Uncertain bilevel knapsack problem based on an improved binary wolf pack algorithm

Abstract

To address indeterminism in the bilevel knapsack problem, an uncertain bilevel knapsack problem (UBKP) model is proposed. Then, an uncertain solution for UBKP is proposed by defining the $${\mathcal{P}_E}$$ Nash equilibrium and $${\mathcal{P}_E}$$ Stackelberg-Nash equilibrium. To improve the computational efficiency of the uncertain solution, an evolutionary algorithm, the improved binary wolf pack algorithm, is constructed with one rule (wolf leader regulation), two operators (invert operator and move operator), and three intelligent behaviors (scouting behavior, intelligent hunting behavior, and upgrading). The UBKP model and the $${\mathcal{P}_E}$$ uncertain solution are applied to an armament transportation problem as a case study.