Evolutionary Bi-objective Optimization for the Dynamic Chance-Constrained Knapsack Problem Based on Tail Bound Objectives
This work addresses stochastic and dynamic combinatorial optimization problems, offering an incremental improvement for decision-making in uncertain environments.
The paper tackles the dynamic chance-constrained knapsack problem with stochastic weights and dynamic capacity by introducing an additional objective to estimate minimal capacity bounds, and applies evolutionary algorithms to show that bi-objective optimization can handle such dynamic constraints effectively.
Real-world combinatorial optimization problems are often stochastic and dynamic. Therefore, it is essential to make optimal and reliable decisions with a holistic approach. In this paper, we consider the dynamic chance-constrained knapsack problem where the weight of each item is stochastic, the capacity constraint changes dynamically over time, and the objective is to maximize the total profit subject to the probability that total weight exceeds the capacity. We make use of prominent tail inequalities such as Chebyshev's inequality, and Chernoff bound to approximate the probabilistic constraint. Our key contribution is to introduce an additional objective which estimates the minimal capacity bound for a given stochastic solution that still meets the chance constraint. This objective helps to cater for dynamic changes to the stochastic problem. We apply single- and multi-objective evolutionary algorithms to the problem and show how bi-objective optimization can help to deal with dynamic chance-constrained problems.