In the present paper a bi-objective integer linear programming problem (BILP) is discussed. The main effort in this work is to effectively implement the ϵ-constraint method to produce a complete set ...

A two-person, noncooperative game in which the players move in sequence can be modeled as a bilevel optimization problem. In this paper, we examine the case where each player tries to maximize the ...

Formulations of mathematical programs often require that some of the decision variables take only integer values. Consider the formulation You can follow the same steps to identify binary variables.

Integer linear programming can help find the answer to a variety of real-world problems. Now researchers have found a much faster way to do it. The traveling salesperson problem is one of the oldest ...

THE AUDIENCE came with calculators in hand, ready to trip up Arthur Benjamin — the human calculator, the walking computer — the mathematician who can figure out math problems faster than the best-made ...

The feasibility pump is a well-established primal heuristic for mixed integer programming (MIP) that alternates between solving a linear programming (LP) relaxation of the original problem and ...