Interactive constraint systems often suffer from infeasibility (no solution) due to conflicting user constraints. A common approach to recover feasibility is to eliminate the constraints that cause the conflicts in the system. This approach allows the system to provide an explanation as: “if the user is willing to drop some of their constraints, there exists a solution”. However, this form of explanation might not be very informative. A counter-factual explanation is a type of explanation that can provide a basis for the user to recover feasibility by helping them understand what changes can be applied to their existing constraints rather than removing them. We propose an efficient approach NoPropCounter-factualXplain to find counter-factual explanations for infeasible problems. We also propose a version of this algorithm which takes into account preferences called PrefnoPropCounter-factualXplain. We showcase it's usability in real world scenario using the producer/consumer constraint which is useful in problems which involve resource allocation.

This paper presents the hybrid, flexible flowshop problem with transportation times between stages, which is an extension of an existing scheduling problem that is well-studied in the literature. We explore different models for the problem with Constraint Programming, MILP, and local search, and compare them on generated benchmark problems that reflect the problem of the industrial partner. We then study two different factory layout design problems, and use the optimization tool to understand the impact of the design choices on the solution quality.

In this paper we describe a complex optimization application arising in maintenance scheduling, developed in close collaboration with an industrial partner. We have to plan and schedule preventive and corrective maintenance activities at customer sites by a group of traveling repair technicians. A specific property of the problem considered here is a mix of customers in both urban centers and rural areas. This means that travel times between customers must be considered when balancing overall workload for each agent. We discuss a problem decomposition compatible with current management practice, describe different solvers for the individual problem steps, and show results on real-world data from the industrial partner.

Boliden Tara Mines Ltd. consumed 184.7 GWh of electricity in 2014, equating to over 1% of the national demand of Ireland or approximately 35,000 homes. Ireland’s industrial electricity prices, at an average of 13 c/KWh in 2014, are amongst the most expensive in Europe. Cost effective electricity procurement is ever more pressing for businesses to remain competitive. In parallel, the proliferation of intelligent devices has led to the industrial Internet of Things paradigm becoming mainstream. As more and more devices become equipped with network connectivity, smart metering is fast becoming a means of giving energy users access to a rich array of consumption data. These modern sensor networks have facilitated the development of applications to process, analyse, and react to continuous data streams in real-time. Subsequently, future procurement and consumption decisions can be informed by a highly detailed evaluation of energy usage. With these considerations in mind, this paper uses variable energy prices from Ireland’s Single Electricity Market, along with smart meter sensor data, to simulate the scheduling of an industrial-sized underground pump station in Tara Mines. The objective is to reduce the overall energy costs whilst still functioning within the system’s operational constraints. An evaluation using real-world electricity prices and detailed sensor data for 2014 demonstrates significant savings of up to 10.72% over the year compared to the existing control systems.

Data centre energy requirements have grown massively in the last few years. One of the optimisation challenges for reducing its energy requirements is to keep servers well utilised by deciding which Virtual Machines (VMs) to migrate, where to migrate, when to migrate, and, when and which servers to switch on/off. Achieving this goal optimally requires the capability of predicting the future time-variable resource demands of VMs accurately and computing the plan for migrating VMs for efficient workload consolidation quickly. We call this Proactive Workload Consolidation Problem (PWCP). Solving PWCP as a giant monolithic problem with infinite time windows is impossible both for forecasting demands and optimal assignments of VMs to servers. We formulate PWCP in a more realistic way by defining a time window of a particular size in which the information is known more accurately and solve a - possibly infinite - sequence of optimisation problems moving forwards in time. The question is how far one is required to look ahead in terms of the number time-periods and still retain the minimum energy cost of a given horizon without violating the Service Level Agreements (SLAs). We perform investigations to understand the relationship between the number of time-periods considered in one optimisation step and migration-limits on the SLAs, energy cost, server-transition cost and migration cost. Our results suggest that looking ahead by only a few more time-periods can lead to more efficient resource provisioning over the entire horizon and consequently higher energy efficiency and close to no SLA violations.

We consider a network design problem arising in the development of an all-optical future generation Internet network called a flex-grid. An optical island is a set of core nodes that can be fully interconnected by transparent wavelength routes. We present a mathematical model for finding an optimal optical island, show that it is an NP-hard problem, and present a decomposition for solving it. In a first phase, we choose network links and route the traffic over the resulting network. In the second phase, we allocate the light-paths associated with the traffic requests to individual fibres and spectrum segments on the fibres. This so-called routing and spectrum assignment (RSA) problem is a generalisation of the well-known routing and wavelength assignment problem (RWA) of conventional optical networks. Flex-grid optical networks allow us to bundle higher capacity connection requests by allocating channels in a number of contiguous frequency slots, providing increased throughput, as long as the connection length is below technological limits. We solve the first part of the decomposition with a large neighborhood search, and the second with a CP model using a single GEOST global constraint. Results for Ireland and Italy show that solutions of high quality can be found by this decomposition.

We describe a constraint-based timetabling system that was developed for the dental school based at Cork University Hospital in Ireland. This system has been deployed since 2010. Dental school timetabling differs from other university course scheduling in that certain clinic sessions can be used by multiple courses at the same time, provided a limit on room capacity is satisfied. Starting from a constraint programming solution using a web interface, we have moved to a mixed integer programming-based solver to deal with multiple objective functions, along with a dedicated Java application, which provides a rich user interface. Solutions for the years 2010, 2011 and 2012 have been used in the dental school, replacing a manual timetabling process, which could no longer cope with increasing student numbers and resulting resource bottlenecks. The use of the automated system allowed the dental school to increase student numbers to the maximum possible given the available resources. It also provides the school with a valuable “what-if” analysis tool.

We provide a filtering algorithm achieving GAC for the conjunction of constraints atleast (b, [x(0),x(1),...,x(n-1)], V) and (a(0)*x(0) +...+ a(n-1)*x(n-1)) <= c, where the atleast constraint enforcesb variables out of x(0), x(1), ..., x(n-1) to be assigned to avalue in the set V. This work was motivated by learning simplepolynomials, i.e. finding the coefficients of polynomialsin several variables from example parameter and function values.We additionally require that coefficients be integers, andthat most coefficients be assigned to zero or integers close to0. These problems occur in the context of learning constraintmodels from sample solutions of different sizes. Experimentswith this more global filtering show an improvement by severalorders of magnitude compared to handling the constraintsin isolation or with cost gcc, while also out-performing a0/1 MIP model of the problem.

Reliability and/or availability are increasingly important aspects in the design of systems, especially networks and service offerings. Optimization here is a multi-criteria process finding the right compromise between cost and quality. At the same time, results should be explored online, either as part of interactive, user-centric design tools or for Web based service negotiation. In this paper we consider a generic method for multi-criteria optimization based on reliability/availability graphs, but also provide a more specialized solution for dealing with the widely used reliability/availability block diagrams. Initial experiments show that the techniques can be applied to realistic problem sizes from the literature.