A Multiobjective Evolutionary Algorithm Using Gaussian Process-Based Inverse Modeling

Abstract

To approximate the Pareto front, most existing multiobjective evolutionary algorithms store the non-dominated solutions found so far in the population or in an external archive during the search. Such algorithms often require a high degree of diversity of the stored solutions and only a limited number of solutions can be achieved. By contrast, model-based algorithms can alleviate the requirement on solution diversity and in principle, as many solutions as needed can be generated. This paper proposes a new model-based method for representing and searching non-dominated solutions. The main idea is to construct Gaussian process based inverse models that map all found non-dominated solutions from the objective space to the decision space. These inverse models are then used to create offspring by sampling the objective space. To facilitate inverse modeling, the multivariate inverse function is decomposed into a group of univariate functions, where the number of inverse models is reduced using a random grouping technique. Extensive empirical simulations demonstrate that the proposed algorithm exhibits robust search performance on a variety of medium to high dimensional multiobjective optimization test problems. Additional non-dominated solutions are generated a posteriori using the constructed models to increase the density of solutions in the preferred regions at a low computational cost.

A Surrogate-Assisted Reference Vector Guided Evolutionary Algorithm for Computationally Expensive Many-Objective Optimization

“…To generate a uniformly distributed set of reference vectors, first a set of uniformly distributed reference points (p) is generated on a unit hyperplane using the canonical simplexlattice design method [11], [7].…”

A Strengthened Dominance Relation Considering Convergence and Diversity for Evolutionary Many-Objective Optimization

“…The non-dominated region identified by grid dominance uniformly distributes in several small regions of each Pareto front, failing to comprehensively cover the whole Pareto front. The is due to the fact that the grids in the grid dominance uniformly distribute in an M -dimensional hypercube, whereas the Pareto front is an (M − 1)-dimensional manifold [37], and thus the grids intersecting with the Pareto front are discrete. For L-dominance, it identifies non-dominated solutions mainly based on their Euclidean distances to the origin in three-objective space, hence only the region closest to the origin can be identified as non-dominated region.…”

Effectiveness and efficiency of non-dominated sorting for evolutionary multi- and many-objective optimization

“…Due to the conflicting nature of the objectives, there exists more than one Pareto optimal solution for an MOP. In particular, for an M-objective continuous MOP, its Pareto optimal solutions constitute an M − 1 dimensional piecewise manifold [32]. Based on the Pareto dominance, solutions in a population P can be divided into L disjoint subsets or ranks…”