A Mixed Integer Quadratic Programming Model for the Low Autocorrelation Binary Sequence Problem

In this paper the low autocorrelation binary sequence problem (LABSP) is modeled as a mixed integer quadratic programming (MIQP) problem and proof of the model’s validity is given. Since the MIQP model is semidefinite, general optimization solvers can be used, and converge in a finite number of iterations. The experimental results show that IQP solvers, based on this MIQP formulation, are capable of optimally solving general/skew-symmetric LABSP instances of up to 30/51 elements in a moderate time. ACM Computing Classification System (1998): G.1.6, I.2.8.This research was partially supported by the Serbian Ministry of Education and Science under projects 174010 and 174033

An electromagnetism-like method for the maximum set splitting problem

In this paper, an electromagnetism-like approach (EM) for solving the maximum set splitting problem (MSSP) is applied. Hybrid approach consisting of the movement based on the attraction-repulsion mechanisms combined with the proposed scaling technique directs EM to promising search regions. Fast implementation of the local search procedure additionally improves the efficiency of overall EM system. The performance of the proposed EM approach is evaluated on two classes of instances from the literature: minimum hitting set and Steiner triple systems. The results show, except in one case, that EM reaches optimal solutions up to 500 elements and 50000 subsets on minimum hitting set instances. It also reaches all optimal/best-known solutions for Steiner triple systems

Using SVG–XML FOR representation of historical graphical data

Modern data representation requires XML-based approach. One of the ways to represent any kind of graphical data in electronic form is to use Scalable Vector Graphics (SVG). So, XML and SVG are ideal means for the digital representation of national heritage. Moreover, for the powerful using of SVG one should learn a very complex syntax and related XML applications. In this paper the advantages and drawbacks of SVG, in processing of national heritage, are specified. Some examples about processing frescos and manuscripts are presented

An Electromagnetism-Like Approach for Solving the Low Autocorrelation Binary Sequence Problem

In this paper an electromagnetism-like approach (EM) for solving the low autocorrelation binary sequence problem (LABSP) is applied. This problem is a notoriously difficult computational problem and represents a major challenge to all search algorithms. Although EM has been applied to the topic of optimization in continuous space and a small number of studies on discrete problems, it has potential for solving this type of problems, since movement based on the attraction-repulsion mechanisms combined with the proposed scaling technique directs EM to promising search regions. Fast implementation of the local search procedure additionally improves the efficiency of the overall EM system

Solving the Task Assignment Problem with a Variable Neighborhood Search

In this paper a variable neighborhood search (VNS) approach for the task assignment problem (TAP) is considered. An appropriate neighborhood scheme along with a shaking operator and local search procedure are constructed specifically for this problem. The computational results are presented for the instances from the literature, and compared to optimal solutions obtained by the CPLEX solver and heuristic solutions generated by the genetic algorithm. It can be seen that the proposed VNS approach reaches all optimal solutions in a quite short amount of computational time.* This research was partially supported by the Serbian Ministry of Science and Ecology under project 144007

A new lower bound for doubly metric dimension and related extremal differences

In this paper a new graph invariant based on the minimal hitting set problem is introduced. It is shown that it represents a tight lower bound for the doubly metric dimension of a graph. Exact values of new invariant for paths, stars, complete graphs and complete bipartite graph are obtained. The paper analyzes some tight bounds for the new invariant in general case. Also several extremal differences between some related invariants are determined

Genetic Algorithm Approach for Solving the Task Assignment Problem

This research was partially supported by the Serbian Ministry of Science and Ecology under project 144007. The authors are grateful to Ivana Ljubić for help in testing and to Vladimir Filipović for useful suggestions and comments.In this paper a genetic algorithm (GA) for the task assignment problem (TAP) is considered.An integer representation with standard genetic operators is used. Computational results are presented for instances from the literature, and compared to optimal solutions obtained by the CPLEX solver. It can be seen that the proposed GA approach reaches 17 of 20 optimal solutions. The GA solutions are obtained in a quite a short amount of computational time