Design, Evaluation and Analysis of Combinatorial Optimization Heuristic Algorithms

TL;DR

This paper explores heuristic algorithms for two NP-hard combinatorial problems, focusing on local search and memetic algorithms, resulting in improved heuristics and state-of-the-art metaheuristics.

Contribution

It systematically advances local search neighborhoods and memetic algorithms for the Generalized Traveling Salesman and Multidimensional Assignment Problems.

Findings

Proposed heuristics outperform existing algorithms in various time/quality scenarios.

Enhanced local search methods significantly improve solution quality.

New memetic algorithms set a state-of-the-art benchmark for these problems.

Abstract

Combinatorial optimization is widely applied in a number of areas nowadays. Unfortunately, many combinatorial optimization problems are NP-hard which usually means that they are unsolvable in practice. However, it is often unnecessary to have an exact solution. In this case one may use heuristic approach to obtain a near-optimal solution in some reasonable time. We focus on two combinatorial optimization problems, namely the Generalized Traveling Salesman Problem and the Multidimensional Assignment Problem. The first problem is an important generalization of the Traveling Salesman Problem; the second one is a generalization of the Assignment Problem for an arbitrary number of dimensions. Both problems are NP-hard and have hosts of applications. In this work, we discuss different aspects of heuristics design and evaluation. A broad spectrum of related subjects, covered in this research, includes test bed generation and analysis, implementation and performance issues, local search neighborhoods and efficient exploration algorithms, metaheuristics design and population sizing in memetic algorithm. The most important results are obtained in the areas of local search and memetic algorithms for the considered problems. In both cases we have significantly advanced the existing knowledge on the local search neighborhoods and algorithms by systematizing and improving the previous results. We have proposed a number of efficient heuristics which dominate the existing algorithms in a wide range of time/quality requirements. Several new approaches, introduced in our memetic algorithms, make them the state-of-the-art metaheuristics for the corresponding problems. Population sizing is one of the most promising among these approaches; it is expected to be applicable to virtually any memetic algorithm.