On cardinality of the set of alternatives in discrete many-criterion problems

Chiarandini

Lecture Notes in Economics and Mathematical Systems

2004

154

177

Abstract. In this article, we study Pareto local optimum sets for the biobjective Traveling Salesman Problem applying straightforward extensions of local search algorithms for the single objective case. The performance of the local search algorithms is illustrated by experimental results obtained for well known benchmark instances and comparisons to methods from literature. In fact, a 3-opt local search is able to compete with the best performing metaheuristics in terms of solution quality. Finally, we also present an empirical study of the features of the solutions found by 3-opt on a set of randomly generated instances. The results indicate the existence of several clusters of near-optimal solutions that are separated by only a few edges.

Section: Characterization Of the Pareto Local Optimum Setsmentioning

confidence: 71%

Pareto Local Optimum Sets in the Biobjective Traveling Salesman Problem: An Experimental Study

Chiarandini

Lecture Notes in Economics and Mathematical Systems

2004

154

177

“…The MTSP is known to be NP-hard [14]; additionally, it is known that the lower bound on the expected size of the efficient set for the MTSP is an exponential function of the instance size [15].…”

Section: Multiobjective Optimization and The Mtspmentioning

confidence: 99%

“…Hence, experimental results obtained for the multiobjective version may also be interpreted in light of the experience on the performance of these techniques for the single objective case. Secondly, despite the fact that the small instances of the single-objective TSP can be solved in a few seconds to optimality by exact algorithms such as concorde (http://www.tsp.gatech.edu/concorde), there are two facts that limit their use under fixed time constraints: the typically large variability in the computation times and the potentially very large number of solutions in the efficient set [15]. Thirdly, significant research efforts have been targeted towards applying SLS algorithms to this problem and it has been studied from several different perspectives: from an approximation [17,18], local search [19][20][21], theoretical [15] and experimental [22] point of view; some related problems have also been studied in the literature [23,24].…”

Section: Multiobjective Optimization and The Mtspmentioning

confidence: 99%

Design and analysis of stochastic local search for the multiobjective traveling salesman problem

Computers & Operations Research

2009

Stochastic local search (SLS) algorithms are typically composed of a number of different components, each of which should contribute significantly to the final algorithm's performance. If the goal is to design and engineer effective SLS algorithms, the algorithm developer requires some insight into the importance and the behavior of possible algorithmic components. In this paper, we analyze algorithmic components of SLS algorithms for the multiobjective travelling salesman problem. The analysis is done using a careful experimental design for a generic class of SLS algorithms for multiobjective combinatorial optimization. Based on the insights gained, we engineer SLS algorithms for this problem. Experimental results show that these SLS algorithms, despite their conceptual simplicity, outperform a well-known memetic algorithm for a range of benchmark instances with two and three objectives.

“…The BTSP is NP-hard [31] and it has been tackled in a number of research efforts [1,2,5,7,12,15,22].…”

Section: Multiobjective Combinatorial Optimizationmentioning

confidence: 99%

On the Performance of Local Search for the Biobjective Traveling Salesman Problem

Advances in Multi-Objective Nature Inspired Computing

2010

Summary. In this chapter we investigate experimentally the performance of multiobjective local search approaches that are based on the component-wise acceptance criterion search model. This model gives a framework for many well-known evolutionary and local search algorithms. Using the biobjective traveling salesman problem as an example application, we analyse the impact of three important algorithmic components on the performance of a simple local search algorithm that follows this search model: initialization strategy, neighborhood structure and archive bounding. By following principles of experimental design, we study the effects of each component, both in terms of solution quality and computation time. The experimental analysis indicates the existence of several complex trade-offs between solution quality and run-time for many of the choices available for each component.