Resilient Team Formation with Stabilisability of Agent Networks for Task Allocation

Team formation (TF) faces the problem of defining teams of agents able to accomplish a set of tasks. Resilience on TF problems aims to provide robustness and adaptability to unforeseen events involving agent deletion. However, agents are unaware of the inherent social welfare in these teams. This article tackles the problem of how teams can minimise their effort in terms of organisation and communication considering these dynamics. Our main contribution is twofold: first, we introduce the Stabilisable Team Formation (STF) as a generalisation of current resilient TF model, where a team is stabilisable if it possesses and preserves its inter-agent organisation from a graph-based perspective. Second, our experiments show that stabilisability is able to reduce the exponential execution time in several units of magnitude with the most restrictive configurations, proving that communication effort in subsequent task allocation problems are relaxed compared with current resilient teams. To do so, we developed SBB-ST, a branch-and-bound algorithm based on Distributed Constrained Optimisation Problems (DCOP) to compute teams. Results evidence that STF improves their predecessors, extends the resilience to subsequent task allocation problems represented as DCOP, and evidence how Stabilisability contributes to resilient TF problems by anticipating decisions for saving resources and minimising the effort on team organisation in dynamic scenarios.

A Kuhn–Tucker model for behaviour in dictator games

We consider a dictator game experiment in which dictators perform a sequence of giving tasks and taking tasks. The data are used to estimate the parameters of a Stone–Geary utility function over own-payoff and other’s payoff. The econometric model incorporates zero observations (e.g. zero-giving or zero-taking) by applying the Kuhn–Tucker theorem and treating zeros as corner solutions in the dictator’s constrained optimisation problem. The method of maximum simulated likelihood (MSL) is used for estimation. We find that selfishness is significantly lower in taking tasks than in giving tasks, and we attribute this difference to the “cold prickle of taking”.

Production Optimiser Pilot for the Large Artificially-Lifted and Mature Samotlor Oil Field

This paper describes a production optimiser Pilot, developed by Rosneft/Samotlorneftegaz, with support from bp and deployed in JSC Samotlorneftegaz - a vast, mature, water-flooded, high water-cut and artificially-lifted oil field. Objectives include creating a digital twin for a sub-system of 600 wells and ~180 km of pipeline network, applying discrete, continuous and constrained optimisation techniques to maximise production, developing sustainable deployment workflows, implementing optimiser recommendations in the field and tracking incremental value realisation. This proof-of-concept Pilot and field trial approach was adopted to understand the optimisation technology capability and work-flow sustainability, prior to a field-wide roll-out. The periodic optimisation activity workflows include the creation of a "Digital Twin", a validated surface infrastructure model that is fully calibrated to mimic field performance, followed by performing optimisation that includes all the relevant constraints. Optimisation was trialled using two different classes of algorithms – based on sequential-modular and equation-oriented techniques. This strategy minimises optimisation failure risks and highlights potential performance issues for such large-scale systems. Optimiser recommendations were consolidated, field-implemented and values tracked. The optimiser Pilot development was undertaken during the fourth quarter of 2019. The delivered minimum viable product and workflows were used for field trials during 2019-20 and continuously improved based on the learnings. Specialists from both bp and Rosneft, along with three consulting organisations (1 in Russia and 2 in the UK) collaborated and worked as one-team to deliver the Pilot. Optimiser recommendations for maximising production include continuous and discrete decisions such as ESP frequency changes, high water-cut well shut-ins and prioritised ESP lists for installing variable speed drives. Field production increase of 1% was achieved in 2020 and tracked. Enduring capabilities were built, and sustainable work-flows developed. Field-wide optimisation for Samotlorneftegaz is non-trivial due to the sheer size, with over 9,000 active wells and due to continuously transient operations arising from frequent well-work, well shut-in's, new well delivery, pipeline modifications and cyclic mode of operations in some wells. This Pilot has provided assurance for the optimisation technical feasibility and workflow sustainability. A second Pilot of similar complexity but with different pressure-flow system response is planned. The combined results will help to decide about the full-field roll-out for this vast field, which is anticipated to deliver around 1% of additional production. This Pilot has demonstrated the applicability of discrete and continuous variable constrained optimisation techniques to large-scale production networks, with very high well-count. Furthermore, the developed workflows for configuring and calibrating the digital twin have several unique components including automation of hydraulic network model generation from static data, well model build automation and fit-for-purpose automated well model calibration. Overall, the results of this approach demonstrate a viable and sustainable methodology to optimise large-scale oil production systems.

Constrained optimisation of divisional load in hierarchically-organised tissues during homeostasis

It has been hypothesised that the structure of tissues and the hierarchy of differentiation from stem cell to terminally-differentiated cell play a significant role in reducing the incidence of cancer in that tissue. One specific mechanism by which this risk can be reduced is by minimising the number of divisions -- and hence the mutational risk -- that cells accumulate as they divide to maintain tissue homeostasis. Here we investigate a mathematical model of cell division in a hierarchical tissue, calculating and minimising the divisional load while constraining parameters such that homeostasis is maintained. We show that the minimal divisional load is achieved by binary division tress with progenitor cells incapable of self-renewal. Contrary to the protection hypothesis, we find that an increased stem cell turnover can lead to lower divisional load. Furthermore, we find that the optimal tissue structure depends on the time horizon of the duration of homeostasis, with faster stem cell division favoured in short-lived organisms and more progenitor compartments favoured in longer-lived organisms.

Analysis, Design, and Optimisation of an Electromagnetic Energy Harvester

One of two major limitations of a vibration energy harvester (VEH), concerns its limited performance due to its confined physical enclosure. The maximum span realizable is attained at a specific excitation level. This excitation level provides the maximum energy harvested by the VEH device. Due to span constraints, VEHs are designed to operate at the maximum span achievable at the maximum excitation level existing within the region of interest. In this study, a constrained optimisation problem (for the VEH) is formulated and investigated. This paper focuses on the analysis, design and optimisation of a nonlinear VEH device.

Stabilised explicit Adams-type methods

In this work we present explicit Adams-type multi-step methods with extended stability intervals, which are analogous to the stabilised Chebyshev Runge – Kutta methods. It is proved that for any k ≥ 1 there exists an explicit k-step Adams-type method of order one with stability interval of length 2k. The first order methods have remarkably simple expressions for their coefficients and error constant. A damped modification of these methods is derived. In the general case, to construct a k-step method of order p it is necessary to solve a constrained optimisation problem in which the objective function and p constraints are second degree polynomials in k variables. We calculate higher-order methods up to order six numerically and perform some numerical experiments to confirm the accuracy and stability of the methods.

When Will a Sequence of Points in a Riemannian Submanifold Converge?

Let X be a Riemannian manifold and xn a sequence of points in X. Assume that we know a priori some properties of the set A of cluster points of xn. The question is under what conditions that xn will converge. An answer to this question serves to understand the convergence behaviour for iterative algorithms for (constrained) optimisation problems, with many applications such as in Deep Learning. We will explore this question, and show by some examples that having X a submanifold (more generally, a metric subspace) of a good Riemannian manifold (even in infinite dimensions) can greatly help.

Multi-objective Beam-ACO for Maximising Reliability and Minimising Communication Overhead in the Component Deployment Problem

Automated deployment of software components into hardware resources is a highly constrained optimisation problem. Hardware memory limits which components can be deployed into the particular hardware unit. Interacting software components have to be deployed either into the same hardware unit, or connected units. Safety concerns could restrict the deployment of two software components into the same unit. All these constraints hinder the search for high quality solutions that optimise quality attributes, such as reliability and communication overhead. When the optimisation problem is multi-objective, as it is the case when considering reliability and communication overhead, existing methods often fail to produce feasible results. Moreover, this problem can be modelled by bipartite graphs with complicating constraints, but known methods do not scale well under the additional restrictions. In this paper, we develop a novel multi-objective Beam search and ant colony optimisation (Beam-ACO) hybrid method, which uses problem specific bounds derived from communication, co-localisation and memory constraints, to guide the search towards feasibility. We conduct an experimental evaluation on a range of component deployment problem instances with varying levels of difficulty. We find that Beam-ACO guided by the co-localisation constraint is most effective in finding high quality feasible solutions.

Abstract numbers and algebra in PETSc

<p><span>Scientific computing related to solving partial differential equations (PDEs) frequently employ both real and complex numbers, consequently computation libraries such as PETSc provide support for these number types and their associated algebra. Other “exotic” number types such dual numbers, hyper-dual numbers and intervals are also highly desirable in the context of solving PDEs, however these are seldom available within HPC linear algebra and or discretisation libraries. </span></p><p><span>I’m this presentation I will summarise several exotic number types and discuss some of their potential uses when solving: linear PDEs, non-linear PDEs, discrete adjoint problems and PDE constrained optimisation problems. Using these as motivation, I will also describe how these exotic numbers can be supported within PETSc. The approach adopted is general (extensible), non invasive and allows users to select the particular number type representation at run-time. Moreover the general design is well suited to the characteristics of modern computational hardware and thus can efficiently exploit different forms of parallelism. Through a series of toy problems, the cost and performance of the exotic number implementations will be assessed.</span></p>