Abstract
This paper presents an efficient outer space branch-and-bound algorithm for globally solving a minimax linear fractional programming problem (MLFP), which has a wide range of applications in data envelopment analysis, engineering optimization, management optimization, and so on. In this algorithm, by introducing auxiliary variables, we first equivalently transform the problem (MLFP) into the problem (EP). By using a new linear relaxation technique, the problem (EP) is reduced to a sequence of linear relaxation problems over the outer space rectangle, which provides the valid lower bound for the optimal value of the problem (EP). Based on the outer space branch-and-bound search and the linear relaxation problem, an outer space branch-and-bound algorithm is constructed for globally solving the problem (MLFP). In addition, the convergence and complexity of the presented algorithm are given. Finally, numerical experimental results demonstrate the feasibility and efficiency of the proposed algorithm.
Highlights
E problem (MLFP) has aroused the interest of many practitioners and researchers
We present an efficient outer space branchand-bound algorithm for globally solving the minimax linear fractional programming problem (MLFP)
We first transform the problem (MLFP) into an outer space equivalent problem (EP) by introducing auxiliary variables. en, in order to obtain the lower bound of the optimal value of the problem (EP), a new linear relaxation technique is proposed to construct the linear relaxation problem (LRP) of the problem (EP) over the outer space rectangle
Summary
We present an efficient outer space branchand-bound algorithm for globally solving the minimax linear fractional programming problem (MLFP). En, based on the outer space partitioning search and the linear relaxation problem, an efficient outer space branch-and-bound algorithm is developed to globally solve the problem (MLFP). Erefore, the proposed algorithm is convergent to the global minimum of the problem (MFLP), and the proof of the theorem is completed. From the numerical results for Examples 1–8, first of all, we can observe that our algorithm can obtain the almost same optimal solution and optimal value as the algorithms presented in the works of Feng et al [8], Jiao and Liu [12], and Wang et al [24].
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