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

A Feature-Based Analysis on the Impact of Set of Constraints for e-Constrained Differential Evolution

Different types of evolutionary algorithms have been developed for constrained continuous optimization. We carry out a feature-based analysis of evolved constrained continuous optimization instances to understand the characteristics of constraints that make problems hard for evolutionary algorithm. In our study, we examine how various sets of constraints can influence the behaviour of e-Constrained Differential Evolution. Investigating the evolved instances, we obtain knowledge of what type of constraints and their features make a problem difficult for the examined algorithm.Comment: 17 Page

A feature-based comparison of local search and the Christofides algorithm for the travelling salesperson problem

Understanding the behaviour of well-known algorithms for classical NP-hard optimisation problems is still a difficult task. With this paper, we contribute to this research direction and carry out a feature based comparison of local search and the well-known Christofides approximation algorithm for the Traveling Salesperson Problem. We use an evolutionary algorithm approach to construct easy and hard instances for the Christofides algorithm, where we measure hardness in terms of approximation ratio. Our results point out important features and lead to hard and easy instances for this famous algorithm. Furthermore, our cross-comparison gives new insights on the complementary benefits of the different approaches.Samadhi Nallaperuma, Markus Wagner, Frank Neumann, Bernd Bischl, Olaf Mersmann, Heike Trautmannhttp://www.sigevo.org/foga-2013

Evolving test instances of the Hamiltonian completion problem

Predicting and comparing algorithm performance on graph instances is challenging for multiple reasons. First, there is usually no standard set of instances to benchmark performance. Second, using existing graph generators results in a restricted spectrum of difficulty and the resulting graphs are usually not diverse enough to draw sound conclusions. That is why recent work proposes a new methodology to generate a diverse set of instances by using an evolutionary algorithm. We can then analyze the resulting graphs and get key insights into which attributes are most related to algorithm performance. We can also fill observed gaps in the instance space in order to generate graphs with previously unseen combinations of features. This methodology is applied to the instance space of the Hamiltonian completion problem using two different solvers, namely the Concorde TSP Solver and a multi-start local search algorithm.Comment: 12 pages, 12 figures, minor revisions in section