Essay: Steady State Genetic Algorithm (GA)

A Steady State Genetic Algorithm (GA) is proposed for the Traveling Salesman Problem with Pickup and Delivery (TSPPD). TSPPD is an extension of the well known Traveling Salesman Problem (TSP). TSPPD is a graph and grouping optimization problem.
In this thesis, TSPPD is differentiated by a group of cities as customers, each of them supplying (picking customer) or demanding (delivery customer) a given amount of a single product. The objective is to find out minimum tour length of the route for a capacitated vehicle in order to transport the product from the pickup to the delivery customers. Each city must be visited exactly once and capacity of vehicle should not be violate.
In this thesis we have used a pheromone based crossover operator that utilizes both local and global information to construct offspring. In addition, we have also used a local search procedure in the genetic algorithm to accelerate convergence. To selecting parents for crossover and mutation operator to generate feasible offspring, we have binary tournament section method. The results of our algorithm have been tested on benchmark instances and computational results show that we have got comparable results to the optimal results.
Chapter – 1
INRODUCTION
1.1 NP-hard Problem
NP-Hardness of a problem is that any possible exact algorithm for the problem will run in time that grows exponentially with the size of problem instance and no polynomial time verification algorithm is known to check the optimality of a proposed solution which causes these problems to become intractable for large instance size [26]. We attempt some of the NP-Hard graph and grouping optimization problems through particular type of approximation techniques by using heuristic and meta-heuristic approach though they do not guarantee optimal solution, for a given problem of any size an algorithm can be designed that can exploit the patterns in search space in an efficient way and provide sufficiently good solutions in reasonable amount of time [25].
Popular NP hard problems are:
*Traveling Salesman Problem
‘Bin Packing
‘N-Queens
00/1 Knapsack
‘Graph Partitioning
1.1.1 Traveling Salesman Problem with Pickup and Delivery (TSPPD)
Traveling salesman problem is a combinatorial problem. Basically in TSP, a set of cities and the distance between these cities has to be given. The main objective of TSP is to find out a minimum distance traveled by salesman and each city must be visited exactly once. The problem can be defined by either coordinates of cities or distance matrix that
gives the distance between two cities. The minimum path is one that visits each city once and only on. Thus, it is a Hamiltonian path.
Traveling salesman problem with pickups and deliveries (TSPPD) is an extension of traveling salesman problem (TSP). TSPPD is characterized by a set of customers; each customer is associated with two types of quantities of goods to be collected and to be delivered. A vehicle with given capacity is located at the depot. The TSPPD involves that a tour will start and end at the depot and each customer must be visited exactly once. In our algorithm, the problem is defined by a distance matrix that gives distance between two cities. The main objective of TSPPD is to minimize the total tour length without violating the capacity of vehicle.
1.1.2 Meta-heuristics
Meta-heuristics have shown their ability to reach good approximation of good solution to numerous NP-hard problems.
Meta-heuristics comes in different types, such as genetic algorithm, simulated annealing, tabu search, greedy search, ant colony optimization and many more. Meta-heuristics is a higher level problem whose applicability is not limited to a particular problem but to a wide range of problem. In this thesis, we have performed a steady state genetic algorithm for traveling salesman problem with pickups and deliveries.
1.1.3 Genetic Algorithm
Genetic algorithm is a general search and optimization strategy that is often used as meta- heuristics to solve otherwise intractable problems. Genetic algorithm (GA) was proposed by John Holland in 1960s and later developed by Holland and his co-worker in 1960s and 1970s [23]. The main reason for the success of genetic algorithm is its robustness and its ability to explore several possible areas of search space at the same
time. GA provides the luxury of not having to think about the internals of a specific problem, and in certain cases can perform quite well as practical heuristics [24]. Such search strategies are also victims of their own generality, and the dagger that pierces them is called a “No Free Lunch” theorem. No Free Lunch theorem is generally of the form that all algorithms that search for an extremism of a cost function perform exactly the same, when averaged over all possible cost functions [24].
Genetic Algorithm is started with a set of solutions which is represented by cromosomes called population. Solutions from one population are selected and used to form a new population. This is motivated by a hope, that the new population will be better than the old one. Solutions which are selected to form new solutions called offspring are selected according to their fitness value because the more suitable they are the more chances they have to reproduce. The procedure is iterated until some condition is satisfied. New populations are generated using selection, crossover, and mutation operator. The following figure shows the basic structure of simple genetic algorithm.[6]
Si mpleGeneticAlgorithm()
{ Initialization of population;
evaluate population;
while TerminationCriteriaNotSatisfied
{ Selection of parents for reproduction;
perform Crossover;
Mutation;
evaluate population; }
We have used the Steady-State Genetic Algorithm where, an old individual having worst fitness in the population is replaced by a new offspring having better fitness through sequential execution.
1.1.3.1 Advantages of Steady State GA over Generational GA
‘ Better solutions could possibly be found faster
‘ Duplicate copies of the same individual in the population is avoided
‘ Problem of premature convergence is averted
‘ Competing conventions may be effectively avoided.
The nature of graph and grouping problems may be observed under many classes, such as one for which adjacency is important (TSP), thereby should carefully architect the structure of GA according to the important information inherent in the structure of the problem thereby achieving better results. Otherwise, GA may not work properly and solutions found may not be of adequate quality.
1.2 Motivation
Transportation of goods and passengers is an important task in the society of today. Excessive amounts of money are spent daily on fuel, equipment, maintenance of equipment and salary. It is therefore obvious to attempt to reduce the amount of money spent on transportation as even small improvements can lead to huge improvements in absolute terms. Several approaches could be taken; one could improve equipment or make the infrastructure better. Operation research has been quite successful in the transportation area. One could see optimization within transportation as one of the successes of OR. Today OR techniques are applied within for example the airline, railway, trucking and shipping industries; and OR techniques are used to optimize the interplay
between the different modes of transportation. Today Or Techniques are also applied Dominoes and Pizza hut deliveries
The OR techniques covers numerous practical applications in the context of reverse logistics, and plays a central role in the efficiency of the operational planning level of distribution/collection systems, for example, goods must be shipped to stores, while at the same time outdated products or empty bottles must be collected and sent back to the distribution point. Reusable packing boxes and containers also create the necessity for reverse material flows. Furthermore, during the last decades, environmental awareness has resulted into legislation forcing companies to take responsibility for their products (tires, lubricants,batteries) for lifetime. Another practical example of TSPPD arises when used products are collected in order to be remanufactured or disassembled into components. Such products may include industrial equipment, car parts, computers etc.
OR has been focus of research interest mainly because of its commercial importance, and the theoretical challenge it find capability in numerous reverse logistics systems: retailers are able to negotiate the return of excess products back to the manufactures with the beneficial effects for both parts.[9]
One problem in the field of transportation related operational research that has been given a lot of attention in the scientific literature is the so called traveling salesman problem (TSP). The main aim of this problem is to find out minimum path where each city traverses exactly once. A subclass of traveling salesman problems is pickup and delivery problems. In this class of problems we are given a number of demands. Each demand consists of a pickup at some location and a delivery at another location. The cost of travelling between each pair of locations is given. Capacity of vehicle is also given. The main aim is to find out minimum path without violating capacity. Each city must be traverse exactly once.
Through the literature survey, we decided to analyze the performance of steady state
model of genetic algorithm on a NP-Hard problem namely traveling salesman problem with pickup and delivery (TSPPD) which have graph and grouping structure and which have been point of focus in recent literatures .
1.3 Problem Statement
Due to the number of different problems versions and minor variations within these, we set out the particular problem that we are addressing in this thesis.
TSPPD is an extension of Traveling salesman problem. In TSPPD, a set of customers is associated with two types of quantities of goods to be collected and to be delivered. There is a single depot that supply and receive the goods from salesman. A salesman cannot carry total load greater then capacity. Here we have used distance matrix. All distances are known. The tour starts from depot and end at the depot. Each city visited exactly once by a salesman.
The problem is to find out a minimum tour length without violating capacity of vehicle. Each city must be visited exactly once. The vehicle capacity must not be exceeded after visiting a pickup customer and any delivery customer can be served so long as the load on the vehicle is no less than its demand. For example, the customers can be branches of a bank in an area providing or requiring a known amount of money (the product), and the depot is the main branch of the bank.
We are trying to analyze the use of meta-heuristics in NP-Hard problems through the performance analysis of steady state model of genetic algorithm (GA) on the problem traveling salesman problem with pickup and delivery (TSPPD).
1.4 Thesis Organization
This thesis is focused primarily on solving NP-Hard graph and grouping optimization problem through genetic algorithm. It is divided into seven chapters beginning with this introduction. In the following, we outline the content of each of these chapters.
Chapter 2 is about literature survey of traveling salesman problem in which previous approach to solve the particular problem will be discussed and besides that also discussed some similar works which is required in our approach. Chapter 3 explains about the NP-hard problem and Meta heuristics. Chapter 4 explain the Genetic Algorithm which a type of Meta-heuristics. This chapter also describes the permutation and grouping genetic algorithm. Chapter 5 explain the algorithm of our approach which a steady-state genetic algorithm for TSPPD. Chapter 6 contains computational results of two classes of instances of a particular problem and comparison graphs between these two classes of instances. Chapter 7 is about conclusion and future work of this problem.