We study a particular case of integer polynomial optimization: Minimize a polynomial F̂ on the set of integer points described by an inequality system F1 ≤ 0, . . . , Fs ≤ 0, where F̂ , F1, . . . , Fs are quasiconvex polynomials in n variables with integer coefficients. We design an algorithm solving this problem that belongs to the time-complexity class O(s) · lO(1) · dO(n) · 2O(n 3), where d ≥ ...

the set covering problem (scp) is a well-known combinatorial optimization problem. this paper investigates development of a local branching approach for the scp. this solution strategy is exact in nature, though it is designed to improve the heuristic behavior of the mixed integer programming solver. the algorithm parameters are tuned by design of experiments approach. the proposed method is te...

In this paper a novel method based on evolutionary algorithms is presented to estimate the harmonic components. In general, the optimization of the harmonic estimation process is a multi-component problem, in which evaluation of the phase and harmonic frequency is the nonlinear part of the problem and is solved based on the mathematical and evolutionary methods; while estimation of amplitude of...

A novel application to the optimization of neural networks is presented in this paper. Here, the weight and architecture optimization of neural networks can be formulated as a mixed-integer optimization problem. And then a mixed-integer evolutionary algorithm (Mixed-Integer Hybrid Differential Evolution, MIHDE) is used to optimize the neural network. Finally, the optimized neural network is app...

presented here is a generalization of the implicit enumeration algorithm that can be applied when the objec-tive function is being maximized and can be rewritten as the difference of two non-decreasing functions. also developed is a computational algorithm, named linear speedup, to use whatever explicit linear constraints are present to speedup the search for a solution. the method is easy to u...

We present a version of GMI (Gomory mixed-integer) cuts in a way so that they are derived with respect to a “dual form” mixed-integer optimization problem and applied on the standard-form primal side as columns, using the primal simplex algorithm. This follows the general scheme of He and Lee, who did the case of Gomory pure-integer cuts. Our input mixed-integer problem is not in standard form,...

Integer programming is a combinatorial optimization method that has been successfully applied to the protein threading problem. We seek to expand the model optimized by this technique to allow for a more accurate description of protein threading. We have developed and implemented an expanded model of integer programming that has the capability to model secondary structure element deletion, whic...

This paper presents particle swarm optimization (PSO) method to find the prime factors of a composite number. Integer factorization is a well known NP hard problem and security of many cryptosystem is based on difficulty of integer factorization. A particle swarm optimization algorithm for integer factorization has been devised and tested on different 100 numbers. It has been found that the PSO...