A Hybrid Simplex Non-dominated Sorting Genetic Algorithm for Multi-Objective Optimization

This paper introduces a hybrid scheme for multi-objective optimization problems via utility of two established heuristic algorithms. The proposed hybrid scheme consists of two parts that include the Nelder-Mead simplex algorithm (SA) as well as the Non-dominated Sorting Genetic Algorithm II (NSGA II). In this respect, subsequent to NSGA II sorting for the optimum points, the SA searches the optimum set to find the local optimal points and thus localize a promising area that is likely to contain the global minimum. This is especially helpful since SA is an efficient algorithm that can accurately and quickly exploit the promising area for the optimum point. The proposed hybrid scheme is applied to multi- objective optimization of some bench mark functions and its performance is compared against those of the classical NSGA II as well as the Multi-Objective Particle Swarm Optimization (MOPSO). The numerical results show that the proposed hybrid scheme provides competitive results that outperform those of the existing algorithms.

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

[2]  Rizk M Rizk Allah,et al.  Hybridization of Fruit Fly Optimization Algorithm and Firefly Algorithm for Solving Nonlinear Programming Problems , 2016 .

[3]  Qingfu Zhang,et al.  Multiobjective optimization Test Instances for the CEC 2009 Special Session and Competition , 2009 .

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

[5]  M. El-Hawary,et al.  Hybrid Particle Swarm Optimization Approach for Solving the Discrete OPF Problem Considering the Valve Loading Effects , 2007, IEEE Transactions on Power Systems.

[6]  C. Coello,et al.  Improving PSO-based Multi-Objective Optimization using Crowding , Mutation and �-Dominance , 2005 .

[7]  Urmila M. Diwekar,et al.  Efficient Ant Colony Optimization (EACO) Algorithm for Deterministic Optimization , 2015 .

[8]  Xikui Ma,et al.  NSGA-II Algorithm with a Local Search Strategy for Multiobjective Optimal Design of Dry-Type Air-Core Reactor , 2015 .

[9]  Dieu N. Vo,et al.  Cuckoo Search Algorithm for Minimization of Power Loss and Voltage Deviation , 2016, Int. J. Energy Optim. Eng..

[10]  C. Fonseca,et al.  GENETIC ALGORITHMS FOR MULTI-OBJECTIVE OPTIMIZATION: FORMULATION, DISCUSSION, AND GENERALIZATION , 1993 .

[11]  Carlos A. Coello Coello,et al.  Multi-objective compact differential evolution , 2014, 2014 IEEE Symposium on Differential Evolution (SDE).

[12]  Leandro dos Santos Coelho,et al.  Multi-objective grey wolf optimizer: A novel algorithm for multi-criterion optimization , 2016, Expert Syst. Appl..

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

[14]  G. Kitagawa.  A self-organizing state-space model , 1998 .

[15]  C. A. Coello Coello,et al.  Evolutionary multi-objective optimization: a historical view of the field , 2006, IEEE Computational Intelligence Magazine.

[16]  Ganapati Panda,et al.  Solving multiobjective problems using cat swarm optimization , 2012, Expert Syst. Appl..

[17]  Chaoyong Zhang,et al.  A multi-objective teaching−learning-based optimization algorithm to scheduling in turning processes for minimizing makespan and carbon footprint , 2015 .

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

[19]  Dieu Ngoc Vo,et al.  Pseudo-gradient Based Particle Swarm Optimization with Constriction Factor for Multi Objective Optimal Power Flow , 2015 .

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

[21]  Pj Clarkson,et al.  Biobjective Design Optimization for Axial Compressors Using Tabu Search , 2008 .

[22]  Carlos A. Coello Coello,et al.  Fitness inheritance in multi-objective particle swarm optimization , 2005, Proceedings 2005 IEEE Swarm Intelligence Symposium, 2005. SIS 2005..

[23]  David E. Goldberg,et al.  A niched Pareto genetic algorithm for multiobjective optimization , 1994, Proceedings of the First IEEE Conference on Evolutionary Computation. IEEE World Congress on Computational Intelligence.

[24]  Mengjie Zhang,et al.  A multi-objective artificial bee colony approach to feature selection using fuzzy mutual information , 2015, 2015 IEEE Congress on Evolutionary Computation (CEC).

[25]  Gade Pandu Rangaiah,et al.  Multi-objective optimization : techniques and applications in chemical engineering , 2017 .

[26]  Jonathan F. Bard,et al.  Engineering Optimization: Theory and Practice, Third Edition , 1997 .

[27]  Kerstin Vogler,et al.  Applications Of Multi Objective Evolutionary Algorithms , 2016 .

[28]  Singiresu S. Rao.  Engineering Optimization : Theory and Practice , 2010 .

[29]  David E. Goldberg,et al.  Genetic algorithms and Machine Learning , 1988, Machine Learning.

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

[31]  Guan-Chun Luh,et al.  Multi-objective optimal design of truss structure with immune algorithm , 2004 .

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

[33]  Xiangui Shi,et al.  A Multi-objective Ant Colony Optimization Algorithm Based on Elitist Selection Strategy , 2015 .

[34]  Carlos A. Coello Coello,et al.  Analysis of leader selection strategies in a multi-objective Particle Swarm Optimizer , 2013, 2013 IEEE Congress on Evolutionary Computation.

[35]  Ehsanolah Assareh,et al.  Optimization of hybrid laminated composites using the multi-objective gravitational search algorithm (MOGSA) , 2014 .

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

[37]  H. Abbass,et al.  PDE: a Pareto-frontier differential evolution approach for multi-objective optimization problems , 2001, Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No.01TH8546).