The paper deals with the problems that arise while developing software of such distributed systems as real-time, computer network protocols and distributed information-processing systems. In the introduction, some ess...
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The paper deals with the problems that arise while developing software of such distributed systems as real-time, computer network protocols and distributed information-processing systems. In the introduction, some essential peculiarities typical of distributed systems (DS) and a general scheme for developing such systems are presented. The main idea of this paper is the use of a piece-linear aggregate mathematical method for formal specification, simulation and validation of DS. The main advantage of this approach is that it integrates two tasks of differing nature, i.e. simulation and correctness analysis of specification, on the basis of a single specification. The method of a transformation of aggregate specification to the first-order predicates and its further use for the correctness analysis of the aggregate specification using logic-based programming will also be presented. It will also be shown how to transform an informal description of system functioning to aggregate specification using production rules. The presented methods are explained using illustrative examples.
This paper presents a review of advances in the mathematical programming approach to discrete/continuous optimization problems. We first present a brief review of MILP and MINLP for the case when these problems are mo...
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This paper presents a review of advances in the mathematical programming approach to discrete/continuous optimization problems. We first present a brief review of MILP and MINLP for the case when these problems are modeled with algebraic equations and inequalities. Since algebraic representations have some limitations such as difficulty of formulation and numerical singularities for the nonlinear case, we consider logic-based modeling as an alternative approach, particularly Generalized Disjunctive programming (GDP), which the authors have extensively investigated over the last few years. Solution strategies for GDP models are reviewed, including the continuous relaxation of the disjunctive constraints. Also, we briefly review a hybrid model that integrates disjunctive programming and mixed-integer programming. Finally, the global optimization of nonconvex GDP problems is discussed through a two-level branch and bound procedure.
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