Primal and dual multi-objective linear programming algorithms for linear multiplicative programmes
نویسندگان
چکیده
Multiplicative programming problems (MPPs) are global optimisation problems known to be NP-hard. In this paper, we employ algorithms developed to compute the entire set of nondominated points of multi-objective linear programming (MOLP) problems to solve linear MPPs. First, we improve our own objective space cut and bound algorithm for convex MPPs in the special case of linear MPPs by only solving one linear programme in each iteration instead of two as the previous version indicates. We call this algorithm, which is based on Benson’s outer approximation algorithm for MOLP problems, the primal objective space algorithm. Then, based on the dual variant of Benson’s algorithm, we propose a dual objective space algorithm for solving linear MPPs. The dual algorithm also requires solving only one linear programme in each iteration. We prove the correctness of the dual algorithm and use computational experiments comparing our MOLP based algorithms to a recent global optimisation algorithm for linear MPPs from the literature as well as two general global solvers to demonstrate the superiority of the new algorithms in terms of computation time. Thus we demonstrate that the use of multi-objective optimisation techniques can be beneficial to solve difficult single objective global optimisation problems.
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