A probabilistic solution discovery algorithm for solving 0-1 knapsack problem

Abstract

In this paper, a probabilistic solution discovery algorithm is developed to solve the NP-hard 0-1 knapsack problem. The proposed method consists of three steps: strategy development, strategy analysis, and solution discovery. In the first step, Monte Carlo simulation is used to generate the strategies based on a vector defining the probability that each item is included in the knapsack. In the second step, we analyse the capacity imposed by each strategy previously generated and penalise the objective value for those strategies exceeding the capacity of the knapsack. At the last step, a subset of ordered strategies is used to update the vector that defines the probability of choosing each item. Two numerical examples are used to demonstrate the efficiency and the performance of the proposed method.

Graphical Abstract

Graphical representation of the probabilistic solution discovery algorithm.

Keywords:

• Probabilistic solution discovery algorithm
• 0-1 knapsack problem
• combinational optimization
• evolutionary computation
• Monte Carlo simulation

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The author is grateful to the financial support from the Scientific and Technological Research Program of Chongqing Municipal Education Commission [grant number KJ1603806].