Evolutionary algorithm with multiobjective optimization technique for solving nonlinear equation systems. (English) Zbl 1475.65028
Summary: The challenge of solving nonlinear equation systems is how to locate multiple optimal solutions simultaneously in a single run. To address this issue, this paper proposes a novel algorithm by combining a diversity indicator, multi-objective optimization technique, and clustering technique. Firstly, a diversity indicator is designed to maintain the diversity of the population. Then, a K-means clustering-based selection strategy is introduced to locate the promising solutions. Finally, the local search is used to accelerate the convergence of population. The experimental results on 30 nonlinear equation systems show that the proposed algorithm is better than six state-of-the-art algorithms in terms of convergence rate and success rate.
MSC:
| 65H10 | Numerical computation of solutions to systems of equations |
| 68W50 | Evolutionary algorithms, genetic algorithms (computational aspects) |
| 90C29 | Multi-objective and goal programming |
| 90C59 | Approximation methods and heuristics in mathematical programming |
Keywords:
nonlinear equation systems; transformation technique; multiobjective optimization technique; K-means clustering; differential evolution (DE)References:
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