Analyzing the Effect of Objective Correlation on the Efficient Set of MNK-Landscapes
This work addresses a gap in benchmark design for researchers in multiobjective optimization, but it is incremental as it builds on existing NK-landscapes.
The paper tackles the lack of benchmarks considering objective correlation in multiobjective combinatorial optimization by defining a method to design problems with correlation, extending NK-landscapes, and shows that objective correlation significantly affects search space properties, though no concrete numbers are provided.
In multiobjective combinatorial optimization, there exists two main classes of metaheuristics, based either on multiple aggregations, or on a dominance relation. As in the single objective case, the structure of the search space can explain the difficulty for multiobjective metaheuristics, and guide the design of such methods. In this work we analyze the properties of multiobjective combinatorial search spaces. In particular, we focus on the features related the efficient set, and we pay a particular attention to the correlation between objectives. Few benchmark takes such objective correlation into account. Here, we define a general method to design multiobjective problems with correlation. As an example, we extend the well-known multiobjective NK-landscapes. By measuring different properties of the search space, we show the importance of considering the objective correlation on the design of metaheuristics.