Two-Population Coevolutionary Algorithm with Dynamic Learning Strategy for Many-Objective Optimization

Due to the complexity of many-objective optimization problems, the existing many-objective optimization algorithms cannot solve all the problems well, especially those with complex Pareto front. In order to solve the shortcomings of existing algorithms, this paper proposes a coevolutionary algorithm based on dynamic learning strategy. Evolution is realized mainly through the use of Pareto criterion and non-Pareto criterion, respectively, for two populations, and information exchange between two populations is used to better explore the whole objective space. The dynamic learning strategy acts on the non-Pareto evolutionary to improve the convergence and diversity. Besides, a dynamic convergence factor is proposed, which can be changed according to the evolutionary state of the two populations. Through these effective heuristic strategies, the proposed algorithm can maintain the convergence and diversity of the final solution set. The proposed algorithm is compared with five state-of-the-art algorithms and two weight-sum based algorithms on a many-objective test suite, and the results are measured by inverted generational distance and hypervolume performance indicators. The experimental results show that, compared with the other five state-of-the-art algorithms, the proposed algorithm achieved the optimal performance in 47 of the 90 cases evaluated by the two indicators. When the proposed algorithm is compared with the weight-sum based algorithms, 83 out of 90 examples achieve the optimal performance.

A coevolutionary algorithm based on the auxiliary population for constrained large-scale multi-objective supply chain network

<abstract> <p>Supply chain network is important for the enterprise to improve the operation and management, but has become more complicated to optimize in reality. With the consideration of multiple objectives and constraints, this paper proposes a constrained large-scale multi-objective supply chain network (CLMSCN) optimization model. This model is to minimize the total operation cost (including the costs of production, transportation, and inventory) and to maximize the customer satisfaction under the capacity constraints. Besides, a coevolutionary algorithm based on the auxiliary population (CAAP) is proposed, which uses two populations to solve the CLMSCN problem. One population is to solve the original complex problem, and the other population is to solve the problem without any constraints. If the infeasible solutions are generated in the first population, a linear repair operator will be used to improve the feasibility of these solutions. To validate the effectivity of the CAAP algorithm, the experiment is conducted on the randomly generated instances with three different problem scales. The results show that the CAAP algorithm can outperform other compared algorithms, especially on the large-scale instances.</p> </abstract>