The document describes the hill climbing algorithm and its application to optimize attributes for an autonomous vehicle's travel cost. It defines the problem as minimizing a cost function that considers time, speed, fuel consumed, and distance travelled. The hill climbing algorithm is implemented in Python code to iteratively generate and evaluate random solutions until reaching an optimal value of 0 cost. The code defines classes for the solution space and cost calculation, generates new solutions, performs the hill climbing steps, and includes a stopping criterion for the algorithm.

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Pilani Campus
ACI – Lab Session 2

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Pilani Campus
Optimizing attributes for travel cost
Hill ClimbingAlgorithm
Autonomous car driving agent

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Pilani Campus
The algorithm – Hill climbing

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Hill climbing algorithm is a local search algorithm
which continuously moves in the direction of
increasing value to find the peak of the mountain
or best solution to the problem.
It terminates when it reaches a peak value where
no neighbor has a higher value.
One of the widely discussed examples of Hill
climbing algorithm is Traveling-salesman
Problem in which we need to minimize the
distance traveled by the salesman.
Hill Climbing Algorithm

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Hill climbing algorithm is also called greedy local search
as it only looks to its good immediate neighbor state and
not beyond that.
Its core components include the initial state, successor
function, and objective function.
A node of hill climbing algorithm has two components which
are state and value.
Hill Climbing is mostly used when a good heuristic is
available.
In this algorithm, we don't need to maintain and handle the
search tree or graph as it only keeps a single current
state.
The limitation of Hill Climbing is that it can get stuck in
local optima, which are suboptimal solutions.
Hill Climbing Algorithm

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HillClimbing(problem){
currentState = problem.startState
goal = false
while(!goal){
neighbour = highest valued successor of currentState
if neighbour.value <= currentState.value
goal = true
else
currentState = neighbour
}
}
Hill climbing - function

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Limitation of hill climbing is local best solution
Hill climbing - function

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Pilani Campus
The Problem
Optimizing attributes of autonomous vehicle
8

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Performance measure of an automated driver
Desirable qualities include getting to the correct destination;
minimizing fuel consumption and wear and tear;
minimizing the trip time or cost; minimizing violations of traffic
laws and disturbances to other drivers; maximizing safety
and passenger comfort; maximizing profits. Obviously, some
of these goals conflict, so tradeoffs will be required.
Fuel is one of the main factors contributing to travel cost.
Fuel economy is calculated by using the formula
Average Fuel Consumption (Km/L) = Distance travelled / Litres
of fuel consumed
Travel cost depends on other attributes like speed of the
vehicle, time taken for the travel, type of roads, traffic, driving
behavior, weather, weight, air conditioning, etc.
The problem - Attributes for
fuel economy

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Let us take a few of these for our sub-problem.
A few attributes that influence travel cost are:
Time to travel
Speed
Fuel consumed
Distance travelled
Optimizing these objectives is known as Multi-objective
optimization
The attributes/objectives for
optimization in the example

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A problem that takes more than one objective for
optimization
The objectives can be contradicting ones
Meaning, it is desirable to increase the value of one
objective while decreasing the value of others
Solution representation and evaluation:
The objectives are represented as a vector and can be
evaluated using
– The vector as a whole
– Defining a evaluation function using the objectives
Multi-objective optimization
problem

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In the current autonomous car agent problem the cost or
evaluation function is taken as follows:
Travel Cost = Time + Speed + Fuel – Distance
Here our goal is to reduce the cost. (Minimization problem)
Time travelled and fuel consumed must have lower values
for cost reduction.
Speed must be average (not less not more)
Distance travelled must be maximum to reduce the cost
Cost function / Evaluation
function

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Choose the optimal attribute values to get minimum cost
Goal = 0 cost
Heuristic – Hill climbing
Choose attribute vectors (neighbors) at random (Stochastic
hill climbing)
Evaluate them
Retain the best while forgetting the less optimal values
Heuristic

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Performance – Safety, time, legal drive, comfort.
– In the algorithm, reducing the cost of travel by optimizing the
attributes taken
Environment – Roads, other cars, pedestrians, road signs.
– Acceptable range of values for the attributes Time, Speed, Fuel
and Distance travelled represented as vector of combination of
these values
Actuators – Steering, accelerator, brake, signal, horn.
– Initial solution, Candidate solution, Evaluation function.
Sensors – Fuel indicator, Speedometer, Digital clock in the
display
– Candidate solution with the acceptable range of values (from the
sensors), number of iterations.
PEAS

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Step 1: Evaluate the initial state, if it is goal state then
return success and Stop.
Step 2: Loop Until a solution is found or there is no new
operator left to apply.
Step 3: Select and apply an operator to the current state.
Step 4: Check new state
Step 5: Exit.
Hill climbing algorithm - Steps

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Code Walk through
Stochastic hill climbing in
PYTHON

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import numpy as np
import random;
#The PEAS
#Time, Speed, Fuel, Distance
#Init_solution = [10, 100, 25, 10];
#Init_solution = [2,10,5,100]
#Init_solution = [0, 0, 0, 0];
Iterations = 0
max_itr=1000 #Can be increased or decreased
Final_solution = None #Stores best of each iteration
#PEAS and the initial states

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#Contains an objective vector of attributes to be optimized and
the cost associated with the objectives
class Solu_space:
def __init__(self):
self.obj_vector = None
self.cost = None
def setObj_vector(self, val):
self.obj_vector = val
def setCost(self, cost):
self.cost = cost
def getAttr(self):
return {'Time, Speed, Fuel, Distance': self.obj_vector, 'Cost':
self.cost }
#Class : Solution space

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# Function for calculating the cost - The evaluation function
def calc_cost(objVector):
cost = round((objVector[0] + objVector[1] +
objVector[2] - objVector[3]),2)
#print("Cost"+str(cost))
return abs(cost)
#Function for cost evaluation

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def gen_new_solution():
distance_step=0
speed_step=random.randint(10,100)
time_step=round((random.randint(1,100))/60,2)
try:
distance_step=random.randint(1,round(speed_step*time_step,2))
except:
pass
fuel_step=random.randint(1,25)
objVector=[time_step,speed_step,fuel_step,distance_step]
#print("new solution: "+str(objVector))
return objVector
#Function to generate new
solution

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def Hill_Climb(objVector):
soln_space = Solu_space()
soln_space.setObj_vector(objVector)
oldCost = calc_cost(objVector);
soln_space.setCost(oldCost)
newobjVector = gen_new_solution()
newcost= calc_cost(newobjVector)
#Function Hill climb

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if(newcost < oldCost):
soln_space.setObj_vector(newobjVector)
soln_space.setCost(newcost)
print(str(soln_space.getAttr()))
return soln_space.obj_vector
print(str(soln_space.getAttr()))
return soln_space.obj_vector
#Function Hill climb –
compare solution costs

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def stopit():
globals()
cost=calc_cost(Final_solution)
if cost == 0:
return True
if Iterations == max_itr:
return True
else:
return False
#Function – The stopping
criterion

24. CALLING ALL THE DEFINED
FUNCTIONS

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#Time,speed,fuel,distance
Init_soln=
[random.randint(1,10),
random.randint(1,100),
random.randint(1,25),
random.randint(1,500)]
#Generate initial solution

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Final_solution= Hill_Climb(Init_solution) #Initialize variable Final_solution
print(Final_solution)
while not stopit():
solution=Final_solution
Final_solution=Hill_Climb(solution)
print("Iteration no: "+str(Iterations))
Iterations+=1
print("Solution")
print(str(Final_solution[0])+ " Hrs " +str(Final_solution[1])+ "
Km/Hr " + str(Final_solution[2]) + " Litres " +
str(Final_solution[3]) + " Kms")
print("Cost" + str(calc_cost(Final_solution)))
#Loop the Hill Climb

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{'Time, Speed, Fuel, Distance': [1.3, 70, 12, 55], 'Cost': 28.3} Iteration no: 35
{'Time, Speed, Fuel, Distance': [1.3, 70, 12, 55], 'Cost': 28.3} Iteration no: 36
{'Time, Speed, Fuel, Distance': [1.3, 70, 12, 55], 'Cost': 28.3} Iteration no: 37
{'Time, Speed, Fuel, Distance': [0.13, 10, 2, 0], 'Cost': 12.13} Iteration no: 172
{'Time, Speed, Fuel, Distance': [0.13, 10, 2, 0], 'Cost': 12.13} Iteration no: 173
{'Time, Speed, Fuel, Distance': [0.13, 10, 2, 0], 'Cost': 12.13} Iteration no: 174
{'Time, Speed, Fuel, Distance': [0.13, 10, 2, 0], 'Cost': 12.13} Iteration no: 175
{'Time, Speed, Fuel, Distance': [1.5, 66, 2, 70], 'Cost': 0.5} Iteration no: 991
{'Time, Speed, Fuel, Distance': [1.5, 66, 2, 70], 'Cost': 0.5} Iteration no: 992
{'Time, Speed, Fuel, Distance': [1.5, 66, 2, 70], 'Cost': 0.5} Iteration no: 993
{'Time, Speed, Fuel, Distance': [1.5, 66, 2, 70], 'Cost': 0.5} Iteration no: 994
{'Time, Speed, Fuel, Distance': [1.5, 66, 2, 70], 'Cost': 0.5} Iteration no: 995
{'Time, Speed, Fuel, Distance': [1.5, 66, 2, 70], 'Cost': 0.5} Iteration no: 996
{'Time, Speed, Fuel,Distance': [1.5, 66, 2, 70], 'Cost': 0.5} Iteration no: 997
{'Time, Speed, Fuel, Distance': [1.5, 66, 2, 70], 'Cost': 0.5} Iteration no: 998
{'Time, Speed, Fuel, Distance': [1.5, 66, 2, 70], 'Cost': 0.5} Iteration no: 999
Solution 1.5 Hrs 66 Km/Hr 2 Litres 70 Kms Cost 0.5
Partial sample output

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Add code to convert stochastic hill climb into Random
restart hill climb
Solve the problem using Simulated annealing
Implement the solution for the given problem using genetic
algorithm
That’s all for Hill Climbing
Food for thought