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Multiobjective programming using uniform design and genetic algorithm

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2 Author(s)
Leung, Y.-W. ; Dept. of Comput. Sci., Hong Kong Baptist Univ., Kowloon Tong, China ; Yuping Wang

The notion of Pareto-optimality is one of the major approaches to multiobjective programming. While it is desirable to find more Pareto-optimal solutions, it is also desirable to find the ones scattered uniformly over the Pareto frontier in order to provide a variety of compromise solutions to the decision maker. We design a genetic algorithm for this purpose. We compose multiple fitness functions to guide the search, where each fitness function is equal to a weighted sum of the normalized objective functions and we apply an experimental design method called uniform design to select the weights. As a result, the search directions guided by these fitness functions are scattered uniformly toward the Pareto frontier in the objective space. With multiple fitness functions, we design a selection scheme to maintain a good and diverse population. In addition, we apply the uniform design to generate a good initial population and design a new crossover operator for searching the Pareto-optimal solutions. The numerical results demonstrate that the proposed algorithm can find the Pareto-optimal solutions scattered uniformly over the Pareto frontier.

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Systems, Man, and Cybernetics, Part C: Applications and Reviews, IEEE Transactions on  (Volume:30 ,  Issue: 3 )