Evolutionary algorithms for the chance-constrained knapsack problem

Abstract

The chance-constrained knapsack problem is a variant of the classical knapsack problem where each item has a weight distribution instead of a deterministic weight. The objective is to maximize the total profit of the selected items under the condition that the weight of the selected items only exceeds the given weight bound with a small probability of α. In this paper, consider problem-specific single-objective and multi-objective approaches for the problem. We examine the use of heavy-tail mutations and introduce a problem-specific crossover operator to deal with the chance-constrained knapsack problem. Empirical results for single-objective evolutionary algorithms show the effectiveness of our operators compared to the use of classical operators. Moreover, we introduce a new effective multi-objective model for the chance-constrained knapsack problem. We use this model in combination with the problem-specific crossover operator in multiobjective evolutionary algorithms to solve the problem. Our experimental results show that this leads to significant performance improvements when using the approach in evolutionary multi-objective algorithms such as GSEMO and NSGA-II.

Optimization of Chance-Constrained Submodular Functions

“…Roostapour et al (2019) showed that the adaptation of greedy approaches to monotone submodular problems with dynamic constraints might lead arbitrarily bad approximation behavior, whereas a Pareto optimization approach can effectively deal with dynamic changes. Evolutionary algorithms for the chanceconstrained knapsack problem, which constitutes a subclass of the chance-constrained submodular problems examined in this paper, have been experimentally investigated by Xie et al (2019).…”

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

“…end if 7: end while In this paper, we assume the weights of items are correlated uniformly, and its hard to calculate the exact probability of violating the chance constraint. Similar to recent work on the uncorrelated problem [27], we use the one-sided Chebyshev's inequality (cf. Theorem 2.2) to construct a usable surrogate of the chance constraint (2).…”

“…The goal is to maximize the total profit under the constraint that the knapsack capacity bound is violated with a probability of at most a pre-defined tolerance α. Recent papers [27,28] study a chance-constrained knapsack problem where the weight of the items are stochastic variables and independent to each other. They introduce the use of suitable probabilistic tools such as Chebyshev's inequality and Chernoff bounds to estimate the probability of violating the constraint of a given solution, providing surrogate functions for the chance constraint, and present single-and multi-objective evolutionary algorithms for the problem.…”

Heuristic Strategies for Solving Complex Interacting Stockpile Blending Problem with Chance Constraints

“…To address this challenge, this paper proposes two repair operators to tackles the complex constraints. Follow the paper [25], we present the surrogate functions of the chance constraints by using Chebyshev's inequality. Furthermore, a well-known evolutionary algorithm, the Differential Evolution (DE) algorithm is introduced to solve the stockpile blending problem.…”