TY - JOUR
T1 - Multiobjective programming using uniform design and genetic algorithm
AU - Leung, Yiu Wing
N1 - Funding Information:
Manuscript received June 18, 1999; revised August 7, 2000. This work was supported by the HKBU FRG under Research Grant FRG/98-99/II-62. Y.-W. Leung is with the Department of Computer Science, Hong Kong Baptist University, Kowloon Tong, Hong Kong (http://www.comp.hkbu.edu.hk/~ywleung). Y. Wang is with the Department of Applied Mathematics, Xidian University, Xi’an 710071, China. Publisher Item Identifier S 1094-6977(00)09082-9.
PY - 2000/8
Y1 - 2000/8
N2 - 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. In this paper, 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.
AB - 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. In this paper, 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.
UR - http://www.scopus.com/inward/record.url?scp=0034240488&partnerID=8YFLogxK
U2 - 10.1109/5326.885111
DO - 10.1109/5326.885111
M3 - Journal article
AN - SCOPUS:0034240488
SN - 1094-6977
VL - 30
SP - 293
EP - 304
JO - IEEE Transactions on Systems, Man and Cybernetics Part C: Applications and Reviews
JF - IEEE Transactions on Systems, Man and Cybernetics Part C: Applications and Reviews
IS - 3
ER -