Precision constrained optimization by exponential ranking

Demonstrative results of a probabilistic constraint handling approach that is exclusively using evolutionary computation are presented. In contrast to other works involving the same probabilistic considerations, in this study local search has been omitted, in order to assess the necessity of this deterministic local search procedure in connection with the evolutionary one. The precision stems from the non-linear probabilistic distance measure that maintains stable evolutionary selection pressure towards the feasible region throughout the search, up to micro level in the range of 10-10 or beyond. The details of the theory are revealed in another paper [1]. In this paper the implementation results are presented, where the non-linear distance measure is used in the ranking of the solutions for effective tournament selection. The test problems used are selected from the existing literature. The evolutionary implementation without local search turns out to be already competitively accurate with sophisticated and accurate state-of-the-art constrained optimization algorithms. This indicates the potential for enhancement of the sophisticated algorithms, as to their precision and accuracy, by the integration of the proposed approach.

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

[2]  Kalyanmoy Deb,et al.  A fast and accurate solution of constrained optimization problems using a hybrid bi-objective and penalty function approach , 2010, IEEE Congress on Evolutionary Computation.

[3]  L. Lasdon,et al.  On a bicriterion formation of the problems of integrated system identification and system optimization , 1971 .

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

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

[6]  Lotfi A. Zadeh,et al.  Optimality and non-scalar-valued performance criteria , 1963 .

[7]  Sana Ben Hamida,et al.  An Adaptive Algorithm for Constrained Optimization Problems , 2000, PPSN.

[8]  Carlos A. Coello Coello,et al.  Use of a self-adaptive penalty approach for engineering optimization problems , 2000 .

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

[10]  Zbigniew Michalewicz,et al.  Evolutionary Algorithms for Constrained Parameter Optimization Problems , 1996, Evolutionary Computation.

[11]  Kalyanmoy Deb,et al.  A combined genetic adaptive search (GeneAS) for engineering design , 1996 .

[12]  Peter J. Fleming,et al.  An Overview of Evolutionary Algorithms in Multiobjective Optimization , 1995, Evolutionary Computation.

[13]  Lothar Thiele,et al.  Multiobjective Optimization Using Evolutionary Algorithms - A Comparative Case Study , 1998, PPSN.

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

[15]  Rituparna Datta,et al.  Further note on the probabilistic constraint handling , 2016, 2016 IEEE Congress on Evolutionary Computation (CEC).

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

[17]  Kalyanmoy Deb,et al.  Simulated Binary Crossover for Continuous Search Space , 1995, Complex Syst..

[18]  T. L. Saaty,et al.  The computational algorithm for the parametric objective function , 1955 .

[19]  Kalyanmoy Deb,et al.  Probabilistic constraint handling in the framework of joint evolutionary-classical optimization with engineering applications , 2012, 2012 IEEE Congress on Evolutionary Computation.

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

[21]  Z. Michalewicz.  Genetic Algorithms , Numerical Optimization , and Constraints , 1995 .

[22]  Carlos A. Coello Coello,et al.  A simple multimembered evolution strategy to solve constrained optimization problems , 2005, IEEE Transactions on Evolutionary Computation.