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Computational Complexity Theory

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CHAPTER – 1
INTRODUCTION

1.1 INTRODUCTION
In theoretical computer science, the computer is expected to solve the computational problems in a reasonable amount of time with minimum space requirement using the classical algorithms. But practically all computational problems can’t be solved by the classical algorithms with a lesser time and space complexity as different problems exhibit different complexity. The computational theory has given different theories. One of the important theories among them is the computational complexity theory. The computational complexity theory determines whether a computer can solve a computational problem or not and describes its efficiency also. The efficiency is computed in the terms of time and space …show more content…

But some intractable problems like travelling salesman problem with pickup and delivery (TSPPD), multiple travelling salesman problem with pickup and delivery (MTSPPD) and many more problems have not been implemented using the ABC algorithm till now. So, in this thesis, travelling salesman problem with pickup and delivery has been implemented using the ABC algorithm and then the results are compared with the results of Ant Colony Optimization (ACO) algorithm. The comparison of results has been done between ABC and ACO algorithm because both of these algorithms are the algorithms of Swarm Intelligence. So, it will be helpful in giving a clear picture of the two algorithms of the Swarm Intelligence. This will clear whose solutions are better and which algorithm is …show more content…

There exists a one-to-one relationship between the pickup and delivery vertices.

1.3 RESEARCH OBJECTIVES
OBJECTIVE 1: To study the Artificial Bee Colony Algorithm
This objective is carried out to understand the concepts, the advantages, disadvantages and applications of ABC algorithm. To understand what kind of problems can be implemented through this algorithm and how they can be implemented so that the new problem can be identified for the thesis.
OBJECTIVE 2: To implement Intractable Problem using Artificial Bee Colony Algorithm
This objective is carried out to implement the TSPPD, which is an intractable problem, using the ABC algorithm as ABC. The intractable problems can’t be solved by the classical algorithms hence TSPPD has been solved by the ABC algorithm.
OBJECTIVE 3: To compare the performance of Artificial Bee Colony Algorithm and Ant Colony Optimization Algorithm
This objective is carried out to compare the performance of ABC algorithm with that of ACO algorithm so that the efficiency of the ABC algorithm can be measured. The ACO algorithm has been chosen for the comparison because both the ABC and ACO algorithms belong to the Swarm

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