_value_2>,
}}
}}
In "reasoning", explain the problem: 1. what the #Instruction means 2. what the #Feedback on #Output means to #Variables considering how #Variables are used in #Code and other values in #Documentation, #Inputs, #Others. 3. Reasoning about the suggested changes in #Variables (if needed) and the expected result.
If #Instruction asks for an answer, write it down in "answer".
If you need to suggest a change in the values of #Variables, write down the suggested values in "suggestion". Remember you can change only the values in #Variables, not others. When <type> of a variable is (code), you should write the new definition in the format of python code without syntax errors, and you should not change the function name or the function signature.
If no changes or answer are needed, just output TERMINATE.
Now you see problem instance:
================================
#Instruction
You should suggest values for the variables so that the OVERALL SCORE is as small as possible.
There is a trade-off in setting the green light durations.
If the green light duration for a given direction is set too low, then vehicles will queue up over time and experience delays, thereby lowering the score for the intersection.
If the green light duration for a given direction is set too high, vehicles in the other direction will queue up and experience delays, thereby lowering the score for the intersection.
The goal is to find a balance for each direction (East-West and North-South) that minimizes the overall score of the intersection.
You need to change the <value> of the variables in #Variables to improve the output in accordance to #Feedback.
#Code
create_world5 = create_world(EW_time=int0, NS_time=int1)
analyze_world5 = analyze_world(W=create_world5)
#Documentation
[create_world] .
[analyze_world] .
#Variables
(int) int0=30
(int) int1=45
#Constraints
(int) int0: [15,90]
(int) int1: [15,90]
#Inputs
#Others
(World) create_world5=<uxsim.uxsim.World object at 0x7fe8ae8d1390>
#Outputs
(dict) analyze_world5={'Avg. Delay': 38.01457055214724, (<Node W1>, <Node E1>): {'Trips attempted': 226, 'Trips completed': 222, 'Time lost per vehicle': 275.2433628318584}, (<Node W1>, <Node N1>): {'Trips attempted': 105, 'Trips completed': 102, 'Time lost per vehicle': 250.9142857142857}, (<Node W1>, <Node S1>): {'Trips attempted': 86, 'Trips completed': 79, 'Time lost per vehicle': 214.48837209302326}, (<Node E1>, <Node W1>): {'Trips attempted': 238, 'Trips completed': 162, 'Time lost per vehicle': 190.85714285714286}, (<Node E1>, <Node N1>): {'Trips attempted': 104, 'Trips completed': 87, 'Time lost per vehicle': 173.78846153846155}, (<Node E1>, <Node S1>): {'Trips attempted': 93, 'Trips completed': 77, 'Time lost per vehicle': 163.33333333333334}, (<Node N1>, <Node W1>): {'Trips attempted': 98, 'Trips completed': 92, 'Time lost per vehicle': 36.16326530612245}, (<Node N1>, <Node E1>): {'Trips attempted': 100, 'Trips completed': 97, 'Time lost per vehicle': 37.69}, (<Node N1>, <Node S1>): {'Trips attempted': 98, 'Trips completed': 94, 'Time lost per vehicle': 38.795918367346935}, (<Node S1>, <Node W1>): {'Trips attempted': 111, 'Trips completed': 104, 'Time lost per vehicle': 39.513513513513516}, (<Node S1>, <Node E1>): {'Trips attempted': 93, 'Trips completed': 87, 'Time lost per vehicle': 38.68817204301075}, (<Node S1>, <Node N1>): {'Trips attempted': 104, 'Trips completed': 101, 'Time lost per vehicle': 36.96153846153846}, 'Best-Case Estimated Delay': 143.28846153846155, 'OVERALL SCORE': 237.62846989573112}
#Feedback
OVERALL SCORE: 237.62846989573112
Please try to optimize the intersection further. If you are certain that you have found the optimal solution, please suggest it again.
================================
Your response:
LLM response:
{
"reasoning": "The OVERALL SCORE from the output indicates the performance of the intersection configuration given the green light durations for East-West (EW_time) and North-South (NS_time). The objective is to minimize this score which represents the average delay and other inefficiencies in vehicle movement through the intersection. From the 'Feedback', we see that the current OVERALL SCORE is 237.62846989573112, which suggests that there is room for improvement. The goal is to adjust the time values for EW_time and NS_time within provided constraints (15 to 90 seconds) to seek a configuration that might balance the traffic flow more optimally across all directions at the intersection. The reported high time lost per vehicle for some node combinations also suggests that the current setup isn't balanced efficiently. Adjusting both time values by either increasing or decreasing them might help in finding a more balanced traffic flow, thus potentially reducing the OVERALL SCORE.",
"answer": "The aim is to find better values for EW_time and NS_time that would result in the lowest possible 'OVERALL SCORE'.",
"suggestion": {
"int0": 35,
"int1": 35
}
}
Prompt
You're tasked to solve a coding/algorithm problem. You will see the instruction, the code, the documentation of each function used in the code, and the feedback about the execution result.
Specifically, a problem will be composed of the following parts:
- #Instruction: the instruction which describes the things you need to do or the question you should answer.
- #Code: the code defined in the problem.
- #Documentation: the documentation of each function used in #Code. The explanation might be incomplete and just contain high-level description. You can use the values in #Others to help infer how those functions work.
- #Variables: the input variables that you can change.
- #Constraints: the constraints or descriptions of the variables in #Variables.
- #Inputs: the values of other inputs to the code, which are not changeable.
- #Others: the intermediate values created through the code execution.
- #Outputs: the result of the code output.
- #Feedback: the feedback about the code's execution result.
In #Variables, #Inputs, #Outputs, and #Others, the format is:
<data_type> <variable_name> = <value>
If <type> is (code), it means <value> is the source code of a python code, which may include docstring and definitions.
Output_format: Your output should be in the following json format, satisfying the json syntax:
{{
"reasoning": <Your reasoning>,
"answer": <Your answer>,
"suggestion": {{
<variable_1>: <suggested_value_1>,
<variable_2>: <suggested_value_2>,
}}
}}
In "reasoning", explain the problem: 1. what the #Instruction means 2. what the #Feedback on #Output means to #Variables considering how #Variables are used in #Code and other values in #Documentation, #Inputs, #Others. 3. Reasoning about the suggested changes in #Variables (if needed) and the expected result.
If #Instruction asks for an answer, write it down in "answer".
If you need to suggest a change in the values of #Variables, write down the suggested values in "suggestion". Remember you can change only the values in #Variables, not others. When <type> of a variable is (code), you should write the new definition in the format of python code without syntax errors, and you should not change the function name or the function signature.
If no changes or answer are needed, just output TERMINATE.
Now you see problem instance:
================================
#Instruction
You should suggest values for the variables so that the OVERALL SCORE is as small as possible.
There is a trade-off in setting the green light durations.
If the green light duration for a given direction is set too low, then vehicles will queue up over time and experience delays, thereby lowering the score for the intersection.
If the green light duration for a given direction is set too high, vehicles in the other direction will queue up and experience delays, thereby lowering the score for the intersection.
The goal is to find a balance for each direction (East-West and North-South) that minimizes the overall score of the intersection.
You need to change the <value> of the variables in #Variables to improve the output in accordance to #Feedback.
#Code
create_world6 = create_world(EW_time=int0, NS_time=int1)
analyze_world6 = analyze_world(W=create_world6)
#Documentation
[create_world] .
[analyze_world] .
#Variables
(int) int0=35
(int) int1=35
#Constraints
(int) int0: [15,90]
(int) int1: [15,90]
#Inputs
#Others
(World) create_world6=<uxsim.uxsim.World object at 0x7fe8adb0c9a0>
#Outputs
(dict) analyze_world6={'Avg. Delay': 18.235955056179776, (<Node W1>, <Node E1>): {'Trips attempted': 226, 'Trips completed': 224, 'Time lost per vehicle': 70.32743362831859}, (<Node W1>, <Node N1>): {'Trips attempted': 105, 'Trips completed': 103, 'Time lost per vehicle': 65.11428571428571}, (<Node W1>, <Node S1>): {'Trips attempted': 86, 'Trips completed': 80, 'Time lost per vehicle': 52.13953488372093}, (<Node E1>, <Node W1>): {'Trips attempted': 238, 'Trips completed': 188, 'Time lost per vehicle': 110.0546218487395}, (<Node E1>, <Node N1>): {'Trips attempted': 104, 'Trips completed': 94, 'Time lost per vehicle': 102.14423076923077}, (<Node E1>, <Node S1>): {'Trips attempted': 93, 'Trips completed': 82, 'Time lost per vehicle': 93.10752688172043}, (<Node N1>, <Node W1>): {'Trips attempted': 98, 'Trips completed': 91, 'Time lost per vehicle': 47.36734693877551}, (<Node N1>, <Node E1>): {'Trips attempted': 100, 'Trips completed': 93, 'Time lost per vehicle': 48.6}, (<Node N1>, <Node S1>): {'Trips attempted': 98, 'Trips completed': 93, 'Time lost per vehicle': 48.53061224489796}, (<Node S1>, <Node W1>): {'Trips attempted': 111, 'Trips completed': 102, 'Time lost per vehicle': 43.86486486486486}, (<Node S1>, <Node E1>): {'Trips attempted': 93, 'Trips completed': 85, 'Time lost per vehicle': 43.215053763440864}, (<Node S1>, <Node N1>): {'Trips attempted': 104, 'Trips completed': 100, 'Time lost per vehicle': 43.25961538461539}, 'Best-Case Estimated Delay': 68.9114010989011, 'OVERALL SCORE': 94.12023967317415}
#Feedback
OVERALL SCORE: 94.12023967317415
Please try to optimize the intersection further. If you are certain that you have found the optimal solution, please suggest it again.
================================
Your response:
LLM response:
{
"reasoning": "The instruction requires minimizing the 'OVERALL SCORE' by adjusting the green light timings for the East-West (EW_time) and North-South (NS_time) directions. According to the #Outputs section, the current setting for both int0 (EW_time) and int1 (NS_time) at 35 seconds results in an OVERALL SCORE of 94.12. To optimize this, we need to consider balancing the delay and completion rates for all directions. Notably, directional delays such as from 'Node E1' to 'Node W1' and 'Node E1' to 'Node N1' show significantly high values, indicating a possible imbalance in light durations favoring or disfavoring certain flows. Adjusting the timings might reduce such high delays and balance the flow across all directions, hence possibly improving the OVERALL SCORE. We should try changing these timings within the constraints [15,90] and analyze the results dynamically. However, based on observed high delays from East to West, reducing East-West timing (EW_time) slightly while increasing North-South timing (NS_time) might redistribute the traffic more effectively.",
"suggestion": {
"int0": 30,
"int1": 40
}
}
Prompt
You're tasked to solve a coding/algorithm problem. You will see the instruction, the code, the documentation of each function used in the code, and the feedback about the execution result.
Specifically, a problem will be composed of the following parts:
- #Instruction: the instruction which describes the things you need to do or the question you should answer.
- #Code: the code defined in the problem.
- #Documentation: the documentation of each function used in #Code. The explanation might be incomplete and just contain high-level description. You can use the values in #Others to help infer how those functions work.
- #Variables: the input variables that you can change.
- #Constraints: the constraints or descriptions of the variables in #Variables.
- #Inputs: the values of other inputs to the code, which are not changeable.
- #Others: the intermediate values created through the code execution.
- #Outputs: the result of the code output.
- #Feedback: the feedback about the code's execution result.
In #Variables, #Inputs, #Outputs, and #Others, the format is:
<data_type> <variable_name> = <value>
If <type> is (code), it means <value> is the source code of a python code, which may include docstring and definitions.
Output_format: Your output should be in the following json format, satisfying the json syntax:
{{
"reasoning": <Your reasoning>,
"answer": <Your answer>,
"suggestion": {{
<variable_1>: <suggested_value_1>,
<variable_2>: <suggested_value_2>,
}}
}}
In "reasoning", explain the problem: 1. what the #Instruction means 2. what the #Feedback on #Output means to #Variables considering how #Variables are used in #Code and other values in #Documentation, #Inputs, #Others. 3. Reasoning about the suggested changes in #Variables (if needed) and the expected result.
If #Instruction asks for an answer, write it down in "answer".
If you need to suggest a change in the values of #Variables, write down the suggested values in "suggestion". Remember you can change only the values in #Variables, not others. When <type> of a variable is (code), you should write the new definition in the format of python code without syntax errors, and you should not change the function name or the function signature.
If no changes or answer are needed, just output TERMINATE.
Now you see problem instance:
================================
#Instruction
You should suggest values for the variables so that the OVERALL SCORE is as small as possible.
There is a trade-off in setting the green light durations.
If the green light duration for a given direction is set too low, then vehicles will queue up over time and experience delays, thereby lowering the score for the intersection.
If the green light duration for a given direction is set too high, vehicles in the other direction will queue up and experience delays, thereby lowering the score for the intersection.
The goal is to find a balance for each direction (East-West and North-South) that minimizes the overall score of the intersection.
You need to change the <value> of the variables in #Variables to improve the output in accordance to #Feedback.
#Code
create_world7 = create_world(EW_time=int0, NS_time=int1)
analyze_world7 = analyze_world(W=create_world7)
#Documentation
[create_world] .
[analyze_world] .
#Variables
(int) int0=30
(int) int1=40
#Constraints
(int) int0: [15,90]
(int) int1: [15,90]
#Inputs
#Others
(World) create_world7=<uxsim.uxsim.World object at 0x7fe8acc87d30>
#Outputs
(dict) analyze_world7={'Avg. Delay': 32.196946564885494, (<Node W1>, <Node E1>): {'Trips attempted': 226, 'Trips completed': 224, 'Time lost per vehicle': 212.6769911504425}, (<Node W1>, <Node N1>): {'Trips attempted': 105, 'Trips completed': 103, 'Time lost per vehicle': 191.61904761904762}, (<Node W1>, <Node S1>): {'Trips attempted': 86, 'Trips completed': 80, 'Time lost per vehicle': 165.48837209302326}, (<Node E1>, <Node W1>): {'Trips attempted': 238, 'Trips completed': 169, 'Time lost per vehicle': 184.1638655462185}, (<Node E1>, <Node N1>): {'Trips attempted': 104, 'Trips completed': 90, 'Time lost per vehicle': 166.39423076923077}, (<Node E1>, <Node S1>): {'Trips attempted': 93, 'Trips completed': 80, 'Time lost per vehicle': 159.5268817204301}, (<Node N1>, <Node W1>): {'Trips attempted': 98, 'Trips completed': 91, 'Time lost per vehicle': 37.92857142857143}, (<Node N1>, <Node E1>): {'Trips attempted': 100, 'Trips completed': 93, 'Time lost per vehicle': 38.93}, (<Node N1>, <Node S1>): {'Trips attempted': 98, 'Trips completed': 93, 'Time lost per vehicle': 38.795918367346935}, (<Node S1>, <Node W1>): {'Trips attempted': 111, 'Trips completed': 102, 'Time lost per vehicle': 36.567567567567565}, (<Node S1>, <Node E1>): {'Trips attempted': 93, 'Trips completed': 85, 'Time lost per vehicle': 35.075268817204304}, (<Node S1>, <Node N1>): {'Trips attempted': 104, 'Trips completed': 100, 'Time lost per vehicle': 36.26923076923077}, 'Best-Case Estimated Delay': 124.24038461538461, 'OVERALL SCORE': 198.90332897820912}
#Feedback
OVERALL SCORE: 198.90332897820912
Please try to optimize the intersection further. If you are certain that you have found the optimal solution, please suggest it again.
================================
Your response:
LLM response:
{
"reasoning": "We need to adjust the values of int0 (East-West green light duration) and int1 (North-South green light duration) to find a balance that minimizes the overall score of the intersection. From the output, it is observed that the OVERALL SCORE is relatively high with current settings of 30 seconds for East-West and 40 seconds for North-South. The goal is to optimize green time to balance the flow in all directions, thus reducing the overall delay and score. Given that `int0` and `int1` have constraints ranging from 15 to 90, the initial setting seems biased towards North-South traffic (40 seconds) as compared to East-West (30 seconds). The reported OVERALL SCORE suggests that optimization is necessary but does not specifically indicate if queues are longer in East-West or North-South. A good starting strategy is to bring a closer balance between int0 and int1 values and then make fine adjustments based on results. A suggested next step could be to experiment by reducing `int1` slightly and increasing `int0`, moving towards a more balanced configuration between the two traffic flows.",
"suggestion": {
"int0": 35,
"int1": 35
}
}
Prompt
You're tasked to solve a coding/algorithm problem. You will see the instruction, the code, the documentation of each function used in the code, and the feedback about the execution result.
Specifically, a problem will be composed of the following parts:
- #Instruction: the instruction which describes the things you need to do or the question you should answer.
- #Code: the code defined in the problem.
- #Documentation: the documentation of each function used in #Code. The explanation might be incomplete and just contain high-level description. You can use the values in #Others to help infer how those functions work.
- #Variables: the input variables that you can change.
- #Constraints: the constraints or descriptions of the variables in #Variables.
- #Inputs: the values of other inputs to the code, which are not changeable.
- #Others: the intermediate values created through the code execution.
- #Outputs: the result of the code output.
- #Feedback: the feedback about the code's execution result.
In #Variables, #Inputs, #Outputs, and #Others, the format is:
<data_type> <variable_name> = <value>
If <type> is (code), it means <value> is the source code of a python code, which may include docstring and definitions.
Output_format: Your output should be in the following json format, satisfying the json syntax:
{{
"reasoning": <Your reasoning>,
"answer": <Your answer>,
"suggestion": {{
<variable_1>: <suggested_value_1>,
<variable_2>: <suggested_value_2>,
}}
}}
In "reasoning", explain the problem: 1. what the #Instruction means 2. what the #Feedback on #Output means to #Variables considering how #Variables are used in #Code and other values in #Documentation, #Inputs, #Others. 3. Reasoning about the suggested changes in #Variables (if needed) and the expected result.
If #Instruction asks for an answer, write it down in "answer".
If you need to suggest a change in the values of #Variables, write down the suggested values in "suggestion". Remember you can change only the values in #Variables, not others. When <type> of a variable is (code), you should write the new definition in the format of python code without syntax errors, and you should not change the function name or the function signature.
If no changes or answer are needed, just output TERMINATE.
Now you see problem instance:
================================
#Instruction
You should suggest values for the variables so that the OVERALL SCORE is as small as possible.
There is a trade-off in setting the green light durations.
If the green light duration for a given direction is set too low, then vehicles will queue up over time and experience delays, thereby lowering the score for the intersection.
If the green light duration for a given direction is set too high, vehicles in the other direction will queue up and experience delays, thereby lowering the score for the intersection.
The goal is to find a balance for each direction (East-West and North-South) that minimizes the overall score of the intersection.
You need to change the <value> of the variables in #Variables to improve the output in accordance to #Feedback.
#Code
create_world8 = create_world(EW_time=int0, NS_time=int1)
analyze_world8 = analyze_world(W=create_world8)
#Documentation
[create_world] .
[analyze_world] .
#Variables
(int) int0=35
(int) int1=35
#Constraints
(int) int0: [15,90]
(int) int1: [15,90]
#Inputs
#Others
(World) create_world8=<uxsim.uxsim.World object at 0x7fe8ac006d40>
#Outputs
(dict) analyze_world8={'Avg. Delay': 18.235955056179776, (<Node W1>, <Node E1>): {'Trips attempted': 226, 'Trips completed': 224, 'Time lost per vehicle': 70.32743362831859}, (<Node W1>, <Node N1>): {'Trips attempted': 105, 'Trips completed': 103, 'Time lost per vehicle': 65.11428571428571}, (<Node W1>, <Node S1>): {'Trips attempted': 86, 'Trips completed': 80, 'Time lost per vehicle': 52.13953488372093}, (<Node E1>, <Node W1>): {'Trips attempted': 238, 'Trips completed': 188, 'Time lost per vehicle': 110.0546218487395}, (<Node E1>, <Node N1>): {'Trips attempted': 104, 'Trips completed': 94, 'Time lost per vehicle': 102.14423076923077}, (<Node E1>, <Node S1>): {'Trips attempted': 93, 'Trips completed': 82, 'Time lost per vehicle': 93.10752688172043}, (<Node N1>, <Node W1>): {'Trips attempted': 98, 'Trips completed': 91, 'Time lost per vehicle': 47.36734693877551}, (<Node N1>, <Node E1>): {'Trips attempted': 100, 'Trips completed': 93, 'Time lost per vehicle': 48.6}, (<Node N1>, <Node S1>): {'Trips attempted': 98, 'Trips completed': 93, 'Time lost per vehicle': 48.53061224489796}, (<Node S1>, <Node W1>): {'Trips attempted': 111, 'Trips completed': 102, 'Time lost per vehicle': 43.86486486486486}, (<Node S1>, <Node E1>): {'Trips attempted': 93, 'Trips completed': 85, 'Time lost per vehicle': 43.215053763440864}, (<Node S1>, <Node N1>): {'Trips attempted': 104, 'Trips completed': 100, 'Time lost per vehicle': 43.25961538461539}, 'Best-Case Estimated Delay': 68.9114010989011, 'OVERALL SCORE': 94.12023967317415}
#Feedback
OVERALL SCORE: 94.12023967317415
Please try to optimize the intersection further. If you are certain that you have found the optimal solution, please suggest it again.
================================
Your response:
LLM response:
{
"reasoning": "The task is to adjust the green light durations (variables int0 and int1 representing East-West and North-South respectively) to obtain the smallest possible OVERALL SCORE. The OVERALL SCORE in the outputs (94.12023967317415) is based on 'Time lost per vehicle' which varies significantly across different directions, implying some durations may be suboptimal. Adjusting these durations closer to equilibrium could potentially minimize the delay and the overall score. Analysis of 'Time lost per vehicle', looking particularly at higher values, suggests an imbalance. For instance, East-West directions (int0) have higher delays compared to North-South, suggesting current setting might be disproportionately favoring one of the directions.",
"answer": "We aim to adjust the value of int0 and int1 in order to minimize 'Time lost per vehicle' equally across all directions, thereby reducing 'OVERALL SCORE'.",
"suggestion": {
"int0": 25,
"int1": 45
}
}
Prompt
You're tasked to solve a coding/algorithm problem. You will see the instruction, the code, the documentation of each function used in the code, and the feedback about the execution result.
Specifically, a problem will be composed of the following parts:
- #Instruction: the instruction which describes the things you need to do or the question you should answer.
- #Code: the code defined in the problem.
- #Documentation: the documentation of each function used in #Code. The explanation might be incomplete and just contain high-level description. You can use the values in #Others to help infer how those functions work.
- #Variables: the input variables that you can change.
- #Constraints: the constraints or descriptions of the variables in #Variables.
- #Inputs: the values of other inputs to the code, which are not changeable.
- #Others: the intermediate values created through the code execution.
- #Outputs: the result of the code output.
- #Feedback: the feedback about the code's execution result.
In #Variables, #Inputs, #Outputs, and #Others, the format is:
<data_type> <variable_name> = <value>
If <type> is (code), it means <value> is the source code of a python code, which may include docstring and definitions.
Output_format: Your output should be in the following json format, satisfying the json syntax:
{{
"reasoning": <Your reasoning>,
"answer": <Your answer>,
"suggestion": {{
<variable_1>: <suggested_value_1>,
<variable_2>: <suggested_value_2>,
}}
}}
In "reasoning", explain the problem: 1. what the #Instruction means 2. what the #Feedback on #Output means to #Variables considering how #Variables are used in #Code and other values in #Documentation, #Inputs, #Others. 3. Reasoning about the suggested changes in #Variables (if needed) and the expected result.
If #Instruction asks for an answer, write it down in "answer".
If you need to suggest a change in the values of #Variables, write down the suggested values in "suggestion". Remember you can change only the values in #Variables, not others. When <type> of a variable is (code), you should write the new definition in the format of python code without syntax errors, and you should not change the function name or the function signature.
If no changes or answer are needed, just output TERMINATE.
Now you see problem instance:
================================
#Instruction
You should suggest values for the variables so that the OVERALL SCORE is as small as possible.
There is a trade-off in setting the green light durations.
If the green light duration for a given direction is set too low, then vehicles will queue up over time and experience delays, thereby lowering the score for the intersection.
If the green light duration for a given direction is set too high, vehicles in the other direction will queue up and experience delays, thereby lowering the score for the intersection.
The goal is to find a balance for each direction (East-West and North-South) that minimizes the overall score of the intersection.
You need to change the <value> of the variables in #Variables to improve the output in accordance to #Feedback.
#Code
create_world9 = create_world(EW_time=int0, NS_time=int1)
analyze_world9 = analyze_world(W=create_world9)
#Documentation
[create_world] .
[analyze_world] .
#Variables
(int) int0=25
(int) int1=45
#Constraints
(int) int0: [15,90]
(int) int1: [15,90]
#Inputs
#Others
(World) create_world9=<uxsim.uxsim.World object at 0x7fe8aaf3aa40>
#Outputs
(dict) analyze_world9={'Avg. Delay': 53.25426356589147, (<Node W1>, <Node E1>): {'Trips attempted': 226, 'Trips completed': 224, 'Time lost per vehicle': 360.77433628318585}, (<Node W1>, <Node N1>): {'Trips attempted': 105, 'Trips completed': 103, 'Time lost per vehicle': 361.7142857142857}, (<Node W1>, <Node S1>): {'Trips attempted': 86, 'Trips completed': 80, 'Time lost per vehicle': 335.3837209302326}, (<Node E1>, <Node W1>): {'Trips attempted': 238, 'Trips completed': 156, 'Time lost per vehicle': 230.9033613445378}, (<Node E1>, <Node N1>): {'Trips attempted': 104, 'Trips completed': 86, 'Time lost per vehicle': 210.6153846153846}, (<Node E1>, <Node S1>): {'Trips attempted': 93, 'Trips completed': 77, 'Time lost per vehicle': 197.94623655913978}, (<Node N1>, <Node W1>): {'Trips attempted': 98, 'Trips completed': 91, 'Time lost per vehicle': 31.081632653061224}, (<Node N1>, <Node E1>): {'Trips attempted': 100, 'Trips completed': 93, 'Time lost per vehicle': 31.88}, (<Node N1>, <Node S1>): {'Trips attempted': 98, 'Trips completed': 93, 'Time lost per vehicle': 32.01020408163265}, (<Node S1>, <Node W1>): {'Trips attempted': 111, 'Trips completed': 102, 'Time lost per vehicle': 29.72072072072072}, (<Node S1>, <Node E1>): {'Trips attempted': 93, 'Trips completed': 85, 'Time lost per vehicle': 28.258064516129032}, (<Node S1>, <Node N1>): {'Trips attempted': 104, 'Trips completed': 100, 'Time lost per vehicle': 29.596153846153847}, 'Best-Case Estimated Delay': 179.94642857142858, 'OVERALL SCORE': 316.5947156657663}
#Feedback
OVERALL SCORE: 316.5947156657663
Please try to optimize the intersection further. If you are certain that you have found the optimal solution, please suggest it again.
================================
Your response:
LLM response:
{
"reasoning": "To achieve a minimal OVERALL SCORE, we need to balance the green light durations for East-West (EW) and North-South (NS) directions at the intersection. Increasing or decreasing the green light duration too much for any direction will result in vehicles queuing up in one direction, leading to increased delays and hence a higher overall score. From the constraint range ([15,90]), the initial settings give East-West a moderately high duration (25 seconds) and North-South a considerably high duration (45 seconds). Observing the output, particularly 'Time lost per vehicle', we see that vehicles moving East-West (from E1 to W1) are significantly delayed, suggesting that the North-South green light might be too lengthy causing longer waits for East-West travelling vehicles. By adjusting the green light duration cycles for both directions closer to the middle of their respective ranges, balance could potentially be improved, potentially decreasing the overall score.",
"suggestion": {
"int0": 35,
"int1": 35
}
}
[[ 15. 15. 77.29993651]
[ 25. 25. 87.2529551 ]
[ 35. 30. 68.040316 ]
[ 40. 35. 78.47073722]
[ 35. 40. 133.3654877 ]
[ 30. 45. 237.6284699 ]
[ 35. 35. 94.12023967]
[ 30. 40. 198.90332898]
[ 35. 35. 94.12023967]
[ 25. 45. 316.59471567]]
This completes the tutorial on using the Trace package for numerical optimization in a traffic simulation. Happy optimizing!