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Transformation of Logical Specification into IP-formulas

Qiang Li, Tetsuo Ida
Institute of Information Sciences and Electronics
University of Tsukuba, Japan;

Yike Guo
Department of Computing
Imperial College, London, UK

The classical algebraic modeling approach for integer programming (IP) is not suitable for some real-world IP problems, since the algebraic formulations allow only for the description of mathematical relations, not logical relations. In this paper, we present a language L+ for IP, in which we write a logical specification of an IP problem. L+ is a language based on predicate logic but extended with meta predicates such as "at least" (m, S), where m is a non-negative integer, meaning that at least m predicates in the set S of formulas hold. The meta predicates are introduced to facilitate reasoning about a model of an IP problem rigorously and logically. Using Mathematica, we can represent the logical formulas, called "L+ formulas", efficiently and completely, and we can define a set of transformation rules and transform L+ formulas into IP formulas, finally simplifying the IP formulas in Mathematica. Also, by using MathLink and CGI programming, we develop a web-based interface to support the system with modeling language, transformation of IP, and IP solvers. This provides a web-based client-server model, in which the power of high-level IP modeling and high-performance IP solving can be integrated and developed for a wide range of business users to solve large-scale decision-making problems. The primary experiment indicates that Mathematica is a powerful tool for representing logical formulas and for the transformation of formulas and that MathLink is convenient for connecting Mathematica to other software platforms.

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