The Traveling Salesman Problem: An Analysis and Comparison of Metaheuristics and Algorithms

One of the most investigated topics in operations research is the Traveling Salesman Problem (TSP) and the algorithms that can be used to solve it. Despite its relatively simple formulation, its computational difficulty keeps it and potential solution methods at the forefront of current research. This paper defines and analyzes numerous proposed solutions to the TSP in order to facilitate understanding of the problem. Additionally, the efficiencies of different heuristics are studied and compared to the aforementioned algorithms’ accuracy, as a quick algorithm is often formulated at the expense of an exact solution

Evolutionary computation applied to combinatorial optimisation problems

This thesis addresses the issues associated with conventional genetic algorithms (GA) when applied to hard optimisation problems. In particular it examines the problem of selecting and implementing appropriate genetic operators in order to meet the validity constraints for constrained optimisation problems. The problem selected is the travelling salesman problem (TSP), a well known NP-hard problem. Following a review of conventional genetic algorithms, this thesis advocates the use of a repair technique for genetic algorithms: GeneRepair. We evaluate the effectiveness of this operator against a wide range of benchmark problems and compare these results with conventional genetic algorithm approaches. A comparison between GeneRepair and the conventional GA approaches is made in two forms: firstly a handcrafted approach compares GAs without repair against those using GeneRepair. A second automated approach is then presented. This meta-genetic algorithm examines different configurations of operators and parameters. Through the use of a cost/benefit (Quality-Time Tradeoff) function, the user can balance the computational effort against the quality of the solution and thus allow the user to specify exactly what the cost benefit point should be for the search. Results have identified the optimal configuration settings for solving selected TSP problems. These results show that GeneRepair when used consistently generates very good TSP solutions for 50, 70 and 100 city problems. GeneRepair assists in finding TSP solutions in an extremely efficient manner, in both time and number of evaluations required

Algorithms for Variants of Routing Problems

In this thesis, we propose mathematical optimization models and algorithms for variants of routing problems. The first contribution consists of models and algorithms for the Traveling Salesman Problem with Time-dependent Service times (TSP-TS). We propose a new Mixed Integer Programming model and develop a multi-operator genetic algorithm and two Branch-and-Cut methods, based on the proposed model. The algorithms are tested on benchmark symmetric and asymmetric instances from the literature, and compared with an existing approach, showing the effectiveness of the proposed algorithms. The second work concerns the Pollution Traveling Salesman Problem (PTSP). We present a Mixed Integer Programming model for the PTSP and two mataheuristic algorithms: an Iterated Local Search algorithm and a Multi-operator Genetic algorithm. We performed extensive computational experiments on benchmark instances. The last contribution considers a rich version of the Waste Collection Problem (WCP) with multiple depots and stochastic demands using Horizontal Cooperation strategies. We developed a hybrid algorithm combining metaheuristics with simulation. We tested the proposed algorithm on a set of large-sized WCP instances in non-cooperative scenarios and cooperative scenarios

UML modeling for traveling salesman problem based on genetic algorithms

The major purpose of this paper is to present a way of solving problems through so-called visual planning and programming using object-oriented concepts. This paper describes the process of UML modeling for solving the traveling salesman problem using one of the metaheuristic-genetic algorithms. The analysis and problem solving in this way has many advantages just because it provides a clear definition of requirements and specific plan that we will later use to create specific applications. This is a good way to resolve because the UML describes the source code, models help to visualize the system as it is or what it should be and allow you to determine the structure and behavior of the system. Static and dynamic diagrams implemented in developing tools for modeling, as well as a description of specific applications and testing are mentioned. With this approach we describe modeling tool that can be used in the development of specific solutions and a way of establishing explicit links between concepts and execution code

A self-adaptive genetic algorithm for the flying sidekick travelling salesman problem

This paper presents a novel approach to solving the Flying Sidekick Travelling Salesman Problem (FSTSP) using a state-of-the-art self-adaptive genetic algorithm. The Flying Sidekick Travelling Salesman Problem is a combinatorial optimisation problem that extends the Travelling Salesman Problem (TSP) by introducing the use of drones. In FSTSP, the objective is to minimise the total time to visit all locations while strategically deploying a drone to serve hard-to-reach customer locations. Also, to the best of my knowledge, this is the first time a self-adaptive genetic algorithm (GA) has been used to solve the FSTSP problem. Experimental results on smaller-sized problem instances demonstrate that this algorithm can find a higher quantity of optimal solutions and a lower percentage gap to the optimal solution compared to rival algorithms. Moreover, on larger-sized problem instances, this algorithm outperforms all rival algorithms on each problem size while maintaining a reasonably low computation time.Comment: 17 pages, 9 figure

Genetic Algorithm for Combinatorial Path Planning: The Subtour Problem

The purpose of this paper is to present a combinatorial planner for autonomous systems. The approach is demonstrated on the so-called subtour problem, a variant of the classical traveling salesman problem (TSP): given a set of possible goals/targets, the optimal strategy is sought that connects ≤ goals. The proposed solution method is a Genetic Algorithm coupled with a heuristic local search. To validate the approach, the method has been benchmarked against TSPs and subtour problems with known optimal solutions. Numerical experiments demonstrate the success of the approach

Parameterized Complexity Analysis of Randomized Search Heuristics

This chapter compiles a number of results that apply the theory of parameterized algorithmics to the running-time analysis of randomized search heuristics such as evolutionary algorithms. The parameterized approach articulates the running time of algorithms solving combinatorial problems in finer detail than traditional approaches from classical complexity theory. We outline the main results and proof techniques for a collection of randomized search heuristics tasked to solve NP-hard combinatorial optimization problems such as finding a minimum vertex cover in a graph, finding a maximum leaf spanning tree in a graph, and the traveling salesperson problem.Comment: This is a preliminary version of a chapter in the book "Theory of Evolutionary Computation: Recent Developments in Discrete Optimization", edited by Benjamin Doerr and Frank Neumann, published by Springe