Sensitivity Analysis on Constraints of Combinatorial Optimization Problems

• Published in: Learning and Intelligent Optimization Vol. 12931; pp. 394 - 408
• Main Authors: Schulte, Julian, Nissen, Volker
• Format: Book Chapter
• Language: English
• Published: Switzerland Springer International Publishing AG 2021; Springer International Publishing
• Series: Lecture Notes in Computer Science
• Subjects: Combinatorial optimization; Data mining; Evolutionary bilevel optimization; Generalized assignment; Sensitivity analysis
• ISBN: 3030921204; 9783030921200
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-030-92121-7_30

Combinatorial optimization problems in practice are subject to a variety of constraints, such as resource limitations or organizational regulations. Since these model parameters can have a major impact, for example, on the performance of a scheduling system, it is crucial to know how changes in the constraints affect the optimal solution value. The question of how changes in input parameters of an optimization model, such as right-hand side values of constraints, affect the output of the model is the main concern of sensitivity analysis. Although well established in the domain of linear programming, the literature on combinatorial optimization lacks universal sensitivity analysis approaches which are applicable to practical problems. In this paper, a general approach is proposed which allows to identify how the optimal solution of a combinatorial optimization problem is affected when model parameters, such as constraints, are changed. Using evolutionary bilevel optimization in combination with data mining and visualization techniques, the suggested concept of bilevel innovization allows to find trade-offs among constraints and objective function value. Additionally, it enables decision-makers to gain insights into the overall model behavior under changing framework conditions. The concept of bilevel innovization as a tool for sensitivity analysis is illustrated, without loss of generality, by the example of the generalized assignment problem.