A New Linearizing Method for Sum of Linear Ratios Problem with Coefficients

[摘要] A new linearizing method is presented for globally solving sumof linear ratios problem with coefficients. By using the linearizing method, linear relaxationprogramming (LRP) of the sum of linear ratios problem with coefficients is established,which can provide the reliable lower bound of the optimal value of the initial problem. Thus,a branch and bound algorithm for solving the sum of linear ratios problem with coefficientsis put forward. By successively partitioning the linear relaxation of the feasible region andsolving a series of the LRP, the proposed algorithm is convergent to the global optimalsolution of the initial problem. Compared with the known methods, numerical experimentalresults show that the proposed method has the higher computational efficiency in finding theglobal optimum of the sum of linear ratios problem with coefficients.

[学科分类] 应用数学