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The evaluation of multiobjective evolutionary algorithms (MOEAs) involves many metrics, it can be considered as a multiple-criteria decision making (MCDM) problem. A framework is proposed to estimate MOEAs, in which six MOEAs, five performance metrics, and two MCDM methods are used. An experimental study is designed and thirteen benchmark functions are selected to validate the proposed framework. The experimental results have indicated that the framework is effective in evaluating MOEAs.

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Abstract:In the past two decades, China's manufacturing industry has achieved great success. However, pollution and environmental impacts have become more serious while this industry has grown. The economic and emission dispatch (EED) problem is a typical multi-objective optimization problem with conflicting fuel costs and pollution emission objectives. An ensemble multi-objective differential evolution (EMODE) is proposed to tackle the EED problem. First, the equality constraints of the problem have been transformed into inequality constraints. Next, two mutation strategies DE/rand/1 and DE/current-to-rand/1 have been implemented to improve the conventional DE. The performance of the proposed algorithm is evaluated on six test functions and the numerical results have indicated that the proposed algorithm is effective. The proposed algorithm EMODE is used to solve a series of six generators and eleven generators in the EED problem. The experimental results obtained are compared with those reported using single optimization algorithms and multi-objective evolutionary algorithms (MOEAs). The results have revealed that the proposed algorithm EMODE either matches or outperforms those algorithms. The proposed algorithm is an effective candidate to optimize the manufacturing industry of China.