MOEA/D with biased weight adjustment inspired by user preference and its application on multi-objective reservoir flood control problem

Abstract

Related to the safety of public lives and property in the lower area of reservoirs, flood control is a priority for most large reservoirs. Considering both dam safety and downstream flood control, reservoir flood control is a multi-objective problem (MOP). To meet the needs of irriCommunicated by V. Loia. B Fang Liu gation and generating electricity after the flood, the decision maker usually has his/her preferred final scheduling water level. To deal with this kind of MOP with user-preference information, we incorporate user-preference information into the framework of MOEA/D (multi-objective evolutionary algorithm-based decomposition). The widely used preference information is mainly composed of reference points and preference directions. Compared with the Pareto dominancebased multi-objective evolutionary algorithms (MOEAs), MOEA/D can naturally include two kinds of preference information since MOEA/D is directly based on the reference point and the preference direction. The weight vector of a subproblem in MOEA/D is just its preference. Aiming to obtain uniformly distributed solutions on the objective space, one of innovation points in this paper is using modified Tchebycheff decomposition instead of Tchebycheff decomposition as the decomposition method. To focus the search on the interesting regions of decision maker, the other innovation point in this paper is to integrate biased subproblem (weight vector) adjustment into the framework of MOEA/D. The distribution of subproblems (weight vectors) are adjusted periodically so that the subproblems are re-distributed adaptively to search the interesting regions. Some subproblems, which are far away from the preference regions, are deleted. And then some new subproblems, which are expected to search the preference regions, are added into the current evolutionary population. The efficiency and the effectiveness of the proposed algorithm are assessed through multi-objective reservoir flood control problem and two-to ten-objective test problems.Keywords Multi-objective optimization · Evolutionary algorithm · Decomposition · Preference · Biased weight vector adjustment · Reservoir flood control 123 X. Ma et al.

A Reference Vector Guided Evolutionary Algorithm for Many-Objective Optimization

“…The idea is to dynamically adjust the distribution of the weight vectors according to the preferred region specified by a hypersphere. In [62], Ma et al have proposed to apply the light beam search (LBS) [63] in MOEA/D to incorporate user preferences, where the preference information is specified by an aspiration point and a reservation point, together with a preference neighborhood parameter. Most recently, Mohammadi et al have also proposed to integrate user preferences for manyobjective optimization [64], where the preferred region is specified by a hypercube.…”

A modified MOEA/D approach to the solution of multi-objective optimal power flow problem

“…MOEA/D is a simple yet efficient MOEA and has been dedicated to knapsack problem [41][42][43][44], job shop scheduling [45], traveling salesman problem [46][47][48][49], test task scheduling problem [50], antenna array synthesis [49], wireless sensor networks [51], portfolio management [52] and reservoir flood control [6]. The experimental and practical results all show perfect performance of the MOEA/D.…”

“…Then the decision-maker chooses one of the obtained Pareto candidates as the most preferred solution based on his/her preference information. This posterior approach which searches the whole Pareto optimal solutions before multi-criterion decision [6] represents the main trend for solving multi-objective optimizations. This type of method tries to obtain a good representation of the Pareto Front (PF) to present to a decision maker.…”

“…Also, it is a natural way of expressing the preference information as a target the decision-maker is hoping to obtain [6]. For this type of preference information expression, Zhang and Li [40] proposed a multi-objective evolutionary algorithm based on decomposition (MOEA/D) approach in 2007.…”

Evolutionary Multiobjective Optimization including Practically Desirable Solutions

“…In the presence of several optimal solutions, a decision-maker often considers preferences in objective space and can choose one or few candidate solutions for implementation [3]. Several optimization methods that combine preferences with multiobjective evolutionary algorithms have been proposed; see, for example, [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. Preferences can be determined a priori, during the search, or a posteriori.…”