An Enhanced Differential Evolution Based Algorithm with Simulated Annealing for Solving Multiobjective Optimization Problems

An enhanced differential evolution based algorithm, named multi-objective differential evolution with simulated annealing algorithm (MODESA), is presented for solving multiobjective optimization problems (MOPs). The proposed algorithm utilizes the advantage of simulated annealing for guiding the algorithm to explore more regions of the search space for a better convergence to the true Pareto-optimal front. In the proposed simulated annealing approach, a new acceptance probability computation function based on domination is proposed and some potential solutions are assigned a life cycle to have a priority to be selected entering the next generation. Moreover, it incorporates an efficient diversity maintenance approach, which is used to prune the obtained nondominated solutions for a good distributed Pareto front. The feasibility of the proposed algorithm is investigated on a set of five biobjective and two triobjective optimization problems and the results are compared with three other algorithms. The experimental results illustrate the effectiveness of the proposed algorithm.

[1]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[2]  Donald Geman,et al.  Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images , 1984 .

[3]  Kalyanmoy Deb,et al.  A Fast and Effective Method for Pruning of Non-dominated Solutions in Many-Objective Problems , 2006, PPSN.

[4]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[5]  Dimitris K. Tasoulis,et al.  Vector evaluated differential evolution for multiobjective optimization , 2004, Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753).

[6]  Mehmet Fatih Tasgetiren,et al.  Multi-objective optimization based on self-adaptive differential evolution algorithm , 2007, 2007 IEEE Congress on Evolutionary Computation.

[7]  Millie Pant,et al.  An efficient Differential Evolution based algorithm for solving multi-objective optimization problems , 2011, Eur. J. Oper. Res..

[8]  Carlos A. Coello Coello,et al.  Solving Multiobjective Optimization Problems Using an Artificial Immune System , 2005, Genetic Programming and Evolvable Machines.

[9]  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).

[10]  Ujjwal Maulik,et al.  A Simulated Annealing-Based Multiobjective Optimization Algorithm: AMOSA , 2008, IEEE Transactions on Evolutionary Computation.

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

[12]  B. Suman,et al.  A survey of simulated annealing as a tool for single and multiobjective optimization , 2006, J. Oper. Res. Soc..

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

[14]  K..  Multiobjective Optimization Using a Pareto Differential Evolution Approach , 2022 .

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

[16]  Arthur C. Sanderson,et al.  Multi-objective differential evolution and its application to enterprise planning , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[17]  Carlos A. Coello Coello,et al.  A new proposal for multi-objective optimization using differential evolution and rough sets theory , 2006, GECCO '06.

[18]  Jouni Lampinen,et al.  An Extension of Generalized Differential Evolution for Multi-objective Optimization with Constraints , 2004, PPSN.

[19]  Jouni Lampinen,et al.  GDE3: the third evolution step of generalized differential evolution , 2005, 2005 IEEE Congress on Evolutionary Computation.

[20]  R. Storn,et al.  Differential Evolution - A simple and efficient adaptive scheme for global optimization over continuous spaces , 2004 .

[21]  Ponnuthurai N. Suganthan,et al.  Multi-objective optimization using self-adaptive differential evolution algorithm , 2009, 2009 IEEE Congress on Evolutionary Computation.

[22]  Carlos A. Coello Coello,et al.  An updated survey of GA-based multiobjective optimization techniques , 2000, CSUR.

[23]  Yaonan Wang,et al.  Multi-objective self-adaptive differential evolution with elitist archive and crowding entropy-based diversity measure , 2010, Soft Comput..

[24]  K. Price.  Differential evolution vs. the functions of the 2/sup nd/ ICEO , 1997, Proceedings of 1997 IEEE International Conference on Evolutionary Computation (ICEC '97).

[25]  H. Abbass.  The self-adaptive Pareto differential evolution algorithm , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[26]  Kaisa Miettinen,et al.  Nonlinear multiobjective optimization , 1998, International series in operations research and management science.

[27]  Qingfu Zhang,et al.  Multiobjective evolutionary algorithms: A survey of the state of the art , 2011, Swarm Evol. Comput..

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

[29]  Qingfu Zhang,et al.  Multiobjective Optimization Problems With Complicated Pareto Sets, MOEA/D and NSGA-II , 2009, IEEE Transactions on Evolutionary Computation.

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

[31]  Hamid R. Tizhoosh,et al.  Opposition-Based Learning: A New Scheme for Machine Intelligence , 2005, International Conference on Computational Intelligence for Modelling, Control and Automation and International Conference on Intelligent Agents, Web Technologies and Internet Commerce (CIMCA-IAWTIC'06).

[32]  Ajith Abraham,et al.  A Modified Differential Evolution Algorithm and Its Application to Engineering Problems , 2009, 2009 International Conference of Soft Computing and Pattern Recognition.

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