Selection mechanisms based on the maximin fitness function to solve multi-objective optimization problems

In this paper, we study three selection mechanisms based on the maximin fitness function and we propose another one. These selection mechanisms give rise to the following MOEAs: "MC-MOEA", "MD-MOEA", "MH-MOEA" and "MAH-MOEA". We validated them using standard test functions taken from the specialized literature, having from three up to ten objective functions. We compare these four MOEAs among them and also with respect to MOEA/D (which is based on decomposition), and to SMS-EMOA (which is based on the hypervolume indicator). Our preliminary results indicate that "MD-MOEA" and "MAH-MOEA" are promising alternatives for solving MOPs with either low or high dimensionality.

[1]  Xin-She Yang,et al.  Multi-Objective Flower Algorithm for Optimization , 2014, ICCS.

[2]  K. S. Swarup,et al.  Multi Objective Harmony Search Algorithm For Optimal Power Flow , 2010 .

[3]  David W. Corne,et al.  Properties of an adaptive archiving algorithm for storing nondominated vectors , 2003, IEEE Trans. Evol. Comput..

[4]  Tobias Friedrich,et al.  Approximating the volume of unions and intersections of high-dimensional geometric objects , 2008, Comput. Geom..

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

[6]  L Manuel,et al.  The Automatic Design of Multi-Objective Ant Colony Optimization Algorithms , 2012 .

[7]  Stefan Roth,et al.  Covariance Matrix Adaptation for Multi-objective Optimization , 2007, Evolutionary Computation.

[8]  Adriana Menchaca-Mendez,et al.  An alternative hypervolume-based selection mechanism for multi-objective evolutionary algorithms , 2017, Soft Comput..

[9]  Adriana Menchaca-Mendez,et al.  A new selection mechanism based on hypervolume and its locality property , 2013, 2013 IEEE Congress on Evolutionary Computation.

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

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

[12]  Xiaoxia Huang,et al.  Optimizing expressway maintenance planning by coupling ant algorithm and geography information system transportation in Hubei province, China , 2011, 2011 IEEE International Geoscience and Remote Sensing Symposium.

[13]  Luigi Barone,et al.  An evolution strategy with probabilistic mutation for multi-objective optimisation , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[14]  M Reyes Sierra,et al.  Multi-Objective Particle Swarm Optimizers: A Survey of the State-of-the-Art , 2006 .

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

[16]  Adriana Menchaca-Mendez,et al.  MH-MOEA: A New Multi-Objective Evolutionary Algorithm Based on the Maximin Fitness Function and the Hypervolume Indicator , 2014, PPSN.

[17]  Xiaodong Li,et al.  Better Spread and Convergence: Particle Swarm Multiobjective Optimization Using the Maximin Fitness Function , 2004, GECCO.

[18]  John E. Dennis,et al.  Normal-Boundary Intersection: A New Method for Generating the Pareto Surface in Nonlinear Multicriteria Optimization Problems , 1998, SIAM J. Optim..

[19]  Nicola Beume,et al.  An EMO Algorithm Using the Hypervolume Measure as Selection Criterion , 2005, EMO.

[20]  M. Farina,et al.  On the optimal solution definition for many-criteria optimization problems , 2002, 2002 Annual Meeting of the North American Fuzzy Information Processing Society Proceedings. NAFIPS-FLINT 2002 (Cat. No. 02TH8622).

[21]  R. J. Balling,et al.  The maximin fitness function for multi-objective evolutionary computation: application to city planning , 2001 .

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

[23]  Jürgen Branke,et al.  Multi-objective particle swarm optimization on computer grids , 2007, GECCO '07.

[24]  Adriana Menchaca-Mendez,et al.  Selection Operators Based on Maximin Fitness Function for Multi-Objective Evolutionary Algorithms , 2013, EMO.

[25]  Thomas Stützle,et al.  The impact of design choices of multiobjective antcolony optimization algorithms on performance: an experimental study on the biobjective TSP , 2010, GECCO '10.

[26]  Tobias Friedrich,et al.  Approximating the least hypervolume contributor: NP-hard in general, but fast in practice , 2008, Theor. Comput. Sci..

[27]  Xin-She Yang,et al.  Multiobjective firefly algorithm for continuous optimization , 2012, Engineering with Computers.

[28]  Richard Balling,et al.  The Maximin Fitness Function; Multi-objective City and Regional Planning , 2003, EMO.

[29]  R. Lyndon While,et al.  A review of multiobjective test problems and a scalable test problem toolkit , 2006, IEEE Transactions on Evolutionary Computation.

[30]  Xiaodong Li,et al.  On performance metrics and particle swarm methods for dynamic multiobjective optimization problems , 2007, 2007 IEEE Congress on Evolutionary Computation.

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

[32]  Adriana Menchaca-Mendez,et al.  MD-MOEA : A new MOEA based on the maximin fitness function and Euclidean distances between solutions , 2014, 2014 IEEE Congress on Evolutionary Computation (CEC).