Logic, modeling, and programming

In this paper we discuss the integration of logic, modeling, and programming in order to solve problems in operations research, artificial intelligence, and decision support programming in general. Our goals are to integrate modeling into the larger programming scheme of things and, conversely, to inject programming into modeling. To accomplish these ends, we use the language 2LP, which is based on ideas from constraint logic programming. This leads to a technologically open way to handle problems, one which supports flexible treatment of goal programming, hybrid MIP/local search algorithms, libraries for distributed processing, disjunctive programming, etc. An additional advantage of the programming language approach is that problem solving and model management can be abetted by software engineering techniques. In this paper, by means of variations on a single example, we will illustrate how the logical connectives and linear constraints interact in the solution of a linear program, a goal program, a disjunctive program, a branch and bound search, a randomized shuffle algorithm, and a parallel solution to a model with stochastic data.