Computational Intelligence, Volume 34, Number 1, 2018
LEXIMIN ASYMMETRIC MULTIPLE OBJECTIVE DISTRIBUTED
CONSTRAINT OPTIMIZATION PROBLEM
Nagoya Institute of Technology, Nagoya, Japan
Florida Institute of Technology, Melbourne, Florida
Kobe University, Kobe, Japan
Kyushu University, Fukuoka, Japan
The Distributed Constraint Optimization Problem (DCOP) lies at the foundations of multiagent cooperation.
With DCOPs, the optimization in distributed resource allocation problems is formalized using constraint optimiza-
tion problems. The solvers for the problem are designed based on decentralized cooperative algorithms that are
performed by multiple agents. In a conventional DCOP, a single objective is considered.
The Multiple Objective Distributed Constraint Optimization Problem (MODCOP) is an extension of the
DCOP framework, where agents cooperatively have to optimize simultaneously multiple objective functions. In
the conventional MODCOPs, a few objectives are globally deﬁned and agents cooperate to ﬁnd the Pareto optimal
solution. However, such models do not capture the interests of each agent. On the other hand, in several practical
problems, the share of each agent is important. Such shares are modeled as preference values of agents. This class
of problems can be deﬁned using the MODCOP on the preferences of agents. In particular, we deﬁne optimization
problems based on leximin ordering and Asymmetric DCOPs (Leximin AMODCOPs). The leximin deﬁnes an
ordering among vectors of objective values. In addition, Asymmetric DCOPs capture the preferences of agents.
Because the optimization based on the leximin ordering improves the equality among the satisﬁed preferences of
the agents, this class of problems is important. We propose several solution methods for Leximin AMODCOPs
generalizing traditional operators into the operators on sorted objective vectors and leximin. The solution methods
applied to the Leximin AMODCOPs are based on pseudo trees. Also, the investigated search methods employ the
concept of boundaries of the sorted vectors.
Received 15 November 2015; Revised 1 June 2016; Accepted 1 September 2016
Key words: leximin, preference, multiple objectives, distributed constraint optimization, multiagent,
The Distributed Constraint Optimization Problem (DCOP) lies at the foundations of
multiagent cooperation (Modi et al. 2005; Petcu and Faltings 2005; Farinelli et al. 2008;
Zivan 2008). With DCOPs, the optimization in distributed resource allocation including dis-
tributed sensor networks (Zhang et al. 2005), meeting scheduling (Maheswaran et al. 2004),
disaster response (Ramchurn et al. 2010), and smart grids (Miller et al. 2012) is formal-
ized using constraint optimization problems. In a conventional DCOP, a single objective
is optimized. The solvers for the problem are designed based on decentralized cooperative
algorithms that are performed by multiple agents. The solution methods are categorized into
complete and incomplete methods. Several complete methods employ techniques including
dynamic programming and tree search that are performed based on a graph structure called
pseudo tree. DPOP (Petcu and Faltings 2005) is a solution method based on dynamic pro-
gramming, which performs bucket elimination (Dechter 1999) on a pseudo tree. ADOPT
(Modi et al. 2005) performs a tree search with memory-bounded dynamic programming.
Address correspondence to Toshihiro Matsui, Nagoya Institute of Technology, Gokiso-cho Showa-ku Nagoya 466-8555,
Japan; e-mail: email@example.com
© 2017 Wiley Periodicals, Inc.