We study a class of non-convex optimization problems involving sigmoid functions. We show that sigmoid functions impart a combinatorial element to the optimization variables and make the global optimization computationally hard. We formulate versions of the knapsack problem, the generalized...

In this paper we suggest a new e.cient technique for solving integer knapsack problems. Our algorithms can be seen as application of Fast Fourier Transform to generating functions of integer polytopes.Using this approach, it is possible to count the number of boolean solutions of a single...

In this paper we analyze computational performance of dual trigonometric generating functions on some integer programming problems. We show that if the number of equality constraints is fixed, then this technique allows to solve the problems in time, which is polynomial in the dimension of the...

В этом исследовании рассмотрено применение классической задачи 0-1 ранце с одним ограничением для решения задачи выбора пакетов телевизионной рекламы в...

In this paper we discuss a solver that is developed to solve set partitioning problems.The methods used include problem reduction techniques, lagrangean relaxation and primal and dual heuristics.The optimal solution is found using a branch and bound approach.In this paper we discuss these...

This article proposes a novel approach to construct optimal balanced multi-level supersaturated designs using linear integer programming. We illustrate the approach with an example. Using the proposed approach, we construct and catalogue optimal balanced multi-level supersaturated designs in the...