Maxime Clement

Modeling and Algorithm for Dynamic Multi-objective Weighted Constraint Satisfaction Problem

A Constraint Satisfaction Problem (CSP) is a fundamental problem that can formalize various applications related to Artificial Intelligence problems. A Weighted Constraint Satisfaction Problem (WCSP) is a CSP where constraints can be violated, and the aim of this problem is to find an assignment that minimizes the sum of weights of the violated constraints. Most researches have focused on developing algorithms for solv- ing static mono-objective problems. However, many real world satisfaction/optimization problems involve multiple criteria that should be considered separately and satisfied/optimized simultaneously. Additionally, they are often dynamic, i.e., the problem changes at runtime. In this paper, we introduce a Multi-Objective WCSP (MO-WCSP) and develop a novel MO-WCSP algorithm called Multi-Objective Branch and Bound (MO-BnB), which is based on a new solution criterion called (l, s)-Pareto solution. Furthermore, we first for- malize a Dynamic MO-WCSP (DMO-WCSP). As an initial step forward developing an algorithm for solving a DMO-WCSP, we focus on the change of weights of constraints and develop the first algorithm called Dynamic Multi-Objective Branch and Bound (DMO-BnB) for solving a DMO-WCSPs, which is based on MO-BnB. Finally, we provide the complexity of our algorithm and evaluate DMO-BnB with different problem settings.

Local Search Based Approximate Algorithm for Multi-Objective DCOPs

Many real world optimization problems involve multiple criteria that should be considered separately and optimized simultaneously. A Multi-Objective Distributed Constraint Optimization Problem (MO-DCOP) is the extension of a mono-objective Distributed Constraint Optimization Problem (DCOP). A DCOP is a fundamental problem that can formalize various applications related to multi-agent cooperation. Solving an MO-DCOP is to find the Pareto front which is a set of cost vectors obtained by Pareto optimal solutions. In MO-DCOPs, even if a constraint graph has the simplest tree structure, the size of the Pareto front (the number of Pareto optimal solutions) is often exponential in the number of agents. Since finding all Pareto optimal solutions becomes easily intractable, it is important to consider fast but approximate algorithms. Various sophisticated algorithms have been developed for solving a DCOP and an MO-COP. However, there exists few works on an MO-DCOP. The Bounded Multi-Objective Max-Sum (B-MOMS) algorithm is the first and only existing approximate MO-DCOP algorithm. In this paper, we develop a novel approximate MO-DCOP algorithm called Distributed Iterated Pareto Local Search (DIPLS) and empirically show that DIPLS outperforms the state-of-the-art B-MOMS algorithm.

Model and Algorithm for Dynamic Multi-Objective Distributed Optimization

Many problems in multi-agent systems can be represented as a Distributed Constraint Optimization Problem (DCOP) where the goal is to find the best assignment to variables in order to minimize the cost. More complex problems including several criteria can be represented as a Multi-Objective Distributed Constraint Optimization Problem (MO-DCOP) where the goal is to optimize several criteria at the same time. However, many problems are subject to changes over time and need to be represented as dynamic problems. In this paper, we formalize the Dynamic Multi-Objective Distributed Constraint Optimization Problem (DMO-DCOP) and introduce the first algorithm called DMOBB to handle changes in the number of objectives.

AOF-Based Algorithm for Dynamic Multi-Objective Distributed Constraint Optimization

Many real world problems involve multiple criteria that should be considered separately and optimized simultaneously. A Multi-Objective Distributed Constraint Optimization Problem MO-DCOP is the extension of a mono-objective Distributed Constraint Optimization Problem DCOP. A DCOP is a fundamental problem that can formalize various applications related to multi-agent cooperation. This problem consists of a set of agents, each of which needs to decide the value assignment of its variables so that the sum of the resulting rewards is maximized. An MO-DCOP is a DCOP which involves multiple criteria. Most researches have focused on developing algorithms for solving static problems. However, many real world problems are dynamic. In this paper, we focus on a change of criteria/objectives and model a Dynamic MO-DCOP DMO-DCOP which is defined by a sequence of static MO-DCOPs. Furthermore, we develop a novel algorithm for DMO-DCOPs. The characteristics of this algorithm are as follows: i it is a reused algorithm which finds Pareto optimal solutions for all MO-DCOPs in a sequence using the information of previous solutions, ii it utilizes the Aggregate Objective Function AOF technique which is the widely used classical method to find Pareto optimal solutions, and iii the complexity of this algorithm is determined by the induced width of problem instances.