Runtime Analysis of RLS and the (1+1) EA for the Chance-constrained Knapsack Problem with Correlated Uniform Weights

Abstract

Addressing a complex real-world optimization problem is a challenging task. The chance-constrained knapsack problem with correlated uniform weights plays an important role in the case where dependent stochastic components are considered. We perform a runtime analysis of a randomized search algorithm (RSA) and a basic evolutionary algorithm (EA) for the chance-constrained knapsack problem with correlated uniform weights. We prove bounds for both algorithms for producing a feasible solution. Furthermore, we investigate the behavior of the algorithms and carry out analyses on two settings: uniform profit value and the setting in which every group shares an arbitrary profit profile. We provide insight into the structure of these problems and show how the weight correlations and the different types of profit profiles influence the runtime behavior of both algorithms in the chance-constrained setting.