Decomposition-Based Approach for Solving Large Scale Multi-objective Problems

A novel encoding for separable large-scale multi-objective problems and its application to the optimisation of housing stock improvements

“…Additionally, often features like separability are unknown. It will be of interest to consider integrating approaches for detecting separability in the objectives automatically based on linkage detection, similar to the approach of [8], or random grouping [7,39].…”

“…All of the above research focuses on single-objective problems:, however, there is some evidence [37,38] that commonly-used evolutionary multi-objective algorithms do not scale well with the number of decision variables, emphasising the importance of techniques which can perform well with larger numbers of decision variables. As far as the authors are aware, there have been very few attempts (exceptions being studies by [6][7][8][9]) at multi-objective optimisation of problems with thousands of decision variables. SPO represents a novel approach to adapting existing multi-objective algorithms for large-scale problems.…”

“…SPO represents a novel approach to adapting existing multi-objective algorithms for large-scale problems. Furthermore, while many of the above approaches to large-scale single-objective problems use some form of decomposition, these tend to be problem specific (though Antonio and Coello [7], Qiu et al [39] use randomised grouping of variables with some success). An interesting method in [10] used a problem transformation scheme to reduce dimensionality of search space, whereby weights were applied to decision variables in groups and these were optimised to approximate the global Pareto front.…”

“…Large-scale global optimisation (LSGO) has attracted a lot of attention in recent years among evolutionary computation researchers, with varied real-world applications and diverse approaches appearing in the literature [1][2][3][4][5]. Much of the focus has been on single-objective LSGO, although recently there has been growing interest in multi-objective LSGO problems [6][7][8][9][10]. There is no universal definition of a LSGO problem, but typically one involves thousands or more decision variables.…”

Evolutionary Computation for Large-scale Multi-objective Optimization: A Decade of Progresses

“…To our knowledge, the only two related works in this direction before that are the comparative study presented in [48] in which the performance of four MOEAs (strength Pareto evolutionary algorthm (SPEA) [49] , memetic-Pareto archive evolution strategy (M-PAES) [50] , Ishibuchi's and Murata's multipleobjective genetic local search (IMMOGLS) [5] and multiple-objective genetic local search (MOGLS) [51] ) are investigated on multi-objective 0/1 knapsack problems with up to 750 decision variables, and a study on the scalability of multi-objective estimation of distribution algorithms (MOEDAs) [26] . An increasing interest in studying the scalability of MOEAs has begun mainly since the systematic experimental studies were presented in [24,25], where eight representative MOEAs (including nondominated sorting genetic algorithm II (NSGA-II) [8] , SPEA2 [52] Pareto envelop based search algorithm II (PESA-II) [53] , Pareto archived evolution strategy (PAES) [54] , one multiobjective particle swarm optimizer (OMOPSO) [55] , multiobjective cellular genetic algorithm (MOCel)l [56] , generalized differential evolution 3 (GDE3) [57] and archive-based hybrid scatter search (AbYSS) [58] ) are examined on largescale benchmark problems with up to 2 048 decision variables. By using the number of objective function evaluations required by an algorithm to reach an acceptable approximation of the Pareto front (i.e., an approximate set with its hypervolume larger than 98% of the hypervolume of the Pareto front) as the evaluation criterion of scalability, this work reveals the severe performance deterioration of the above eight MOEAs when increasing the number of decision variables from 8 to 2 048.…”