An analysis of control parameters of MOEA/D under two different optimization scenarios

Comparison of multi-objective evolutionary algorithms applied to watershed management problem

Simulation-based optimization (S-O) frameworks are effective in developing cost-effective watershed management strategies, where optimization algorithms have substantial effect on the quality of strategies. Despite the development and improvement of multi-objective evolutionary algorithms (MOEAs) provide more robust alternatives for optimization, they typically have limited applications in real-world decision contexts. In this study, three advanced MOEAs, including NSGA-II, MOEA/D and NSGA-III, were introduced into the S-O framework and applied to a real-world watershed management problem, and their performance and characteristics were quantified through performance metrics. Results show that a higher crossover or mutation probability do not necessarily promote convergence and diversity of solutions, while a larger generation and population size is helpful for MOEAs to find high-quality solutions. Compared to the other two MOEAs, NSGA-II consistently exhibits robust performance in finding solutions with good convergence and high diversity, and provides more options at the same computational cost, while the degenerate Pareto front of the proposed watershed management problem may account for the poor performance of MOEA/D and NSGA-III in terms of diversity. For a 10% TN or TP reduction target, the average cost of the NSGA-II optimized strategies is 32.22% or 47.83% of the commonly used strategies. In addition, this study also discussed the development of resilient watershed management to buffer the impacts of climate change on aquatic system, the incorporation of fuzzy programming into the S-O framework to develop robust watershed management strategies under uncertainty, and the application of machine learning-based surrogate models to reduce computational cost of the S-O framework. These results can contribute to the understanding of MOEAs and provide useful guidance to decision makers.

A Bounded Archiver for Hausdorff Approximations of the Pareto Front for Multi-Objective Evolutionary Algorithms

Multi-objective evolutionary algorithms (MOEAs) have been successfully applied for the numerical treatment of multi-objective optimization problems (MOP) during the last three decades. One important task within MOEAs is the archiving (or selection) of the computed candidate solutions, since one can expect that an MOP has infinitely many solutions. We present and analyze in this work ArchiveUpdateHD, which is a bounded archiver that aims for Hausdorff approximations of the Pareto front. We show that the sequence of archives generated by ArchiveUpdateHD yields under certain (mild) assumptions with a probability of one after finitely many steps a Δ+-approximation of the Pareto front, where the value Δ+ is computed by the archiver within the run of the algorithm without any prior knowledge of the Pareto front. The knowledge of this value is of great importance for the decision maker, since it is a measure for the “completeness” of the Pareto front approximation. Numerical results on several well-known academic test problems as well as the usage of ArchiveUpdateHD as an external archiver within three state-of-the-art MOEAs indicate the benefit of the novel strategy.

Running Time Analysis of MOEA/D on Pseudo-Boolean Functions

Decomposition-based multiobjective evolutionary algorithms (MOEAs) are a class of popular methods for solving the multiobjective optimization problems (MOPs), and have been widely studied in numerical experiments and successfully applied in practice. However, we know little about these algorithms from the theoretical aspect. In this paper, we present running time analysis of a simple MOEA with mutation and crossover based on the MOEA/D framework (MOEA/D-C) on five pseudo-Boolean functions. Our rigorous theoretical analysis shows that by properly setting the number of subproblems, the upper bounds of expected running time of MOEA/D-C obtaining a set of solutions to cover the Pareto fronts (PFs) of these problems are apparently lower than those of the one with mutation-only (MOEA/D-M). Moreover, to effectively obtain a set of solutions to cover the PFs of these problem, MOEA/D-C only needs to decompose these MOPs into several subproblems with a set of simple weight vectors while MOEA/D-M needs to find Ω(n) optimally decomposed weight vectors. This result suggests that the use of crossover in decomposition-based MOEA can simplify the setting of weight vectors for different problems and make the algorithm more efficient. This paper provides some insights into the working principles of MOEA/D and explains why some existing decomposition-based MOEAs work well in computational experiments.