Abstract
Many evolutionary algorithms have been proposed for multi-/many-objective optimization problems; however, the tradeoff of convergence and diversity is still the challenge for optimization algorithms. In this paper, we propose a modified particle swarm optimization based on decomposition framework with different ideal points on each reference vector, called MPSO/DD, for many-objective optimization problems. In the MPSO/DD algorithm, the decomposition strategy is used to ensure the diversity of the population, and the ideal point on each reference vector can draw the population converge faster to the optimal front. The position of each individual will be updated by learning the demonstrators in its neighborhood that have less distance to the ideal point along the reference vector. Eight state-of-the-art evolutionary multi-/many-objective optimization algorithms are adopted to compare the performance with MPSO/DD for solving many-objective optimization problems. The experimental results on seven DTLZ test problems with 3, 5, 8, 10, 15 and 20 objectives, respectively, show the efficiency of our proposed method on solving problems with high-dimensional objective space.
Highlights
Multi-objective optimization problems (MOP) are widely involved in the real-world applications, for example, industrial scheduling [21], software engineering [19], and control system design [10]
The obtained results are compared with those of NSGA-III, KnEA, RVEA, MOEA/DD, SPEAR, grid-based many-objective evolutionary algorithm (GrEA) and BiGE [16] that are state-of-the-art algorithms for many-objective problems, and compared with NMPSO [17], which is proposed for many-objective optimization based on PSO
The experimental results of these seven algorithms are run on PlatEMO proposed by Tian [28]
Summary
Multi-objective optimization problems (MOP) are widely involved in the real-world applications, for example, industrial scheduling [21], software engineering [19], and control system design [10]. N }; 4: Initialize the position and velocity of each individual in the populationP, and calculate the objective values for each individual in P; 5: Save all non-dominated solutions in P to the archive Ar c; 6: /* Main loop*/; 7: while t ≤ tmax do 8: Update the ideal point for each reference vector; (Refer to Algorithm 2) 9: Associate the reference vector to an individual; 10: Find neighbor individuals to each individual; 11: Generate a new offspring population; (Refer to Algorithm 3) 12: Environmental selection; (Refer to Algorithm 4) 13: Update the archive Ar c; (Refer to Algorithm 5) 14: t = t + 1; 15: end while. All individuals in Ar c(t − 1) will be kept to Ar c(t)
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