AbYSS: Adapting Scatter Search to Multiobjective Optimization

We propose the use of a new algorithm to solve multiobjective optimization problems. Our proposal adapts the well-known scatter search template for single-objective optimization to the multiobjective domain. The result is a hybrid metaheuristic algorithm called Archive-Based hYbrid Scatter Search (AbYSS), which follows the scatter search structure but uses mutation and crossover operators from evolutionary algorithms. AbYSS incorporates typical concepts from the multiobjective field, such as Pareto dominance, density estimation, and an external archive to store the nondominated solutions. We evaluate AbYSS with a standard benchmark including both unconstrained and constrained problems, and it is compared with two state-of-the-art multiobjective optimizers, NSGA-II and SPEA2. The results obtained indicate that, according to the benchmark and parameter settings used, AbYSS outperforms the other two algorithms as regards the diversity of the solutions, and it obtains very competitive results according to the convergence to the true Pareto fronts and the hypervolume metric.

[1]  Rafael Caballero,et al.  SSPMO: A Scatter Tabu Search Procedure for Non-Linear Multiobjective Optimization , 2007, INFORMS J. Comput..

[2]  Alluru Gopala Krishna,et al.  Multi-objective optimisation of surface grinding operations using scatter search approach , 2006 .

[3]  A. Osyczka,et al.  A new method to solve generalized multicriteria optimization problems using the simple genetic algorithm , 1995 .

[4]  Manuel Laguna,et al.  Assigning Proctors to Exams with Scatter Search , 2001 .

[5]  Enrique Alba,et al.  Multi-Objective Optimization using Grid Computing , 2007, Soft Comput..

[6]  Francisco Herrera,et al.  Continuous scatter search: An analysis of the integration of some combination methods and improvement strategies , 2006, Eur. J. Oper. Res..

[7]  Lothar Thiele,et al.  Comparison of Multiobjective Evolutionary Algorithms: Empirical Results , 2000, Evolutionary Computation.

[8]  F. Glover,et al.  Handbook of Metaheuristics , 2019, International Series in Operations Research & Management Science.

[9]  R. Lyndon While,et al.  A Scalable Multi-objective Test Problem Toolkit , 2005, EMO.

[10]  Marco Laumanns,et al.  SPEA2: Improving the strength pareto evolutionary algorithm , 2001 .

[11]  Fred W. Glover,et al.  A Template for Scatter Search and Path Relinking , 1997, Artificial Evolution.

[12]  Christian Fonteix,et al.  Multicriteria optimization using a genetic algorithm for determining a Pareto set , 1996, Int. J. Syst. Sci..

[13]  Frank Kursawe,et al.  A Variant of Evolution Strategies for Vector Optimization , 1990, PPSN.

[14]  R. K. Ursem.  Multi-objective Optimization using Evolutionary Algorithms , 2009 .

[15]  David Corne,et al.  The Pareto archived evolution strategy: a new baseline algorithm for Pareto multiobjective optimisation , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[16]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..

[17]  DebK.,et al.  A fast and elitist multiobjective genetic algorithm , 2002 .

[18]  José Luis González Velarde,et al.  Computing tools for modeling, optimization and simulation : interfaces in computer science and operations research , 2000 .

[19]  Marco Laumanns,et al.  PISA: A Platform and Programming Language Independent Interface for Search Algorithms , 2003, EMO.

[20]  Carlos A. Coello Coello,et al.  Handling multiple objectives with particle swarm optimization , 2004, IEEE Transactions on Evolutionary Computation.

[21]  José Rui Figueira,et al.  A Scatter Search Method for the Bi-Criteria Multi-dimensional {0,1}-Knapsack Problem using Surrogate Relaxation , 2004, J. Math. Model. Algorithms.

[22]  Peter J. Fleming,et al.  Multiobjective optimization and multiple constraint handling with evolutionary algorithms. II. Application example , 1998, IEEE Trans. Syst. Man Cybern. Part A.

[23]  Lothar Thiele,et al.  An evolutionary algorithm for multiobjective optimization: the strength Pareto approach , 1998 .

[24]  Kalyanmoy Deb,et al.  MULTI-OBJECTIVE FUNCTION OPTIMIZATION USING NON-DOMINATED SORTING GENETIC ALGORITHMS , 1994 .

[25]  Enrique Alba,et al.  New Ideas in Applying Scatter Search to Multiobjective Optimization , 2005, EMO.

[26]  Kalyanmoy Deb,et al.  Muiltiobjective Optimization Using Nondominated Sorting in Genetic Algorithms , 1994, Evolutionary Computation.

[27]  K. C. Seow,et al.  MULTIOBJECTIVE DESIGN OPTIMIZATION BY AN EVOLUTIONARY ALGORITHM , 2001 .

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

[29]  Ángel Corberán,et al.  Heuristic solutions to the problem of routing school buses with multiple objectives , 2002, J. Oper. Res. Soc..

[30]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[31]  F. Glover,et al.  Fundamentals of Scatter Search and Path Relinking , 2000 .

[32]  Masahiro Tanaka,et al.  GA-based decision support system for multicriteria optimization , 1995, 1995 IEEE International Conference on Systems, Man and Cybernetics. Intelligent Systems for the 21st Century.

[33]  J. Vasconcelos,et al.  Scatter search techniques applied to electromagnetic problems , 2005, IEEE Transactions on Magnetics.

[34]  Janez Demsar,et al.  Statistical Comparisons of Classifiers over Multiple Data Sets , 2006, J. Mach. Learn. Res..

[35]  Shapour Azarm,et al.  Constraint handling improvements for multiobjective genetic algorithms , 2002 .

[36]  Qingfu Zhang,et al.  Combining Model-based and Genetics-based Offspring Generation for Multi-objective Optimization Using a Convergence Criterion , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[37]  A. Rama Mohan Rao,et al.  A scatter search algorithm for stacking sequence optimisation of laminate composites , 2005 .

[38]  Francisco Luna,et al.  jMetal: a Java Framework for Developing Multi-Objective Optimization Metaheuristics , 2006 .

[39]  Ricardo P. Beausoleil,et al.  "MOSS" multiobjective scatter search applied to non-linear multiple criteria optimization , 2006, Eur. J. Oper. Res..

[40]  Marco Laumanns,et al.  Scalable Test Problems for Evolutionary Multiobjective Optimization , 2005, Evolutionary Multiobjective Optimization.

[41]  Gary B. Lamont,et al.  Evolutionary Algorithms for Solving Multi-Objective Problems , 2002, Genetic Algorithms and Evolutionary Computation.

[42]  Maliha S. Nash,et al.  Handbook of Parametric and Nonparametric Statistical Procedures , 2001, Technometrics.

[43]  Kalyanmoy Deb,et al.  Simulated Binary Crossover for Continuous Search Space , 1995, Complex Syst..

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