Decomposition-Based Multiobjective Optimization for Variable-Length Mixed-Variable Pareto Optimization and Its Application in Cloud Service Allocation

In real-world applications, a specific class of multiobjective optimization problems, such as the cloud service allocation problem (CSAOPs), possess the characteristic of variable-length and mixed variables, termed as variable multiobjective optimization problems (VMMOPs). Unfortunately, little research has been reported to solve them. To fill the gap, we propose a tailored enhanced decomposition-based algorithm to handle the VMMOPs. Specifically, a variable-length coding structure is designed to flexibly represent the solutions of VMMOPs. In order to facilitate the solution generation, a simple dimensionality incremental learning strategy is developed to choose representative solutions for the training of two learning models. The one is the fast-clustering-based histogram model, which is built for the sampling of solutions in the continuous decision space, while the other one is the incremental learning-based histogram model, designed to sample solutions in discrete decision space. Following the traditional constructor of the DTLZ test suite and the features of CSAOPs, we present a test suite of VMMOPs for the verification of the performance of the methods in handling VMMOPs. Experimental results on a number of benchmark problems and two real CSAOPs have shown the effectiveness and competitiveness of the proposed method in handling VMMOPs.