Towards Constant Calculation in Disjunctive Inequalities Using Wound Treatment Optimization

When using the mixed-integer programming to model situations where the limit of the variables follows a box constraint, we find nonlinear problems. To solve this, linearization techniques of these disjunctive inequality constraints are typically used, including constants associated to the variable bounds called M-constants or big-M. Calculation of these constants is an open problem since their values affect the reliability of the optimal solution and convergence of the optimization algorithm. To solve this problem, this work proposes a new population-based metaheuristic optimization method, namely wound treatment optimization (WTO) for calculating the M-constant in a typical domain known as the fixed-charge transportation problem. WTO is inspired on the social wound treatment present in ants after raids. This method allows population diversity that allows to find near-optimal solutions. Experiments of the WTO method on the fixed-charge transportation problem validated its performance and efficiency to find tighten solutions of the M-constant that minimizes the objective function of the problem. © Springer Nature Switzerland AG 2019.