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Solving Three-Objective Optimization Problems Using Evolutionary Dynamic Weighted Aggregation: Results and Analysis
Yaochu Jin, Tatsuya Okabe, and Bernhard Sendhoff
Honda Research Institute Europe
Carl-Legien-Str. 30,
63073 Offenbach/Main, Germany
yaochu.jin@honda-ri.de
Abstract. The main purposes of this paper is twofold. First, the evolutionary dynamic weighted aggregation (EDWA) [1] approaches are extended to the optimization of three-objective problems. Fig. 1 shows two example patterns for weight change. Through two three-objective test problems [2], the methods have shown to be e.ective. Theoretical analyses reveal that the success of the weighted aggregation based methods can largely be attributed to the following facts:
- The change of the weights is equivalent to the rotation of the Pareto front
about the origin. All Pareto-optimal solutions, no matter whether they are
located in the convex or concave region, are dynamically capturable. In contrast,
classical analyses of the weighted aggregation method only consider
the static stability of the Pareto-optimal solutions. Note that a dynamically
capturable Pareto-optimal solution is not necessarily statically stable.
- Many multiobjective optimization problems exhibit the characteristics
known as global convexity, which means that most Pareto-optimal solutions
are concentrated in a small fraction of the parameter space. Furthermore,
the solutions in the neighborhood in the .tness space are also in the neighborhood
in the parameter space, and vice versa. This property is also known
as the connectedness.
- The evolution strategies are able to carry out locally causal search. Once the population has reached any point on the Pareto front, the local search ability is very important for the algorithms to "scan" the Pareto front point by point smoothly. The resolution of the scanning is determined by the speed of the weight change.
LNCS 2723, p. 636 f.
lncs@springer.de
© Springer-Verlag Berlin Heidelberg 2003