Constraint Optimisation Techniques for Real-World Applications

Constraint optimisation represents a fundamental technique that has been successfully employed in Multi-Agent Systems (MAS) in order to face a number of multi-agent coordination challenges. In this thesis we focus on Coalition Formation (CF), one of the key approaches for coordination in MAS. CF aims at the formation of groups that maximise a particular objective functions (e.g., arrange shared rides among multiple agents in order to minimise travel costs). Specifically, we discuss a special case of CF known as Graph-Constrained CF (GCCF) where a network connecting the agents constrains the formation of coalitions. We focus on this type of problem given that in many real-world applications, agents may be connected by a communication network or only trust certain peers in their social network. In particular, the contributions of this thesis are the following. We propose a novel representation of this problem and we design an efficient solution algorithm, i.e., CFSS. We evaluate CFSS on GCCF scenarios like collective energy purchasing and social ridesharing using realistic data (i.e., energy consumption profiles from households in the UK, GeoLife for spatial data, and Twitter as social network). Results show that CFSS outperforms state of the art GCCF approaches both in terms of runtime and scalability. CFSS is the first algorithm that provides solutions with good quality guarantees for large-scale GCCF instances with thousands of agents (i.e., more that 2700). In addition, we address the problem of computing the transfer or payment to each agent to ensure it is fairly rewarded for its contribution to its coalition. This aspect of CF, denoted as payment computation, is of utmost importance in scenario characterised by agents with rational behaviours, such as collective energy purchasing and social ridesharing. In this perspective, we propose PK, the first method to compute payments in large-scale GCCF scenarios that are also stable in a game-theoretic sense. Finally, we provide an alternative method for the solution of GCCF, by exploiting the close relation between such problem and Constraint Optimisation Problems (COPs). We consider Bucket Elimination (BE), one of the most important algorithmic frameworks to solve COPs, and we propose CUBE, a highly-parallel GPU implementation of the most computationally intensive operations of BE. CUBE adopts an efficient memory layout that results in a high computational throughput. In addition, CUBE is not limited by the amount of memory of the GPU and, hence, it can cope with problems of realistic nature. CUBE has been tested on the SPOT5 dataset, which contains several satellite management problems modelled as COPs. Moreover, we use CUBE to solve COP-GCCF, the first COP formalisation of GCCF that results in a linear number of constraints with respect to the number of agents. This property is crucial to ensure the scalability of our approach. Results show that COP-GCCF produces significant improvements with respect to state of the art algorithms when applied to a realistic graph topology (i.e., Twitter), both in terms of runtime and memory. Overall, this thesis provides a novel perspective on important techniques in the context of MAS (such as CF and constraint optimisation), allowing to solve realistic problems involving thousands of agents for the first time.