Machine learning-based framework to cover optimal Pareto-front in many-objective optimization

Abstract

One of the crucial challenges of solving many-objective optimization problems is uniformly well covering of the Pareto-front (PF). However, many the state-of-the-art optimization algorithms are capable of approximating the shape of many-objective PF by generating a limited number of non-dominated solutions. The exponential increase of the population size is an inefficient strategy that increases the computational complexity of the algorithm dramatically—especially when solving many-objective problems. In this paper, we introduce a machine learning-based framework to cover sparse PF surface which is initially generated by many-objective optimization algorithms; either by classical or meta-heuristic methods. The proposed method, called many-objective reverse mapping (MORM), is based on constructing a learning model on the initial PF set as the training data to reversely map the objective values to corresponding decision variables. Using the trained model, a set of candidate solutions can be generated by a variety of inexpensive generative techniques such as Opposition-based Learning and Latin Hypercube Sampling in both objective and decision spaces. Iteratively generated non-dominated candidate solutions cover the initial PF efficiently with no further need to utilize any optimization algorithm. We validate the proposed framework using a set of well-known many-objective optimization benchmarks and two well-known real-world problems. The coverage of PF is illustrated and numerically compared with the state-of-the-art many-objective algorithms. The statistical tests conducted on comparison measures such as HV, IGD, and the contribution ratio on the built PF reveal that the proposed collaborative framework surpasses the competitors on most of the problems. In addition, MORM covers the PF effectively compared to other methods even with the aid of large population size.