A multi-objective scheduling method for operational coordination time using improved triangular fuzzy number representation

In modern warfare, the comprehensiveness of combat domain and the complexity of tasks pose great challenges to operational coordination.To address this challenge, we use the improved triangular fuzzy number to express the combat mission time, first present a new multi-objective operational cooperative time scheduling model that takes the fluctuation of combat coordinative time and the time flexibility between each task into account. The resulting model is essentially a large-scale multi-objective combinatorial optimization problem, intractably complicated to solve optimally. We next propose multi-objective improved Bat algorithm based on angle decomposition (MOIBA/AD) to quickly identify high-quality solutions to the model. Our proposed algorithm improves the decomposition strategy by replacing the planar space with the angle space, which helps greatly reduce the difficulty of processing evolutionary individuals and hence the time complexity of the multi-objective evolutionary algorithm based on decomposition (MOEA/D). Moreover, the population replacement strategy is enhanced utilizing the improved bat algorithm, which helps evolutionary individuals avoid getting trapped in local optima. Computational experiments on multi-objective operational cooperative time scheduling (MOOCTS) problems of different scales demonstrate the superiority of our proposed method over four state-of-the-art multi-objective evolutionary algorithms (MOEAs), including multi-objective bat Algorithm (MOBA), MOEA/D, non-dominated sorting genetic algorithm version II (NSGA-II) and multi-objective particle swarm optimization algorithm (MOPSO). Our proposed method performs better in terms of four performance criteria, producing solutions of higher quality while keeping a better distribution of the Pareto solution set.