# An Estimation of Distribution Based Algorithm for Continuous Distributed Constraint Optimization Problems

## Authors

• Meifeng Shi College of Computer Science and Engineering, Chongqing University of Technology, Chongqing, China; Faculty of Information Science and Electrical Engineering, Kyushu University, Fukuoka, Japan
• Peng Zhang College of Computer Science and Engineering, Chongqing University of Technology, Chongqing, China
• Xin Liao College of Computer Science and Engineering, Chongqing University of Technology, Chongqing, China
• Zhijian Xue College of Computer Science and Engineering, Chongqing University of Technology, Chongqing, China

## Keywords:

Estimation of Distribution Algorithm, C-DCOP, Multi-agent System, Breadth First Search Pseudo-tree

## Abstract

Continuous Distributed Constraint Optimization Problem(C-DCOP) is a constraint processing framework for continuous variables problems in multi-agent systems. There is a constraint cost function between two mutually restrictive agents in C-DCOP. The goal of the C-DCOP solving algorithm is to keep the sum of constraint cost functions in an extreme state. In a C-DCOP, each function is defined by a set of continuous variables. At present, some C-DCOP solving algorithms have been proposed, but there are some common problems such as the limitation of constraints cost function form, easy to fall into local optimum, and lack of anytime attribute. Aiming at these thorny problems, we propose a parallel optimization algorithm named Estimation of Distribution Based Algorithm for Continuous Distributed Constraint Optimization Problems (EDA-CD). In EDA-CD, each solution is regarded as an individual, and the distribution of agent value is jointly described by all outstanding individuals. Firstly, all agents cooperate to hold a distributed population. Secondly, each agent calculates the mean and variance of its variables to build probability models in parallel. Finally, the agent evaluates the fitness of samples and updates the probability model through cooperative communication on Breadth First Search (BFS) pseudo-tree. We theoretically prove that EDA-CD is an anytime algorithm. The extensive experimental results on four types of benchmark problems show that the proposed EDA-CD outperforms the state-of-the-art C-DCOP algorithms and has about 20% improvement in solution quality.