Identifying the redundant, and ranking the critical, constraints in practical optimization problems

This article presents a procedure for identification of the redundant constraints and ranking of the critical constraints by order of their importance, in single- and multi-objective optimization problems. The revelation of the redundant constraints throws light on the physics of the problem which may otherwise not be obvious to the engineers. Furthermore, the ranking of critical constraints allows for an exploration of the potential gain in objective value(s) through a logical elimination of certain constraints. Given a constrained optimization problem, the proposed procedure transforms the constraints into additional objectives (constraint objectives) and obtains a set of non-dominated solutions for the transformed problem by using a multi-objective evolutionary algorithm. Then, operating on the objective vectors of the obtained solutions, the procedure identifies the redundant, and ranks the critical constraints, based on the range of the constraint objectives and their correlations. The utility of the proposed procedure is demonstrated on four practical optimization problems.

[1]  J. Golinski,et al.  An adaptive optimization system applied to machine synthesis , 1973 .

[2]  David L. Waltz,et al.  Understanding Line drawings of Scenes with Shadows , 1975 .

[3]  Joseph J. Talavage,et al.  A Tradeoff Cut Approach to Multiple Objective Optimization , 1980, Oper. Res..

[4]  R. DeVor,et al.  An application of multiple criteria decision making principles for planning machining operations , 1984 .

[5]  Milan Zeleny,et al.  OPTIMIZING GIVEN SYSTEMS vs. DESIGNING OPTIMAL SYSTEMS: THE DE NOVO PROGRAMMING APPROACH , 1990 .

[6]  C. Coello.  TREATING CONSTRAINTS AS OBJECTIVES FOR SINGLE-OBJECTIVE EVOLUTIONARY OPTIMIZATION , 2000 .

[7]  Richard A. Watson,et al.  Reducing Local Optima in Single-Objective Problems by Multi-objectivization , 2001, EMO.

[8]  Jonathan A. Wright,et al.  An Infeasibility Objective for Use in Constrained Pareto Optimization , 2001, EMO.

[9]  R. Rackwitz.  Reliability analysis—a review and some perspectives , 2001 .

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

[11]  Carlos Artemio Coello-Coello,et al.  Theoretical and numerical constraint-handling techniques used with evolutionary algorithms: a survey of the state of the art , 2002 .

[12]  J. van Leeuwen,et al.  Evolutionary Multi-Criterion Optimization , 2003, Lecture Notes in Computer Science.

[13]  Gary B. Lamont,et al.  Applications Of Multi-Objective Evolutionary Algorithms , 2004 .

[14]  Miguel A. Salido,et al.  Constrainedness and Redundancy by Constraint Ordering , 2004, IBERAMIA.

[15]  Kazutoshi Sakakibara,et al.  Multi-objective approaches in a single-objective optimization environment , 2005, 2005 IEEE Congress on Evolutionary Computation.

[16]  Kalyanmoy Deb,et al.  Non-linear Dimensionality Reduction Procedures for Certain Large-Dimensional Multi-objective Optimization Problems: Employing Correntropy and a Novel Maximum Variance Unfolding , 2007, EMO.

[17]  Kalyanmoy Deb,et al.  Trading on infeasibility by exploiting constraint’s criticality through multi-objectivization: A system design perspective , 2007, 2007 IEEE Congress on Evolutionary Computation.

[18]  Carlos A. Coello Coello,et al.  Objective reduction using a feature selection technique , 2008, GECCO '08.

[19]  Kalyanmoy Deb,et al.  On Handling a Large Number of Objectives A Posteriori and During Optimization , 2008, Multiobjective Problem Solving from Nature.

[20]  Kalyanmoy Deb,et al.  Dimensionality reduction of objectives and constraints in multi-objective optimization problems: A system design perspective , 2008, 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence).

[21]  Kalyanmoy Deb,et al.  Reliability-Based Optimization Using Evolutionary Algorithms , 2009, IEEE Transactions on Evolutionary Computation.

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

[23]  Bogusław Pytlak,et al.  Multicriteria optimization of hard turning operation of the hardened 18HGT steel , 2010 .

[24]  Tapabrata Ray,et al.  A Pareto Corner Search Evolutionary Algorithm and Dimensionality Reduction in Many-Objective Optimization Problems , 2011, IEEE Transactions on Evolutionary Computation.

[25]  Qingfu Zhang,et al.  Objective Reduction in Many-Objective Optimization: Linear and Nonlinear Algorithms , 2013, IEEE Transactions on Evolutionary Computation.