Random Neural Networks and Optimisation

In this thesis we introduce new models and learning algorithms for the Random Neural Network (RNN), and we develop RNN-based and other approaches for the solution of emergency management optimisation problems. With respect to RNN developments, two novel supervised learning algorithms are proposed. The first, is a gradient descent algorithm for an RNN extension model that we have introduced, the RNN with synchronised interactions (RNNSI), which was inspired from the synchronised firing activity observed in brain neural circuits. The second algorithm is based on modelling the signal-flow equations in RNN as a nonnegative least squares (NNLS) problem. NNLS is solved using a limited-memory quasi-Newton algorithm specifically designed for the RNN case. Regarding the investigation of emergency management optimisation problems, we examine combinatorial assignment problems that require fast, distributed and close to optimal solution, under information uncertainty. We consider three different problems with the above characteristics associated with the assignment of emergency units to incidents with injured civilians (AEUI), the assignment of assets to tasks under execution uncertainty (ATAU), and the deployment of a robotic network to establish communication with trapped civilians (DRNCTC). AEUI is solved by training an RNN tool with instances of the optimisation problem and then using the trained RNN for decision making; training is achieved using the developed learning algorithms. For the solution of ATAU problem, we introduce two different approaches. The first is based on mapping parameters of the optimisation problem to RNN parameters, and the second on solving a sequence of minimum cost flow problems on appropriately constructed networks with estimated arc costs. For the exact solution of DRNCTC problem, we develop a mixed-integer linear programming formulation, which is based on network flows. Finally, we design and implement distributed heuristic algorithms for the deployment of robots when the civilian locations are known or uncertain

Sherali-Adams gaps, flow-cover inequalities and generalized configurations for capacity-constrained Facility Location

Metric facility location is a well-studied problem for which linear programming methods have been used with great success in deriving approximation algorithms. The capacity-constrained generalizations, such as capacitated facility location (CFL) and lower-bounded facility location (LBFL), have proved notorious as far as LP-based approximation is concerned: while there are local-search-based constant-factor approximations, there is no known linear relaxation with constant integrality gap. According to Williamson and Shmoys devising a relaxation-based approximation for \cfl\ is among the top 10 open problems in approximation algorithms. This paper advances significantly the state-of-the-art on the effectiveness of linear programming for capacity-constrained facility location through a host of impossibility results for both CFL and LBFL. We show that the relaxations obtained from the natural LP at $\Omega(n)$ levels of the Sherali-Adams hierarchy have an unbounded gap, partially answering an open question of \cite{LiS13, AnBS13}. Here, $n$ denotes the number of facilities in the instance. Building on the ideas for this result, we prove that the standard CFL relaxation enriched with the generalized flow-cover valid inequalities \cite{AardalPW95} has also an unbounded gap. This disproves a long-standing conjecture of \cite{LeviSS12}. We finally introduce the family of proper relaxations which generalizes to its logical extreme the classic star relaxation and captures general configuration-style LPs. We characterize the behavior of proper relaxations for CFL and LBFL through a sharp threshold phenomenon.Comment: arXiv admin note: substantial text overlap with arXiv:1305.599

Allocation of Heterogeneous Resources of an IoT Device to Flexible Services

Internet of Things (IoT) devices can be equipped with multiple heterogeneous network interfaces. An overwhelmingly large amount of services may demand some or all of these interfaces' available resources. Herein, we present a precise mathematical formulation of assigning services to interfaces with heterogeneous resources in one or more rounds. For reasonable instance sizes, the presented formulation produces optimal solutions for this computationally hard problem. We prove the NP-Completeness of the problem and develop two algorithms to approximate the optimal solution for big instance sizes. The first algorithm allocates the most demanding service requirements first, considering the average cost of interfaces resources. The second one calculates the demanding resource shares and allocates the most demanding of them first by choosing randomly among equally demanding shares. Finally, we provide simulation results giving insight into services splitting over different interfaces for both cases.Comment: IEEE Internet of Things Journa

Phase Transitions and Backbones of the Asymmetric Traveling Salesman Problem

In recent years, there has been much interest in phase transitions of combinatorial problems. Phase transitions have been successfully used to analyze combinatorial optimization problems, characterize their typical-case features and locate the hardest problem instances. In this paper, we study phase transitions of the asymmetric Traveling Salesman Problem (ATSP), an NP-hard combinatorial optimization problem that has many real-world applications. Using random instances of up to 1,500 cities in which intercity distances are uniformly distributed, we empirically show that many properties of the problem, including the optimal tour cost and backbone size, experience sharp transitions as the precision of intercity distances increases across a critical value. Our experimental results on the costs of the ATSP tours and assignment problem agree with the theoretical result that the asymptotic cost of assignment problem is pi ^2 /6 the number of cities goes to infinity. In addition, we show that the average computational cost of the well-known branch-and-bound subtour elimination algorithm for the problem also exhibits a thrashing behavior, transitioning from easy to difficult as the distance precision increases. These results answer positively an open question regarding the existence of phase transitions in the ATSP, and provide guidance on how difficult ATSP problem instances should be generated

A scenario aggregation based approach for determining a robust airline fleet composition

Strategic airline fleet planning is one of the major issues addressed through newly initiated decision support systems, designed to assist airlines and aircraft manufacturers in assessing the benefits of the emerging concept of dynamic capacity allocation. We present background research connected with such a system, which aims to explicitly account for the stochastic nature of passenger demand in supporting decisions related to the fleet composition problem. We address this problem through a scenario aggregation based approach and present results on representative case studies based on realistic data. Our investigations establish clear benefits of a stochastic approach as compared with deterministic formulations, as well as its implementation feasibility using state-of-the-artoptimization software.Dynamic capacity allocation;Airline fleet composition;Stochastic programming;Scenario aggregation;Fleet assignment

Exact solutions to a class of stochastic generalized assignment problems

This paper deals with a stochastic Generalized Assignment Problem with recourse. Only a random subset of the given set of jobs will require to be actually processed. An assignment of each job to an agent is decided a priori, and once the demands are known, reassignments can be performed if there are overloaded agents. We construct a convex approximation of the objective function that is sharp at all feasible solutions. We then present three versions of an exact algorithm to solve this problem, based on branch and bound techniques, optimality cuts, and a special purpose lower bound. numerical results are reported.