An efficient population-based simulated annealing algorithm for 0-1 knapsack problem

0-1 knapsack problem (KP01) is one of the classic variants of knapsack problems in which the aim is to select the items with the total profit to be in the knapsack. In contrast, the constraint of the maximum capacity of the knapsack is satisfied. KP01 has many applications in real-world problems such as resource distribution, portfolio optimization, etc. The purpose of this work is to gather the latest SA-based solvers for KP01 together and compare their performance with the state-of-the-art meta-heuristics in the literature to find the most efficient one(s). This paper not only studies the introduced and non-introduced single-solution SA-based algorithms for KP01 but also proposes a new population-based SA (PSA) for KP01 and compares it with the existing methods. Computational results show that the proposed PSA is the most efficient optimization algorithm for KP01 among all SA-based solvers. Also, PSA's exploration and exploitation are stronger than the other SA-based algorithms since it generates several initial solutions instead of one. Moreover, it finds the neighbor solutions based on the greedy repair and improvement mechanism and uses both mutation and crossover operators to explore and exploit the solution space. Suffice to say that the next version of SA algorithms for KP01 can be enhanced by designing a population-based version of them and choosing the greedy-based approaches for the initial solution phase and local search policy.

Automated summary

The 0-1 knapsack problem is a classic problem with various applications, and this paper compares different SA-based algorithms to find the most efficient one. The proposed population-based SA algorithm (PSA) outperforms other SA-based solvers in terms of exploration and exploitation, making it a promising approach for future optimization algorithms in KP01.