Mark Wallace

Constraint Logic Programming using Eclipse

Providing an introduction to constraint programming, as well as a systematic introduction to the Eclipse system, this text shows how to write constraint programs that solve complex problems, and illustrates the power, versatility and utility of Eclipse.

The Effects of the Social Structure of Digital Networks on Viral Marketing Performance

Viral marketing is a form of peer-to-peer communication in which individuals are encouraged to pass on promotional messages within their social networks. Conventional wisdom holds that the viral marketing process is both random and unmanageable. In this paper, we deconstruct the process and investigate the formation of the activated digital network as distinct from the underlying social network. We then consider the impact of the social structure of digital networks (random, scale free, and small world) and of the transmission behavior of individuals on campaign performance. Specifically, we identify alternative social network models to understand the mediating effects of the social structures of these models on viral marketing campaigns. Next, we analyse an actual viral marketing campaign and use the empirical data to develop and validate a computer simulation model for viral marketing. Finally, we conduct a number of simulation experiments to predict the spread of a viral message within different types of social network structures under different assumptions and scenarios. Our findings confirm that the social structure of digital networks play a critical role in the spread of a viral message. Managers seeking to optimize campaign performance should give consideration to these findings before designing and implementing viral marketing campaigns. We also demonstrate how a simulation model is used to quantify the impact of campaign management inputs and how these learnings can support managerial decision making.

PRACTICAL APPLICATIONS OF CONSTRAINT PROGRAMMING

Constraint programming offers facilities for problem modelling, constraint propagation and search. This paper discusses the resulting benefits for practical applications which exploit these facilities.The modelling facilities are particularly exploited in applications to verification, both of circuits and of real time control systems. The propagation facilities are exploited in applications involving user feedback and graphical interfaces. The search facilities are exploited in applications such as scheduling and resource allocation, which involve combinatorial problems.The paper surveys applications under each of these three headings.

Probe Backtrack Search for Minimal Perturbation in DynamicScheduling

This paperdescribes an algorithm designed to minimally reconfigure schedulesin response to a changing environment. External factors havecaused an existing schedule to become invalid, perhaps due tothe withdrawal of resources, or because of changes to the setof scheduled activities. The total shift in the start and endtimes of already scheduled activities should be kept to a minimum.This optimization requirement may be captured using a linearoptimization function over linear constraints. However, the disjunctivenature of the resource constraints impairs traditional mathematicalprogramming approaches. The unimodular probing algorithm interleavesconstraint programming and linear programming. The linear programmingsolver handles only a controlled subset of the problem constraints,to guarantee that the values returned are discrete. Using probebacktracking, a complete, repair-based method for search, thesevalues are simply integrated into constraint programming. Unimodularprobing is compared with alternatives on a set of dynamic schedulingbenchmarks, demonstrating its effectiveness.In the final discussion, we conjecture that analogous probebacktracking strategies may obtain performance improvements overconventional backtrack algorithms for a broad range of constraintsatisfaction and optimization problems.

The Design of the Zinc Modelling Language

Zinc is a new modelling language developed as part of the G12 project. It has four important characteristics. First, Zinc allows specification of models using a natural mathematical-like notation. To do so it supports overloaded functions and predicates and automatic coercion and provides arithmetic, finite domain and set constraints. Second, while Zinc is a relatively simple and small language, it can be readily extended to different application areas by means of powerful language constructs such as user-defined predicates and functions and constrained types. Third, Zinc provides sophisticated type and instantiation checking which allows early detection of errors in models. Finally, perhaps the main novelty in Zinc is that it is designed to support a modelling methodology in which the same conceptual model can be automatically mapped into different design models, thus allowing modellers to easily “plug and play” with different solving techniques and so choose the most appropriate for that problem. We describe in detail the various language features of Zinc and the many trade-offs we faced in its design.

A new approach to integrating mixed integer programming and constraint logicprogramming

This paper represents an integration of Mixed Integer Programming (MIP) and ConstraintLogic Programming (CLP) which, like MIP, tightens bounds rather than adding constraintsduring search. The integrated system combines components of the CLP system ECLiPSe[7] and the MIP system CPLEX [5], in which constraints can be handled by either one orboth components. Our approach is introduced in three stages. Firstly, we present an automatictransformation which maps CLP programs onto such CLP programs that any disjunction iseliminated in favour of auxiliary binary variables. Secondly, we present improvements ofthis mapping by using a committed choice operator and translations of pre‐defined non‐linearconstraints. Thirdly, we introduce a new hybrid algorithm which reduces the solutionspace of the problem progressively by calling finite domain propagation of ECLiPSe aswell as dual simplex of CPLEX. The advantages of this integration are illustrated by efficientlysolving difficult optimisation problems like the Hoist Scheduling Problem [23]and the Progressive Party Problem [27].

Land use, transport, and population health: estimating the health benefits of compact cities

Using a health impact assessment framework, we estimated the population health effects arising from alternative land-use and transport policy initiatives in six cities. Land-use changes were modelled to reflect a compact city in which land-use density and diversity were increased and distances to public transport were reduced to produce low motorised mobility, namely a modal shift from private motor vehicles to walking, cycling, and public transport. The modelled compact city scenario resulted in health gains for all cities (for diabetes, cardiovascular disease, and respiratory disease) with overall health gains of 420-826 disability-adjusted life-years (DALYs) per 100 000 population. However, for moderate to highly motorised cities, such as Melbourne, London, and Boston, the compact city scenario predicted a small increase in road trauma for cyclists and pedestrians (health loss of between 34 and 41 DALYs per 100 000 population). The findings suggest that government policies need to actively pursue land-use elements-particularly a focus towards compact cities-that support a modal shift away from private motor vehicles towards walking, cycling, and low-emission public transport. At the same time, these policies need to ensure the provision of safe walking and cycling infrastructure. The findings highlight the opportunities for policy makers to positively influence the overall health of city populations.

Explaining the cumulative propagator

The global cumulative constraint was proposed for modelling cumulative resources in scheduling problems for finite domain (FD) propagation. Since that time a great deal of research has investigated new stronger and faster filtering techniques for cumulative, but still most of these techniques only pay off in limited cases or are not scalable. Recently, the “lazy clause generation” hybrid solving approach has been devised which allows a finite domain propagation engine possible to take advantage of advanced SAT technology, by “lazily” creating a SAT model of an FD problem as computation progresses. This allows the solver to make use of SAT explanation and autonomous search capabilities. In this article we show how, once we use lazy clause generation, modelling the cumulative constraint by decomposition creates a highly competitive version of cumulative. Using decomposition into component parts automatically makes the propagator incremental and able to explain itself. We then show how, using the insights from the behaviour of the decomposition, we can create global cumulative constraints that explain their propagation. We compare these approaches to explaining the cumulative constraint on resource constrained project scheduling problems. All our methods are able to close a substantial number of open problems from the well-established PSPlib benchmark library of resource-constrained project scheduling problems.

A Generic Model and Hybrid Algorithm for Hoist Scheduling Problems

This paper presents a robust approach to solve Hoist Scheduling Problems (HSPs) based on an integration of Constraint Logic Programming (CLP) and Mixed Integer Programming (MIP). By contrast with previous dedicated models and algorithms for solving classes of HSPs, we define only one model and run different solvers. The robust approach is achieved by using a CLP formalism. We show that our models for different classes of industrial HSPs are all based on the same generic model. In our hybrid algorithm search is separated from the handling of constraints. Constraint handling is performed by constraint propagation and linear constraint solving. Search is applied by labelling of boolean and integer variables. Computational experience shows that the hybrid algorithm, combining CLP and MIP solvers, solves classes of HSPs which cannot be handled by previous dedicated algorithms. For example, the hybrid algorithm derives an optimal solution, and proves its optimality, for multiple-hoists scheduling problems.

Hybrid Benders Decomposition Algorithms in Constraint Logic Programming

Benders Decomposition is a form of hybridisation that allows linear programming to be combined with other kinds of algorithms. It extracts new constraints for one subproblem from the dual values of the other subproblem. This paper describes an implementation of Benders Decomposition, in the ECLiPSe language, that enables it to be used within a constraint programming framework. The programmer is spared from having to write down the dual form of any subproblem, because it is derived by the system. Examples are used to show how problem constraints can be modelled in an undecomposed form. The programmer need only specify which variables belong to which subproblems, and the Benders Decomposition is extracted automatically. A class of minimal perturbation problems is used to illustrate how different kinds of algorithms can be used for the different subproblems. The implementation is tested on a set of minimal perturbation benchmarks, and the results are analysed.