A Concise Function Representation for Faster Exact MPE and Constrained Optimisation in Graphical Models

We propose a novel concise function representation for graphical models, a central theoretical framework that provides the basis for many reasoning tasks. We then show how we exploit our concise representation based on deterministic finite state automata within Bucket Elimination (BE), a general approach based on the concept of variable elimination that can be used to solve many inference and optimisation tasks, such as most probable explanation and constrained optimisation. We denote our version of BE as FABE. By using our concise representation within FABE, we dramatically improve the performance of BE in terms of runtime and memory requirements. Results achieved by comparing FABE with state of the art approaches for most probable explanation (i.e., recursive best-first and structured message passing) and constrained optimisation (i.e., CPLEX, GUROBI, and toulbar2) following an established methodology confirm the efficacy of our concise function representation, showing runtime improvements of up to 5 orders of magnitude in our tests.Comment: Submitted to IEEE Transactions on Cybernetic

Sharing rides with friends: a coalition formation algorithm for ridesharing

We consider the Social Ridesharing (SR) problem, where a set of commuters, connected through a social network, arrange one-time rides at short notice. In particular, we focus on the associated optimisation problem of forming cars to minimise the travel cost of the overall system modelling such problem as a graph constrained coalition formation (GCCF) problem, where the set of feasible coalitions is restricted by a graph (i.e., the social network). Moreover, we significantly extend the state of the art algorithm for GCCF, i.e., the CFSS algorithm, to solve our GCCF model of the SR problem. Our empirical evaluation uses a real dataset for both spatial (GeoLife) and social data (Twitter), to validate the applicability of our approach in a realistic application scenario. Empirical results show that our approach computes optimal solutions for systems of medium scale (up to 100 agents) providing significant cost reductions (up to -36.22%). Moreover, we can provide approximate solutions for very large systems (i.e., up to 2000 agents) and good quality guarantees (i.e., with an approximation ratio of 1.41 in the worst case) within minutes (i.e., 100 seconds

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

Optimising Memory Management for Belief Propagation in Junction Trees using GPGPUs

Belief Propagation (BP) in Junction Trees (JT) is one of the most popular approaches to compute posteriors in Bayesian Networks (BN). Such approach has significant computational requirements that can be addressed by using highly parallel architectures (i.e., General Purpose Graphic Processing Units) to parallelise the message update phases of BP. In this paper, we propose a novel approach to parallelise BP with GPGPUs, which focuses on optimising the memory layout of the BN tables so to achieve better performance in terms of increased speedup, reduced data transfers between the host and the GPGPU, and scalability. Our empirical comparison with the state of the art approach on standard datasets confirms significant improvements in speedups (up to +594%), and scalability (as our method can operate on networks whose potential tables exceed the global memory of the GPGPU)

Anytime coalition structure generation on synergy graphs

We consider the coalition structure generation (CSG) problem on synergy graphs, which arises in many practical applications where communication constraints, social or trust relationships must be taken into account when forming coalitions. We propose a novel representation of this problem based on the concept of edge contraction, and an innovative branch and bound approach (CFSS), which is particularly efficient when applied to a general class of characteristic functions. This new model provides a non-redundant partition of the search space, hence allowing an effective parallelisation. We evaluate CFSS on two benchmark functions, the edge sum with coordination cost and the collective energy purchasing functions, comparing its performance with the best algorithm for CSG on synergy graphs: DyCE. The latter approach is centralised and cannot be efficiently parallelised due to the exponential memory requirements in the number of agents, which limits its scalability (while CFSS memory requirements are only polynomial). Our results show that, when the graphs are very sparse, CFSS is 4 orders of magnitude faster than DyCE. Moreover, CFSS is the first approach to provide anytime approximate solutions with quality guarantees for very large systems (i.e., with more than 2700 agents

Algorithms for Graph-Constrained Coalition Formation in the Real World

Coalition formation typically involves the coming together of multiple, heterogeneous, agents to achieve both their individual and collective goals. In this paper, we focus on a special case of coalition formation known as Graph-Constrained Coalition Formation (GCCF) whereby 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. We propose a novel representation of this problem based on the concept of edge contraction, which allows us to model the search space induced by the GCCF problem as a rooted tree. Then, we propose an anytime solution algorithm (CFSS), which is particularly efficient when applied to a general class of characteristic functions called $m+a$ functions. Moreover, we show how CFSS can be efficiently parallelised to solve GCCF using a non-redundant partition of the search space. We benchmark CFSS on both synthetic and realistic scenarios, using a real-world dataset consisting of the energy consumption of a large number of households in the UK. Our results show that, in the best case, the serial version of CFSS is 4 orders of magnitude faster than the state of the art, while the parallel version is 9.44 times faster than the serial version on a 12-core machine. Moreover, CFSS is the first approach to provide anytime approximate solutions with quality guarantees for very large systems of agents (i.e., with more than 2700 agents).Comment: Accepted for publication, cite as "in press

Shared value economics: an axiomatic approach

The concept of shared value was introduced by Porter and Kramer as a new conception of capitalism. Shared value describes the strategy of organizations that simultaneously enhance their competitiveness and the social conditions of related stakeholders such as employees, suppliers and the natural environment. The idea has generated strong interest, but also some controversy due to a lack of a precise definition, measurement techniques and difficulties to connect theory to practice. We overcome these drawbacks by proposing an economic framework based on three key aspects: coalition formation, sustainability and consistency, meaning that conclusions can be tested by means of logical deductions and empirical applications. The presence of multiple agents to create shared value and the optimization of both social and economic criteria in decision making represent the core of our quantitative definition of shared value. We also show how economic models can be characterized as shared value models by means of logical deductions. Summarizing, our proposal builds on the foundations of shared value to improve its understanding and to facilitate the suggestion of economic hypotheses, hence accommodating the concept of shared value within modern economic theory.Comment: 22 pages, 4 figure

A general approach for computing a consensus in group decision making that integrates multiple ethical principles

[EN] We tackle the problem of computing a consensus according to multiple ethical principles - which can include, for example, the principle of maximum freedom associated with the Benthamite doctrine and the principle of maximum fairness associated with the Rawlsian principles - among the preferences of different individuals in the context of Group Decision-Making (GDM). More formally, we put forward a novel formalisation of the above-mentioned problem based on a multi-lp-norm approximation problem that aims at minimising multiple p-metric distance functions, where each parameter p represents a given ethical principle. Our contribution incurs obvious benefits from a social-choice perspective. Firstly, our approach significantly generalises stateof-the-art approaches that were limited to only two ethical principles (p = 1, for maximum freedom, and p = & INFIN;, for maximum fairness). Secondly, our experimental results considering an established test case demonstrate that our approach is capable, thanks to a novel re-weighting scheme, to compute a multi-norm consensus that takes into account each ethical principle in a balanced way, in contrast with state-of-the-art approaches that were heavily biased towards the p =1 ethical principle.Research supported by projects: CI-SUSTAIN, Spain (PID2019-104156GB-I00) ; TAILOR, Spain (H2020-952215) ; 2021 SGR 00754 funded by Generalitat de Catalunya, Spain; VAE TED2021-131295B-C31, funded by MCIN/AEI, Spain/10.13 039/501100011033 and NextGenerationEU/PRTR, Spain; and VALAWAI, Spain (Horizon Europe #101070930) . Funding for open access charge: CRUE-Universitat Politecnica de Valencia.Salas-Molina, F.; Bistaffa, F.; Rodríguez-Aguilar, JA. (2023). A general approach for computing a consensus in group decision making that integrates multiple ethical principles. Socio-Economic Planning Sciences. 89. https://doi.org/10.1016/j.seps.2023.1016948

CUBE: A CUDA approach for Bucket Elimination on GPUs

We consider Bucket Elimination (BE), a popular algorithmic framework to solve Constraint Optimisation Problems (COPs). We focus on the parallelisation of the most computationally intensive operations of BE, i.e., join sum and maximisation, which are key ingredients in several close variants of the BE framework (including Belief Propagation on Junction Trees and Distributed COP techniques such as ActionGDL and DPOP). In particular, we propose CUBE, a highly-parallel GPU implementation of such operations, which adopts an efficient memory layout allowing all threads to independently locate their input and output addresses in memory, hence achieving a high computational throughput. We compare CUBE with the most recent GPU implementation of BE. Our results show that CUBE achieves significant speed-ups (up to two orders of magnitude) w.r.t. the counterpart approach, showing a dramatic decrease of the runtime w.r.t. the serial version (i.e., up to 652x faster). More important, such speed-ups increase when the complexity of the problem grows, showing that CUBE correctly exploits the additional degree of parallelism inherent in the problem