Sensitivity analysis in constrained evolutionary optimization

Abstract

Sensitivity analysis deals with the question of how changes in input parameters of a model affect its outputs. For constrained optimization problems, one question may be how variations in budget or capacity constraints influence the optimal solution value. Although well established in the domain of linear programming, it is hardly addressed in evolutionary computation. In this paper, a general approach is proposed which allows to identify how the outcome of an evolutionary algorithm is affected when model parameters, such as constraints, are changed. Using evolutionary bilevel optimization in combination with data mining and visualization techniques, the recently suggested concept of bilevel innovization allows to find trade-offs among constraints and objective 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 multidimensional knapsack problem. The experimental results show that by applying bilevel innovization it is possible to determine how the solution values are influenced by changes of different constraints. Furthermore, rules were obtained that provide information on how parameters can be modified to achieve efficient trade-offs between constraints and objective value.