Abstract
We investigate the properties of large-scale multi-objective quadratic assignment problems (mQAP) and how they impact the performance of multi-objective evolutionary algorithms. The landscape of a diversified dataset of bi-, multi-, and many-objective mQAP instances is characterized by means of previously-identified features. These features measure complementary facets of problem difficulty based on a sample of solutions collected along random and adaptive walks over the landscape. The strengths and weaknesses of a dominance-based, an indicator-based, and a decomposition-based search algorithm are then highlighted by relating their expected approximation quality in view of landscape features. We also discriminate between algorithms by revealing the most suitable one for subsets of instances. At last, we investigate the performance of a feature-based automated algorithm selection approach. By relying on low-cost features, we show that our recommendation system performs best in more than \(90\%\) of the considered mQAP instances.
This research was conducted in the scope of the French/Japanese MOD\(\bar{\text {O}}\) international lab, and was partially supported by the French national research agency under Project ANR-16-CE23-0013-01.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Breiman, L.: Random forests. Mach. Learn. 45(1), 5–32 (2001)
Carnell, R.: LHS: Latin Hypercube Samples (2018). https://CRAN.R-project.org/package=lhs, r package version 0.16
Coello Coello, C.A., Lamont, G.B., Van Veldhuizen, D.A.: Evolutionary Algorithms for Solving Multi-Objective Problems, 2nd edn. Springer, Heidelberg (2007). https://doi.org/10.1007/978-0-387-36797-2
Daolio, F., Verel, S., Ochoa, G., Tomassini, M.: Local optima networks of the quadratic assignment problem. In: Congress on Evolutionary Computation (CEC 2010)., pp. 1–8. IEEE (2010)
Deb, K.: Multi-Objective Optimization using Evolutionary Algorithms. Wiley, Hoboken (2001)
Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm : NSGA-II. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002)
Durillo, J.J., Nebro, A.J.: jMetal: a Java framework for multi-objective optimization. Adv. Eng. Softw. 42, 760–771 (2011)
Garrett, D., Dasgupta, D.: Analyzing the performance of hybrid evolutionary algorithms for the multiobjective quadratic assignment problem. In: IEEE Congress on Evolutionary Computation (CEC 2006), pp. 1710–1717 (2006)
Garrett, D., Dasgupta, D.: Multiobjective landscape analysis and the generalized assignment problem. In: Maniezzo, V., Battiti, R., Watson, J.-P. (eds.) LION 2007. LNCS, vol. 5313, pp. 110–124. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-92695-5_9
Goldberg, D.E.: Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley, Boston (1989)
Kerschke, P., Hoos, H., Neumann, F., Trautmann, H.: Automated algorithm selection: survey and perspectives. Evol. Comput. 27(1), 3–45 (2019)
Knowles, J., Corne, D.: Towards landscape analyses to inform the design of a hybrid local search for the multiobjective quadratic assignment problem. In: Soft Computing Systems: Design, Management and Applications 2002, pp. 271–279 (2002)
Knowles, J., Corne, D.: Instance generators and test suites for the multiobjective quadratic assignment problem. In: Fonseca, C.M., Fleming, P.J., Zitzler, E., Thiele, L., Deb, K. (eds.) EMO 2003. LNCS, vol. 2632, pp. 295–310. Springer, Heidelberg (2003). https://doi.org/10.1007/3-540-36970-8_21
Liaw, A., Wiener, M.: Classification and regression by randomForest. R News 2(3), 18–22 (2002)
Liefooghe, A., Daolio, F., Verel, S., Derbel, B., Aguirre, H., Tanaka, K.: Landscape-aware performance prediction for evolutionary multi-objective optimization. IEEE Trans. Evol. Comput. 1 (2019, early access)
López-Ibáñez, M., Paquete, L., Stützle, T.: Hybrid population-based algorithms for the bi-objective quadratic assignment problem. J. Math. Model. Algorithms 5(1), 111–137 (2006)
Merz, P.: Advanced fitness landscape analysis and the performance of memetic algorithms. Evol. Comput. 12(3), 303–325 (2004)
Paquete, L., Schiavinotto, T., Stützle, T.: On local optima in multiobjective combinatorial optimization problems. Ann. Oper. Res. 156(1), 83–97 (2007)
Paquete, L., Stützle, T.: A study of stochastic local search algorithms for the biobjective QAP with correlated flow matrices. Eur. J. Oper. Res. 169(3), 943–959 (2006)
Paquete, L., Stützle, T.: Clusters of non-dominated solutions in multiobjective combinatorial optimization: an experimental analysis. In: Barichard, V., Ehrgott, M., Gandibleux, X., T’Kindt, V. (eds.) Multiobjective Programming and Goal Programming: Theoretical Results and Practical Applications. Lecture Notes in Economics and Mathematical Systems, vol. 618, pp. 69–77. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-540-85646-7_7
Pitzer, E., Beham, A., Affenzeller, M.: Correlation of problem hardness and fitness landscapes in the quadratic assignment problem. In: Klempous, R., Nikodem, J., Jacak, W., Chaczko, Z. (eds.) Advanced Methods and Applications in Computational Intelligence. Topics in Intelligent Engineering and Informatics, vol. 6, pp. 165–195. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-319-01436-4_9
Rice, J.R.: The algorithm selection problem. Adv. Comput. 15, 65–118 (1976)
Richter, H., Engelbrecht, A. (eds.): Recent Advances in the Theory and Application of Fitness Landscapes, Emergence, Complexity and Computation. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-41888-4
Sahni, S., Gonzalez, T.: P-complete approximation problems. J. ACM 23(3), 555–565 (1976)
Smith-Miles, K., Lopes, L.: Measuring instance difficulty for combinatorial optimization problems. Comput. Oper. Res. 39(5), 875–889 (2012)
Verel, S., Liefooghe, A., Jourdan, L., Dhaenens, C.: On the structure of multiobjective combinatorial search space: MNK-landscapes with correlated objectives. Eur. J. Oper. Res. 227(2), 331–342 (2013)
Weinberger, E.D.: Correlated and uncorrelatated fitness landscapes and how to tell the difference. Biol. Cybern. 63(5), 325–336 (1990)
Zhang, Q., Li, H.: MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans. Evol. Comput. 11(6), 712–731 (2007)
Zitzler, E., Künzli, S.: Indicator-based selection in multiobjective search. In: Yao, X., et al. (eds.) PPSN 2004. LNCS, vol. 3242, pp. 832–842. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-30217-9_84
Zitzler, E., Thiele, L.: Multiobjective evolutionary algorithms: a comparative case study and the strength pareto approach. IEEE Trans. Evol. Comput. 3(4), 257–271 (1999)
Zitzler, E., Thiele, L., Laumanns, M., Fonseca, C.M., da Fonseca, V.G.: Performance assessment of multiobjective optimizers: an analysis and review. IEEE Trans. Evol. Comput. 7(2), 117–132 (2003)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Liefooghe, A., Verel, S., Derbel, B., Aguirre, H., Tanaka, K. (2020). Dominance, Indicator and Decomposition Based Search for Multi-objective QAP: Landscape Analysis and Automated Algorithm Selection. In: Bäck, T., et al. Parallel Problem Solving from Nature – PPSN XVI. PPSN 2020. Lecture Notes in Computer Science(), vol 12269. Springer, Cham. https://doi.org/10.1007/978-3-030-58112-1_3
Download citation
DOI: https://doi.org/10.1007/978-3-030-58112-1_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-58111-4
Online ISBN: 978-3-030-58112-1
eBook Packages: Computer ScienceComputer Science (R0)