An improved discrete multi-objective artificial protozoa optimizer for solving multi-objective knapsack problems

The multi-objective knapsack problem (MOKP) is a challenging combinatorial optimization problem that traditional methods often fail to solve effectively. Consequently, researchers are increasingly adopting metaheuristic algorithms to address such problems within a reasonable time. This paper introduces an improved discrete multi-objective artificial protozoa optimizer (IDMOAPO) to tackle MOKP. The continuous solution space of the leaded sine cosine multi-objective artificial protozoa optimizer is discretized using two approaches, among which the modulo operation is identified as the most effective and adopted to develop a discrete multi-objective artificial protozoa optimizer (DMOAPO). An enhanced strategy is further incorporated into DMOAPO to improve solution quality, resulting in the development of the proposed IDMOAPO. The proposed IDMOAPO is evaluated across 16 MOKPs of four types and compared against seven algorithms. The performance metrics used for the evaluation are the number of Pareto solutions, generational distance, Spread, and inverted generational distance. Simulation results show that IDMOAPO significantly outperforms other comparison algorithms in most cases. These results highlight the effectiveness of IDMOAPO in obtaining superior Pareto fronts, confirming its suitability for solving MOKP.