Traveling Salesman Problem Case Study

Research Proposal

Prepared By

Omadoye Jedidiah Omatowuoritse

Computer Science

11CG012142

400L

On

Implementing the Travelling Sales Man Problem with Genetic Algorithm (Using Lagos State as a Case Study)

Chapter One: Introduction

Background Information

Travelling salesman problem

The origin of the Travelling Salesman Problem (TSP) is quite obscure, some say the first instance of the TSP was from Euler in 1759 who attempted to move a knight to every position on a chess board exactly once [1], others say that the TSP was simulated or inspired from the Hamiltonian game that attempts to find all the possible paths over an network, or that the travelling salesman idea came into light because of a book written by a German BF Voigt I in 1832

The TSP is a non-deterministic polynomial time hard (NP-Hard) problem which means it is at least as hard as any NP-Problem, although it might in fact be harder than an NP-Hard problem. The basic idea of the travelling salesman problem is to find a path among a given number of cities in a Hamiltonian cycle with three constraints of visiting a city only once, visiting all the selected cities, returning to the start city as the goal state and using the shortest calculated path as its optimal solution. It has no accepted general solution as of now and as such is referred to as an NP-Hard problem. Given N as the number of cities to be visited by the individual, the total number of possible paths to go through all the cities can be give as O(N!). Major applications of TSP include Drilling of printed circuits boards in an optimal amount of time, online delivery of goods to buyers, school bus routing problem

And c_ij = √(〖(Xi-Xj)〗^2+〖(Yi-Yj)〗^2 ) [3]

Genetic Algorithm Genetic algorithms (GAs) were invented by the computer scientist John Holland in the 1960s and were developed by Holland and his students and colleagues at the University of Michigan in the 1960s and the 1970s and by 1992 John Koza has used genetic algorithm to evolve programs to perform certain tasks. He called his method "genetic programming"[4]. It is a type of heuristic technique and adaptive search algorithm that is used to solve optimization problems. The genetic algorithm is a class of evolutionary algorithm that is inspired by Charles Darwin theories on evolution which states that the survival of an organism is affected by rule "the strongest species that survives"[5].

Why Genetic Algorithm

Genetic algorithm can be used to find good approximation solutions to problems that cannot be easily solved using other techniques. It can be used to solve a lot of problems that human beings don’t really know how to solve and get good solutions if any exists and as such has proven to be the best way to solve the optimal path in an Hamiltonian cycle.

Statement of the