An unbiased bi-objective Optimization Model and Algorithm for constrained Optimization

Transforming a constrained optimization problem (COP) into a bi-objective optimization problem (BOP) is an efficient way to solve the COP. However, how to obtain a good balance between the objective function and the constraint violation function is not easy in BOP. To handle this issue, a novel unbiased bi-objective optimization model is proposed, in which both objective functions are equally treated. Furthermore, the novel model is shown to have the unique Pareto optimal vector under proper condition, and the Pareto optimal vector is exactly corresponding to the optimal solution of COP. Moreover, the relationship between the existing biased bi-objective model and the proposed unbiased one is analyzed in detail. For the unbiased model, a generic multi-objective optimization evolutionary algorithm, i.e. a differential evolution (DE), can be used to solve it, and Pareto ranking is employed as the unique selection criterion. The experiments are conducted on 24 well-known benchmark test instances and the results illustrate that the proposed model is not only effective but also efficient.

[1]  H. Kita,et al.  Failure of Pareto-based MOEAs: does non-dominated really mean near to optimal? , 2001, Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No.01TH8546).

[2]  Ruhul A. Sarker,et al.  Integrated strategies differential evolution algorithm with a local search for constrained optimization , 2011, 2011 IEEE Congress of Evolutionary Computation (CEC).

[3]  Min Gan,et al.  An adaptive decision maker for constrained evolutionary optimization , 2010, Appl. Math. Comput..

[4]  Zbigniew Michalewicz,et al.  Handbook of Evolutionary Computation , 1997 .

[5]  Tetsuyuki Takahama,et al.  Constrained Optimization by the epsilon Constrained Hybrid Algorithm of Particle Swarm Optimization and Genetic Algorithm , 2005, Australian Conference on Artificial Intelligence.

[6]  Liang Gao,et al.  An improved electromagnetism-like mechanism algorithm for constrained optimization , 2013, Expert Syst. Appl..

[7]  Xin Yao,et al.  Stochastic ranking for constrained evolutionary optimization , 2000, IEEE Trans. Evol. Comput..

[8]  K. Deb,et al.  A bi-objective constrained optimization algorithm using a hybrid evolutionary and penalty function approach , 2013 .

[9]  Mehmet Fatih Tasgetiren,et al.  An ensemble of differential evolution algorithms for constrained function optimization , 2010, IEEE Congress on Evolutionary Computation.

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

[11]  Ali Wagdy Mohamed,et al.  Constrained optimization based on modified differential evolution algorithm , 2012, Inf. Sci..

[12]  Gary G. Yen,et al.  A generic framework for constrained optimization using genetic algorithms , 2005, IEEE Transactions on Evolutionary Computation.

[13]  Efrn Mezura-Montes,et al.  Constraint-Handling in Evolutionary Optimization , 2009 .

[14]  Yuren Zhou,et al.  An Adaptive Tradeoff Model for Constrained Evolutionary Optimization , 2008, IEEE Transactions on Evolutionary Computation.

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

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

[17]  Efrén Mezura-Montes,et al.  Self-adaptive and Deterministic Parameter Control in Differential Evolution for Constrained Optimization , 2009 .

[18]  K. Deb.  An Efficient Constraint Handling Method for Genetic Algorithms , 2000 .

[19]  Yong Wang,et al.  Combining Multiobjective Optimization With Differential Evolution to Solve Constrained Optimization Problems , 2012, IEEE Transactions on Evolutionary Computation.

[20]  Kalyanmoy Deb,et al.  A Hybrid Bi-Objective Evolutionary-Penalty Approach for Computationally Fast and Accurate Constrained Optimization ∗ , 2010 .

[21]  Jing J. Liang,et al.  Problem Definitions and Evaluation Criteria for the CEC 2005 Special Session on Real-Parameter Optimization , 2005 .

[22]  N. Hansen,et al.  Markov Chain Analysis of Cumulative Step-Size Adaptation on a Linear Constrained Problem , 2015, Evolutionary Computation.

[23]  Xin Yao,et al.  Search biases in constrained evolutionary optimization , 2005, IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews).

[24]  Jing J. Liang,et al.  Problem Deflnitions and Evaluation Criteria for the CEC 2006 Special Session on Constrained Real-Parameter Optimization , 2006 .

[25]  Carlos A. Coello Coello,et al.  Multiobjective-based concepts to handle constraints in evolutionary algorithms , 2003, Proceedings of the Fourth Mexican International Conference on Computer Science, 2003. ENC 2003..

[26]  Carlos A. Coello Coello,et al.  Constraint-handling in nature-inspired numerical optimization: Past, present and future , 2011, Swarm Evol. Comput..