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M. Li, S. Yang, and X. Liu. Pareto or non-Pareto: Bi-criterion evolution in multi-objective optimization. IEEE Transactions on Evolutionary Computation, 20(5), 2016. [PDF] [C code]
M. Li, S. Yang, and X. Liu. Pareto or non-Pareto: Bi-criterion evolution in multi-objective optimization. IEEE Transactions on Evolutionary Computation, 20(5), 2016. [PDF] [C code]
Idea:
Idea:
BCE manipulates two evolutionary populations, called the non-Pareto criterion (NPC) population and the Pareto criterion (PC) population, respectively, each of which is associated with one criterion. The NPC population steers the PC population searching towards the optimal front, while the PC population compensates the possible diversity loss of the NPC population by exploring some undeveloped (or not well-developed), but potentially promising regions in the objective space. The two populations communicate with each other in a generational manner; once one population produces good individuals, the other is able to apply them directly within its search process.
BCE manipulates two evolutionary populations, called the non-Pareto criterion (NPC) population and the Pareto criterion (PC) population, respectively, each of which is associated with one criterion. The NPC population steers the PC population searching towards the optimal front, while the PC population compensates the possible diversity loss of the NPC population by exploring some undeveloped (or not well-developed), but potentially promising regions in the objective space. The two populations communicate with each other in a generational manner; once one population produces good individuals, the other is able to apply them directly within its search process.
Results:
Results:
Comparison of the solution sets (shown by parallel coordinates) obtained by the original IBEA (left) and IBEA working under BCE (right) on the 10-objective DTLZ2. Under the BCE framework, the Pareto criterion population helps the non-Pareto criterion population (here IBEA's population) diversify its solutions to the whole Pareto front.
Comparison of the solution sets (shown by parallel coordinates) obtained by the Pareto criterion evolution (left) and the bi-criterion evolution (right) on the 10-objective DTLZ5(2,10). Under the BCE framework, the non-Pareto criterion population helps the Pareto criterion population converge its solutions to the Pareto front.
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