The multi-objective integer programmingproblem often occurs in multi-criteria decision making situations, where the decision variables are integers. In the present paper, we have discussed an algorithm for finding al...
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The multi-objective integer programmingproblem often occurs in multi-criteria decision making situations, where the decision variables are integers. In the present paper, we have discussed an algorithm for finding all efficient solutions of a multi-objective integer quadratic programmingproblem. The proposed algorithm is based on the aspect that efficient solutions of a multi-objective integer quadratic programmingproblem can be obtained by enumerating ranked solutions of an integer quadratic programmingproblem. For determining ranked solutions of an integer quadratic programmingproblem, we have constructed a related integer linear programmingproblem and from ranked solutions of this integer linear programmingproblem, ranked solutions of the original integer quadratic programmingproblem are generated. Theoretically, we have shown that the developed method generates the set of all efficient solutions in a finite number of steps, and numerically we have elaborated the working of our algorithm and compared our results with existing algorithms. Further, we have analyzed that the developed method is efficient for solving a multi-objective integer quadratic programmingproblem with a large number of constraints, variables and objectives.
The present study proposed a new solution to a tri-objective linear programmingproblem for generation expansion planning by converting the tri-objective linear programmingproblem (i.e. simultaneously maximizing the ...
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The present study proposed a new solution to a tri-objective linear programmingproblem for generation expansion planning by converting the tri-objective linear programmingproblem (i.e. simultaneously maximizing the total power generation, minimizing the total system cost, and minimizing the total CO2 emission) into an equivalent bi-objective linear fractional programmingproblem (i.e. simultaneously maximizing the ratio of the total power generation to the total system cost, and the ratio of the total power generation to the total CO2 emission) to produce a better nondominated solution without any preference information from a decision maker. An approach for solving the bi-objective linear fractional programmingproblem is a newly developed linearization and parameterization approach based on Dinkelbach's theorem and Guzel's approach, which transforms all of linear fractional objective functions into a single objective linear programmingproblem. The proposed bi-objective fractional programming method was applied to a case study of power generation expansion planning problem. Moreover, comparison of the solutions generated by the proposed linearization and parameterization approach and a traditional weighted sum approach has been conducted to demonstrate the effectiveness of the proposed approach in reflecting the trade-offs among the total power generation, the total system cost and the total CO2 emission. (C) 2015 Elsevier Ltd. All rights reserved.
Kostreva and Wiecek [3] introduced a problem called LCP-related weighted problem in connection with a multiple objective programming problem, and suggested that a given linear complementarity problem (LCP) can be solv...
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Kostreva and Wiecek [3] introduced a problem called LCP-related weighted problem in connection with a multiple objective programming problem, and suggested that a given linear complementarity problem (LCP) can be solved by solving the LCP-related weighted problem associated with it. In this note we provide several clarifications of the claims made in [3]. Finally, we feel that solving any LCP by the approach given in [3] may not be as useful as it is claimed.
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