Combining Optimization and Machine Learning for the Formation of Collectives

This thesis considers the problem of forming collectives of agents for real-world applications aligned with Sustainable Development Goals (e.g., shared mobility and cooperative learning). Such problems require fast approaches that can produce solutions of high quality for hundreds of agents. With this goal in mind, existing solutions for the formation of collectives focus on enhancing the optimization approach by exploiting the characteristics of a domain. However, the resulting approaches rely on specific domain knowledge and are not transferable to other collective formation problems. Therefore, approaches that can be applied to various problems need to be studied in order to obtain general approaches that do not require prior knowledge of the domain. Along these lines, this thesis proposes a general approach for the formation of collectives based on a novel combination of machine learning and an \emph{Integer Linear Program}. More precisely, a machine learning component is trained to generate a set of promising collectives that are likely to be part of a solution. Then, such collectives and their corresponding utility values are introduced into an \emph{Integer Linear Program} which finds a solution to the collective formation problem. In that way, the machine learning component learns the structure shared by ``good'' collectives in a particular domain, making the whole approach valid for various applications. In addition, the empirical analysis conducted on two real-world domains (i.e., ridesharing and team formation) shows that the proposed approach provides solutions of comparable quality to state-of-the-art approaches specific to each domain. Finally, this thesis also shows that the proposed approach can be extended to problems that combine the formation of collectives with other optimization objectives. Thus, this thesis proposes an extension of the collective formation approach for assigning pickup and delivery locations to robots in a warehouse environment. The experimental evaluation shows that, although it is possible to use the collective formation approach for that purpose, several improvements are required to compete with state-of-the-art approaches. Overall, this thesis aims to demonstrate that machine learning can be successfully intertwined with classical optimization approaches for the formation of collectives by learning the structure of a domain, reducing the need for ad-hoc algorithms devised for a specific application

An overview of population-based algorithms for multi-objective optimisation

In this work we present an overview of the most prominent population-based algorithms and the methodologies used to extend them to multiple objective problems. Although not exact in the mathematical sense, it has long been recognised that population-based multi-objective optimisation techniques for real-world applications are immensely valuable and versatile. These techniques are usually employed when exact optimisation methods are not easily applicable or simply when, due to sheer complexity, such techniques could potentially be very costly. Another advantage is that since a population of decision vectors is considered in each generation these algorithms are implicitly parallelisable and can generate an approximation of the entire Pareto front at each iteration. A critique of their capabilities is also provided

A Probability Collectives Approach with a Feasibility-Based Rule for Constrained Optimization

This paper demonstrates an attempt to incorporate a simple and generic constraint handling technique to the Probability Collectives (PC) approach for solving constrained optimization problems. The approach of PC optimizes any complex system by decomposing it into smaller subsystems and further treats them in a distributed and decentralized way. These subsystems can be viewed as a Multi-Agent System with rational and self-interested agents optimizing their local goals. However, as there is no inherent constraint handling capability in the PC approach, a real challenge is to take into account constraints and at the same time make the agents work collectively avoiding the tragedy of commons to optimize the global/system objective. At the core of the PC optimization methodology are the concepts of Deterministic Annealing in Statistical Physics, Game Theory and Nash Equilibrium. Moreover, a rule-based procedure is incorporated to handle solutions based on the number of constraints violated and drive the convergence towards feasibility. Two specially developed cases of the Circle Packing Problem with known solutions are solved and the true optimum results are obtained at reasonable computational costs. The proposed algorithm is shown to be sufficiently robust, and strengths and weaknesses of the methodology are also discussed

APPLICATION OF THE RASCH METHOD OF EVALUATING LATENT VARIABLES IN MANAGEMENT AND ADMINISTRATION

In the paper approaches of application of the theory of latent variables for the decision of some problems of management and management are offered. The peculiarity of this work is that mathematical solutions for solving problems are based on Rasch’s model for estimating latent variables.The aim of this paper is to describe a general approach to estimating latent variables using Rasch’s method, based on the method of least squares, and apply this approach to some management tasks. The tasks of applying the Rasch model to the method of organizing team, to evaluating alternatives in decision-making and to the formation of a portfolio of securities were solved.In the field of labour management, three models for organizing group tasks are considered: the formation of work teams, the case of individual performance of a group task, and the case of joint performance of group task jobs. In the field of decision theory, the model for choosing the best alternative is considered, including taking into account the weights of the criteria. We also considered the approach of obtaining estimates of alternatives using the hierarchy analysis method, in which the attractiveness vector of alternatives is computed on the basis of Rasch’s model of estimation of latent variables. In the field of financial management, a method of forming a portfolio of securities in the approach of the theory of latent variables is proposed. It is shown that, in comparison with traditional methods, the approach based on Rasch’s model has advantages: linearity of the obtained estimates, their independence and high accuracy.

Planning Algorithms for Multi-Robot Active Perception

A fundamental task of robotic systems is to use on-board sensors and perception algorithms to understand high-level semantic properties of an environment. These semantic properties may include a map of the environment, the presence of objects, or the parameters of a dynamic field. Observations are highly viewpoint dependent and, thus, the performance of perception algorithms can be improved by planning the motion of the robots to obtain high-value observations. This motivates the problem of active perception, where the goal is to plan the motion of robots to improve perception performance. This fundamental problem is central to many robotics applications, including environmental monitoring, planetary exploration, and precision agriculture. The core contribution of this thesis is a suite of planning algorithms for multi-robot active perception. These algorithms are designed to improve system-level performance on many fronts: online and anytime planning, addressing uncertainty, optimising over a long time horizon, decentralised coordination, robustness to unreliable communication, predicting plans of other agents, and exploiting characteristics of perception models. We first propose the decentralised Monte Carlo tree search algorithm as a generally-applicable, decentralised algorithm for multi-robot planning. We then present a self-organising map algorithm designed to find paths that maximally observe points of interest. Finally, we consider the problem of mission monitoring, where a team of robots monitor the progress of a robotic mission. A spatiotemporal optimal stopping algorithm is proposed and a generalisation for decentralised monitoring. Experimental results are presented for a range of scenarios, such as marine operations and object recognition. Our analytical and empirical results demonstrate theoretically-interesting and practically-relevant properties that support the use of the approaches in practice