58,184 research outputs found
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Transformation of propositional calculus statements into integer and mixed integer programs: An approach towards automatic reformulation
A systematic procedure for transforming a set of logical statements or logical conditions imposed on a model into an Integer Linear Progamming (ILP) formulation Mixed Integer Programming (MIP) formulation is presented. An ILP stated as a system of linear constraints involving integer variables and an objective function, provides a powerful representation of decision problems through a tightly interrelated closed system of choices. It supports direct representation of logical (Boolean or prepositional calculus) expressions. Binary variables (hereafter called logical variables) are first introduced and methods of logically connecting these to other variables are then presented. Simple constraints can be combined to construct logical relationships and the methods of formulating these are discussed. A reformulation procedure which uses the extended reverse polish representation of a compound logical form is then described. These reformulation procedures are illustrated by two examples. A scheme of implementation.ithin an LP modelling system is outlined
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Linear, integer separable and fuzzy programming problems: a united approach towards automatic reformulation
For mathematical programming (MP) to have greater impact as a
decision tool, MP software systems must offer suitable support in
terms of model communication and modelling techniques. In this
paper modelling techniques that allow logical restrictions to be
modelled in integer programming terms are described and their
implications discussed. In addition it is demonstrated that many
classes of non-linearities which are not variable separable may be
after suitable algebraic manipulation put in a variable separable
form. The methods of reformulating the fuzzy linear programming
problem as a Max-Min problem is also introduced. It is shown that
analysis of bounds plays a key role in the following four important
contexts: model reduction, reformulation of logical restrictions
as 0-1 mixed integer programs, reformulation of nonlinear programs
as variable separable programs and reformulation of fuzzy linear
programs. It is observed that as well as incorporating an
interface between the modeller and the optimiser there is a need to
make available to the modeller software facilities which support the
model reformulation techniques described here
An algebraic basis for specifying and enforcing access control in security systems
Security services in a multi-user environment are often based on access control mechanisms. Static aspects of an access control policy can be formalised using abstract algebraic models. We integrate these static aspects into a dynamic framework considering requesting access to resources as a process aiming at the prevention of access control violations when a program is executed. We use another algebraic technique, monads, as a meta-language to integrate access control operations into a functional
programming language. The integration of monads and concepts from a denotational model for process algebras provides a framework for programming of access control in security systems
Spatial optimization for land use allocation: accounting for sustainability concerns
Land-use allocation has long been an important area of research in regional science. Land-use patterns are fundamental to the functions of the biosphere, creating interactions that have substantial impacts on the environment. The spatial arrangement of land uses therefore has implications for activity and travel within a region. Balancing development, economic growth, social interaction, and the protection of the natural environment is at the heart of long-term sustainability. Since land-use patterns are spatially explicit in nature, planning and management necessarily must integrate geographical information system and spatial optimization in meaningful ways if efficiency goals and objectives are to be achieved. This article reviews spatial optimization approaches that have been relied upon to support land-use planning. Characteristics of sustainable land use, particularly compactness, contiguity, and compatibility, are discussed and how spatial optimization techniques have addressed these characteristics are detailed. In particular, objectives and constraints in spatial optimization approaches are examined
Integrating nurse and surgery scheduling.
Scheduling; Surgery scheduling; International; Theory; Applications; Euro; Researchers;
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Software tools for stochastic programming: A Stochastic Programming Integrated Environment (SPInE)
SP models combine the paradigm of dynamic linear programming with
modelling of random parameters, providing optimal decisions which hedge
against future uncertainties. Advances in hardware as well as software
techniques and solution methods have made SP a viable optimisation tool.
We identify a growing need for modelling systems which support the creation
and investigation of SP problems. Our SPInE system integrates a number of
components which include a flexible modelling tool (based on stochastic
extensions of the algebraic modelling languages AMPL and MPL), stochastic
solvers, as well as special purpose scenario generators and database tools.
We introduce an asset/liability management model and illustrate how SPInE
can be used to create and process this model as a multistage SP application
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