Skip to main content Skip to main navigation


Evolutionary Algorithm-based Optimal Parametrization of Multi-objective Mixed-integer Linear Programming Scheduling Models

Vassilios Yfantis; Alexander Babskiy; Bastian Dörig; Thorsten Winterer; Achim Wagner; Martin Ruskowski
In: IFAC-PapersOnLine, Vol. 56, No. 2, Pages 5382-5387, Elsevier, 2023.


Modern manufacturing systems strive to optimize many different key performance indicators. Additionally, mathematical programming-based scheduling models enable the explicit considerations of constraints. However, due to the ever-increasing demand for customized products it is not guaranteed that all constraints can be met at the same time. An approach to circumvent this problem of infeasibility is to replace the constraints by soft-constraints, i.e., to penalize their violation in the objective function. The presence of multiple competing objectives and soft-constraints gives rise to multi-objective optimization problems, where a decision maker has to weigh and balance the different objectives and soft-constraints according to his/her preferences and priorities. Ideally the values of all objectives and soft-constraints should lie within the same order of magnitude, making it easy to weigh them against each other. However, for heterogeneous objectives and soft-constraints with different scales and units this might be challenging. This paper presents an evolutionary algorithm for the optimal parametrization of multi-objective mixed-integer linear programming-based scheduling models. The goal of the evolutionary algorithm is to compute weights for the different terms of the objective which lead to a balanced influence on the overall objective at the optimum. Furthermore, the algorithm is extended by introducing an a priori weighing of the objectives in the fitness function of the evolutionary algorithm. The method is demonstrated on a scheduling problem in which a given set of orders has to be allocated to machines within a manufacturing environment.