Advances and Applications in Statistics
Volume 49, Issue 6, Pages 453 - 483
(December 2016) http://dx.doi.org/10.17654/AS049060453 |
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A COMPUTATIONAL APPROACH BASED ON THE e-CONSTRAINT METHOD IN MULTI-OBJECTIVE OPTIMIZATION PROBLEMS
Behzad Pirouz and Esmaile Khorram
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Abstract: In this paper, we have presented a computational approach based on the e-constraint method for constructing the Pareto front (PF) in multi-objective optimization problems (MOP) by solving a sequence of constrained single-objective problems. A drawback of the original e-constraint method is that epsilon may be selected so that the feasible region becomes empty but our method generates appropriate constraint values during the run. In the proposed method, the PF will be searched by using the controllable steps length. One of the advantages of this method is that, when the decision-maker are looking for a particular Pareto point, by selecting an appropriate step length will be able to reduce the search space to find the desired point. Another advantage of this method is its shorter run time and fewer total function evaluations in comparison with some of the other methods. The effectiveness of the proposed method is demonstrated by comparing it with the Normal Constraint method and modified Normal Boundary Intersection method. To evaluate the quality of these methods, two quality measures (measure of the coverage and measure of spacing) have been used. Moreover, by making some changes, we will obtain some results on the Proper efficiency. |
Keywords and phrases: multi-objective optimization problem, Pareto front, proper efficiency, scalarization techniques, computationally efficient algorithm. |
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