A fast and accurate solution of constrained optimization problems using a hybrid bi-objective and penalty function approach

Deb, Kalyanmoy; Datta, Rituparna

doi:10.1109/cec.2010.5586543

Cited by 49 publications

(38 citation statements)

References 11 publications

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“…This penalization is accomplished by adding a value to the objective function value in proportion to the amount of constraint violation, where the proportionality factor is known as the penalty parameter. A strategy that did not require a penalty parameter in evolutionary constrained optimization was proposed by Deb in 2000 [26], which is superseded by another research with the penalty parameter [27]. In this approach during the tournament selection process an infeasible solution is always treated as inferior compared to a feasible one, or as inferior to a solution that violates the constraints to a lesser extent.…”

Section: Introductionmentioning

confidence: 99%

Further note on the probabilistic constraint handling

Ciftcioglu

Bittermann

Datta

2016

2016 IEEE Congress on Evolutionary Computation (CEC)

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Abstract-A robust probabilistic constraint handling approach in the framework of joint evolutionary-classical optimization has been presented earlier. In this work, the theoretical foundations of the method are presented in detail. The method is known as bi-objective method, where the conventional penalty function approach is implemented. The present work highlights the dynamic variation of the commensurate penalty parameter for each objective treated as constraint. It is shown that the constraint parameters collectively define the right slope of the tangent as to the optimal front during the search. The robust and sustained convergence throughout the search up to micro level in the range of 10 -10 or beyond is explained. The work here is presented as a further note in connection with the previous publication, where the subtle theoretical considerations and their details had been omitted for the sake of detailed results of the experiments demonstrating the effective working of the approach. In contrast to the implementation-centered reporting of the previous work, this work can be considered as a description of the detailed probabilistic basis underlying the previous work. Therefore, this study is of great importance to let the researchers conveniently gain the insight into the work and its implications reported earlier.

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Section: Introductionmentioning

confidence: 99%

Further note on the probabilistic constraint handling

Ciftcioglu

Bittermann

Datta

2016

2016 IEEE Congress on Evolutionary Computation (CEC)

Self Cite

View full text Add to dashboard Cite

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“…This penalization is accomplished by adding a value to the objective function value in proportion to the amount of constraint violation, where the proportionality factor is known as the penalty parameter. A strategy that did not require a penalty parameter in evolutionary constrained optimization was proposed by Deb in 2000 [7], which is superseded by another research with the penalty parameter [8]. In this approach during the tournament selection process an infeasible solution is always treated as inferior compared to a feasible one, or as inferior to a solution that violates the constraints to a lesser extent.…”

Section: Introductionmentioning

confidence: 99%

“…Within the methodological framework of the penalty parameter approach, local search in combination with evolutionary computation (EC) has shown to be effective for solving constrained optimization problems [8]. In this combination the local search is an alternative for selection pressure in precision demanding problems.…”

Section: Introductionmentioning

confidence: 99%

Precision constrained optimization by exponential ranking

Bittermann

Ciftcioglu

2016

2016 IEEE Congress on Evolutionary Computation (CEC)

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Abstract-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.

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“…The above strategy results in a set of Pareto-optimal solutions, being supposedly maximally wide in terms of every objective, each pair among which o ers a trade-o between the con icting criteria [11][12][13][14][15][16][17][18][19][20][21]. Accomplishing maximally-spread multiple solutions was not guaranteed by traditional approaches, because of the demand for more than once implementing the same algorithm with di erent settings [22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

“…Many preference-based MOO algorithms are based on combining all the criteria at hand through scalarizing them and coming up with a single criterion, followed by performing Single-Objective Optimization (SOO) as a special case of MOO, since it has basically been deemed both mathematically and computationally more manageable than MOO [12][13][14]. In other words, for the sake of avoiding the aforementioned de ciencies and misinterpretations, the assumption has been that the degree to which the signi cance of each objective function should a ect the way the optimization procedure is steered could be represented by a weight, i.e.…”

Section: Introductionmentioning

confidence: 99%

PPCOF: A Robust Proportion-Preserving Composite Objective Function for Scale-Invariant Multi-Objective Optimization

et al. 2017

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Abstract. This paper aims to introduce a proportion-preserving composite objective function for multi-objective optimization, namely, PPCOF, and validate its e ciency through demonstrating its applicability to optimization of the kinetostatic performance of planar parallel mechanisms. It exempts the user from both specifying preference factors and conducting decision-making. It consists of two terms. The rst one adds the normalized objective functions up, where the extrema result from single-objective optimization. To make the composite objective function steer the variations of the objective functions while preserving rational proportions between them, as the main contribution of the paper, it is sought that the normalized objective functions take closely similar values, to which end they are juxtaposed inside a vector, which is then scaled such that its Euclidean norm-2 is equal to that of the vector of all ones with the same dimensions. Then, the second term is constructed as the addition of penalty factors standing for the absolute value of the di erence between each element of the foregoing vector from 1. From the obtained results, with considerably smaller computational cost, the PPCOF obtains an optimal solution that is not dominated by any point from a set of Pareto-optimal solutions o ered by NSGA-II.

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A fast and accurate solution of constrained optimization problems using a hybrid bi-objective and penalty function approach

Cited by 49 publications

References 11 publications

Further note on the probabilistic constraint handling

Further note on the probabilistic constraint handling

Precision constrained optimization by exponential ranking

PPCOF: A Robust Proportion-Preserving Composite Objective Function for Scale-Invariant Multi-Objective Optimization

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