Optimizing a linear function over an integer efficient set

The augmented weighted Tchebychev norm for optimizing a linear function over an integer efficient set of a multicriteria linear program

“…For the first time Nguyen (1992) made an attempt to optimize on the integer efficient set, where only an upper bound value for the main objective is proposed. The exact algorithm was developed by Abbas and Chaabane () based on a simple selection technique that improves the main objective value at each iteration. Two types of cuts are used and performed successively until the optimal value is obtained and the current truncated region had no integer feasible solution (see also Chaabane, ).…”

A parallel approach to bi-objective integer programming

“…If we have the complete set S of nondominated solutions for P (1,2) with x 2 k, the complete set S of nondominated solutions for P (2,1) with x 1 l, and we also have the nondominated solution (l, k), then the union S S {(l, k)} is the complete set of nondominated solutions to P.…”

“…The clboip problems P (1,2) and P (2,1) can be solved independently by Algorithm 1, and (l, k) will be found as a solution to these problems. Given Algorithm 3: Our Meeting algorithm, which is a parallel version of the algorithm from [7].…”

“…Recall that in Algorithm 1 we used the specific ordering P (1,2) . We could also solve P (2,1) and obtain the same result.…”

“…If such a relationship, often called a 'utility function', is known then one can optimise this utility function [1,6]. However, if the utility function is unknown, we must instead identify the complete set of nondominated solutions for the Bi-Objective Integer Programming (boip) problem.…”