A Population-Based Search Approach to Solve Continuous Distributed Constraint Optimization Problems

Abstract

Distributed Constraint Optimization Problems (DCOPs) are an efficient framework widely used in multi-agent collaborative modeling. The traditional DCOP framework assumes that variables are discrete and constraint utilities are represented in tabular forms. However, the variables are continuous and constraint utilities are in functional forms in many practical applications. To overcome this limitation, researchers have proposed Continuous DCOPs (C-DCOPs), which can model DCOPs with continuous variables. However, most of the existing C-DCOP algorithms rely on gradient information for optimization, which means that they are unable to solve the situation where the utility function is a non-differentiable function. Although the Particle Swarm-Based C-DCOP (PCD) and Particle Swarm with Local Decision-Based C-DCOP (PCD-LD) algorithms can solve the situation with non-differentiable utility functions, they need to implement Breadth First Search (BFS) pseudo-trees for message passing. Unfortunately, employing the BFS pseudo-tree results in expensive computational overheads and agent privacy leakage, as messages are aggregated to the root node of the BFS pseudo-tree. Therefore, this paper aims to propose a fully distributed C-DCOP algorithm to solve the utility function form problem and avoid the disadvantages caused by the BFS pseudo-tree. Inspired by the population-based algorithms, we propose a fully decentralized local search algorithm, named Population-based Local Search Algorithm (PLSA), for solving C-DCOPs with three-fold advantages: (i) PLSA adopts a heuristic method to guide the local search to achieve a fast search for high-quality solutions; (ii) in contrast to the conventional C-DCOP algorithm, PLSA can solve utility functions of any form; and (iii) compared to PCD and PCD-LD, PLSA avoids complex message passing to achieve efficient computation and agent privacy protection. In addition, we implement an extended version of PLSA, named Population-based Global Search Algorithm (PGSA), and empirically show that our algorithms outperform the state-of-the-art C-DCOP algorithms on three types of benchmark problems.