evolutionary algorithm for constrained optimization - Semantic Scholar
Multi-objective and MGG Evolutionary Algorithm for Constrained Optimization .
Yuren Zhou College of Computer Science and Engineering South China University of Technology Guangzhou 5 10640,.P.R.China zhouviiren!~~liotninil.com
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:Yuanxiang Li State key Lab of Software Engineering Wuhao University , , . ' . , Wuhan 430072, P:R.China: . . I
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Lishan Kang Jun H e . . School of Computer Science The University of Birmingham Edgbaston. Birmioham 8 1 5 2TT. UK
State key Lab of Software Engineering Wuhan University Wuhan 430072, P.R.China
Abstract- This paper presents a new approach to handle constrained optimization using evolutionary algorithms. The new technique converts constrained optimization to a two-objective optimization: one is the original objective function, the other is the degree function violating the constraints. By using Paretodominance in the multi-objective optimization, individual's Pareto strength is defined. Based on Pareto strength and Minimal Generation Gap (MGG) model, a new realrcoded genetic algorithm is designed. The new approach is compared with some other evolutionary Optimization techniques on several benchmark functions. The results show that the new approach outperforms those existing techniques in feasibility, effectiveness and generality. Especially for some complicated optimization problems with inequality and equality constraints, the proposed method provides better numerical accuracy.
nonlinear programming. ' Similar to n&ine& programming with certainty, the main problem faced by evolutionary algorithms to solve constrained optimization is how lo treat the constraints. This paper presents a new approach to convert the constrained optimization (minimization) to minimization of two objective functions, one is the original objective function. the other is the degree function violating constraints. By using Pareto dominance . in the multi-objective optimization, individual's Pareto strength 'is defined. A new real-coded genetic algorithm based on Pareto strength and Minimal Generation Gap (MGG) model is devised to solve the constrained optimization. Experimental studies testified the feasibility and effectiveness of the new approach. For the testing functions with both equality and inequality constraints, the experiments indicate that the new. approach outperforms some of the existing algorithms in accuracy of solution.
1 Introduction
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2 Constrained optimization The non-linear programming (NLP) problem is generally described as solving the objective function Minimize f( 2'). X =(x,. x2,.. . j x,) E R" where 4 t F G S. The objective function f is .defined on the search space S R". and F c S defines the feasible region. Generally, the search space S is defined a s , a ndiinensional rectangle in R" (domains of variables defined by their lower and upper bounds): I ( i ) < q < u ( i ) , i = l , ...,n. where I(i) and u(i) are constants. The feasible region F satisfies m additional constraints of both equality and inequality: g,(?)
Yuren Zhou College of Computer Science and Engineering South China University of Technology Guangzhou 5 10640,.P.R.China zhouviiren!~~liotninil.com
.
:Yuanxiang Li State key Lab of Software Engineering Wuhao University , , . ' . , Wuhan 430072, P:R.China: . . I
'
Lishan Kang Jun H e . . School of Computer Science The University of Birmingham Edgbaston. Birmioham 8 1 5 2TT. UK
State key Lab of Software Engineering Wuhan University Wuhan 430072, P.R.China
Abstract- This paper presents a new approach to handle constrained optimization using evolutionary algorithms. The new technique converts constrained optimization to a two-objective optimization: one is the original objective function, the other is the degree function violating the constraints. By using Paretodominance in the multi-objective optimization, individual's Pareto strength is defined. Based on Pareto strength and Minimal Generation Gap (MGG) model, a new realrcoded genetic algorithm is designed. The new approach is compared with some other evolutionary Optimization techniques on several benchmark functions. The results show that the new approach outperforms those existing techniques in feasibility, effectiveness and generality. Especially for some complicated optimization problems with inequality and equality constraints, the proposed method provides better numerical accuracy.
nonlinear programming. ' Similar to n&ine& programming with certainty, the main problem faced by evolutionary algorithms to solve constrained optimization is how lo treat the constraints. This paper presents a new approach to convert the constrained optimization (minimization) to minimization of two objective functions, one is the original objective function. the other is the degree function violating constraints. By using Pareto dominance . in the multi-objective optimization, individual's Pareto strength 'is defined. A new real-coded genetic algorithm based on Pareto strength and Minimal Generation Gap (MGG) model is devised to solve the constrained optimization. Experimental studies testified the feasibility and effectiveness of the new approach. For the testing functions with both equality and inequality constraints, the experiments indicate that the new. approach outperforms some of the existing algorithms in accuracy of solution.
1 Introduction
.
.
2 Constrained optimization The non-linear programming (NLP) problem is generally described as solving the objective function Minimize f( 2'). X =(x,. x2,.. . j x,) E R" where 4 t F G S. The objective function f is .defined on the search space S R". and F c S defines the feasible region. Generally, the search space S is defined a s , a ndiinensional rectangle in R" (domains of variables defined by their lower and upper bounds): I ( i ) < q < u ( i ) , i = l , ...,n. where I(i) and u(i) are constants. The feasible region F satisfies m additional constraints of both equality and inequality: g,(?)
