Hypervolume-based multi-objective local search

This paper presents a multi-objective local search, where the selection is realized according to the hypervolume contribution of solutions. The HBMOLS algorithm proposed is inspired from the IBEA algorithm, an indicator-based multi-objective evolutionary algorithm proposed by Zitzler and Künzli in 2004, where the optimization goal is defined in terms of a binary indicator defining the selection operator. In this paper, we use the indicator optimization principle, and we apply it to an iterated local search algorithm, using hypervolume contribution indicator as selection mechanism. The methodology proposed here has been defined in order to be easily adaptable and to be as parameter-independent as possible. We carry out a range of experiments on the multi-objective flow shop problem and the multi-objective quadratic assignment problem, using the hypervolume contribution selection as well as two different binary indicators which were initially proposed in the IBEA algorithm. Experimental results indicate that the HBMOLS algorithm is highly effective in comparison with the algorithms based on binary indicators.

[1]  Thomas Stützle,et al.  A study of stochastic local search algorithms for the biobjective QAP with correlated flow matrices , 2006, Eur. J. Oper. Res..

[2]  Tobias Friedrich,et al.  Don't be greedy when calculating hypervolume contributions , 2009, FOGA '09.

[3]  Kalyanmoy Deb,et al.  Faster Hypervolume-Based Search Using Monte Carlo Sampling , 2008, MCDM.

[4]  A. Nagar,et al.  Multiple and bicriteria scheduling : A literature survey , 1995 .

[5]  Gary B. Lamont,et al.  Evolutionary Algorithms for Solving Multi-Objective Problems (Genetic and Evolutionary Computation) , 2006 .

[6]  Qingfu Zhang,et al.  MOEA/D: A Multiobjective Evolutionary Algorithm Based on Decomposition , 2007, IEEE Transactions on Evolutionary Computation.

[7]  Gary B. Lamont,et al.  Multiobjective Quadratic Assignment Problem Solved by an Explicit Building Block Search Algorithm - MOMGA-IIa , 2005, EvoCOP.

[8]  Jan Karel Lenstra,et al.  Complexity of machine scheduling problems , 1975 .

[9]  Nicola Beume,et al.  SMS-EMOA: Multiobjective selection based on dominated hypervolume , 2007, Eur. J. Oper. Res..

[10]  Tobias Friedrich,et al.  Approximating the Volume of Unions and Intersections of High-Dimensional Geometric Objects , 2008, ISAAC.

[11]  Joseph Y.-T. Leung,et al.  Minimizing Total Tardiness on One Machine is NP-Hard , 1990, Math. Oper. Res..

[12]  Sanja Petrovic,et al.  An Introduction to Multiobjective Metaheuristics for Scheduling and Timetabling , 2004, Metaheuristics for Multiobjective Optimisation.

[13]  Lothar Thiele,et al.  Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach , 1999, IEEE Trans. Evol. Comput..

[14]  Nicola Beume,et al.  S-Metric Calculation by Considering Dominated Hypervolume as Klee's Measure Problem , 2009, Evolutionary Computation.

[15]  Éric D. Taillard,et al.  Benchmarks for basic scheduling problems , 1993 .

[16]  Eckart Zitzler,et al.  Indicator-Based Selection in Multiobjective Search , 2004, PPSN.

[17]  Clarisse Dhaenens,et al.  K-PPM: A new exact method to solve multi-objective combinatorial optimization problems , 2010, Eur. J. Oper. Res..

[18]  David W. Corne,et al.  Approximating the Nondominated Front Using the Pareto Archived Evolution Strategy , 2000, Evolutionary Computation.

[19]  Vinícius Amaral Armentano,et al.  Genetic local search for multi-objective flowshop scheduling problems , 2005, Eur. J. Oper. Res..

[20]  Panos M. Pardalos,et al.  The Quadratic Assignment Problem: A Survey and Recent Developments , 1993, Quadratic Assignment and Related Problems.

[21]  Andrzej P. Wierzbicki,et al.  A parallel multiple reference point approach for multi-objective optimization , 2010, Eur. J. Oper. Res..

[22]  Marco Laumanns,et al.  Performance assessment of multiobjective optimizers: an analysis and review , 2003, IEEE Trans. Evol. Comput..

[23]  El-Ghazali Talbi,et al.  Design of multi-objective evolutionary algorithms: application to the flow-shop scheduling problem , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[24]  Teofilo F. Gonzalez,et al.  P-Complete Approximation Problems , 1976, J. ACM.

[25]  Lucas Bradstreet,et al.  A Fast Incremental Hypervolume Algorithm , 2008, IEEE Transactions on Evolutionary Computation.

[26]  Edmund K. Burke,et al.  Indicator-based multi-objective local search , 2007, 2007 IEEE Congress on Evolutionary Computation.

[27]  Lothar Thiele,et al.  A Tutorial on the Performance Assessment of Stochastic Multiobjective Optimizers , 2006 .