Feature-Based Diversity Optimization for Problem Instance Classification

Understanding the behaviour of heuristic search methods is a challenge. This even holds for simple local search methods such as 2-OPT for the Traveling Salesperson problem. In this paper, we present a general framework that is able to construct a diverse set of instances that are hard or easy for a given search heuristic. Such a diverse set is obtained by using an evolutionary algorithm for constructing hard or easy instances that are diverse with respect to different features of the underlying problem. Examining the constructed instance sets, we show that many combinations of two or three features give a good classification of the TSP instances in terms of whether they are hard to be solved by 2-OPT.Comment: 20 pages, 18 figure

Evolving Diverse Sets of Tours for the Travelling Salesperson Problem

Evolving diverse sets of high quality solutions has gained increasing interest in the evolutionary computation literature in recent years. With this paper, we contribute to this area of research by examining evolutionary diversity optimisation approaches for the classical Traveling Salesperson Problem (TSP). We study the impact of using different diversity measures for a given set of tours and the ability of evolutionary algorithms to obtain a diverse set of high quality solutions when adopting these measures. Our studies show that a large variety of diverse high quality tours can be achieved by using our approaches. Furthermore, we compare our approaches in terms of theoretical properties and the final set of tours obtained by the evolutionary diversity optimisation algorithm.Comment: 11 pages, 3 tables, 3 figures, to be published in GECCO '2

Feature-based diversity optimization for problem instance classification

Parallel Problem Solving from Nature – PPSN XIVUnderstanding the behaviour of heuristic search methods is a challenge. This even holds for simple local search methods such as 2-OPT for the Traveling Salesperson problem. In this paper, we present a general framework that is able to construct a diverse set of instances that are hard or easy for a given search heuristic. Such a diverse set is obtained by using an evolutionary algorithm for constructing hard or easy instances that are diverse with respect to different features of the underlying problem. Examining the constructed instance sets, we show that many combinations of two or three features give a good classification of the TSP instances in terms of whether they are hard to be solved by 2-OPT.Wanru Gao, Samadhi Nallaperuma, and Frank Neuman

Discrepancy-based Evolutionary Diversity Optimization

Diversity plays a crucial role in evolutionary computation. While diversity has been mainly used to prevent the population of an evolutionary algorithm from premature convergence, the use of evolutionary algorithms to obtain a diverse set of solutions has gained increasing attention in recent years. Diversity optimization in terms of features on the underlying problem allows to obtain a better understanding of possible solutions to the problem at hand and can be used for algorithm selection when dealing with combinatorial optimization problems such as the Traveling Salesperson Problem. We explore the use of the star-discrepancy measure to guide the diversity optimization process of an evolutionary algorithm. In our experimental investigations, we consider our discrepancy-based diversity optimization approaches for evolving diverse sets of images as well as instances of the Traveling Salesperson problem where a local search is not able to find near optimal solutions. Our experimental investigations comparing three diversity optimization approaches show that a discrepancy-based diversity optimization approach using a tie-breaking rule based on weighted differences to surrounding feature points provides the best results in terms of the star discrepancy measure

Rigorous Performance Analysis of State-of-the-Art TSP Heuristic Solvers

Understanding why some problems are better solved by one algorithm rather than another is still an open problem, and the symmetric Travelling Salesperson Problem (TSP) is no exception. We apply three state-of-the-art heuristic solvers to a large set of TSP instances of varying structure and size, identifying which heuristics solve specific instances to optimality faster than others. The first two solvers considered are variants of the multi-trial Helsgaun's Lin-Kernighan Heuristic (a form of iterated local search), with each utilising a different form of Partition Crossover; the third solver is a genetic algorithm (GA) using Edge Assembly Crossover. Our results show that the GA with Edge Assembly Crossover is the best solver, shown to significantly outperform the other algorithms in 73% of the instances analysed. A comprehensive set of features for all instances is also extracted, and decision trees are used to identify main features which could best inform algorithm selection. The most prominent features identified a high proportion of instances where the GA with Edge Assembly Crossover performed significantly better when solving to optimality