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.

Making Multiple Decisions Adaptively

The asymptotic behavior of multiple decision procedures is studied when the underlying distributions depend on an unknown nuisance parameter. An adaptive procedure must be asymptotically optimal for each value of this nuisance parameter, and it should not depend on its value. A necessary and sufficient condition for the existence of such a procedure is derived. Several examples are investigated in detail, and possible lack of adaptation of the traditional overall maximum likelihood rule is discussed.

An Electromagnetism Metaheuristic for the Uncapacitated Multiple Allocation Hub Location Problem

In this article, the results achieved by applying an electromagnetism (EM) inspired metaheuristic to the uncapacitated multiple allocation hub location problem (UMAHLP) are discussed. An appropriate objective function which natively conform with the problem, 1-swap local search and scaling technique conduce to good overall performance.Computational tests demonstrate the reliability of this method, since the EM-inspired metaheuristic reaches all optimal/best known solutions for UMAHLP, except one, in a reasonable time.

Optimization Problem in a Class of Linear System. Application to Multiple Drug Administration

2000 Mathematics Subject Classification: 62H15, 62P10.

On Multiple Deletion Codes

In 1965 Levenshtein introduced the deletion correcting codes and found an asymptotically optimal family of 1-deletion correcting codes. During the years there has been a little or no research on t-deletion correcting codes for larger values of t. In this paper, we consider the problem of finding the maximal cardinality L2(n;t) of a binary t-deletion correcting code of length n. We construct an infinite family of binary t-deletion correcting codes. By computer search, we construct t-deletion codes for t = 2;3;4;5 with lengths n ≤ 30. Some of these codes improve on earlier results by Hirschberg-Fereira and Swart-Fereira. Finally, we prove a recursive upper bound on L2(n;t) which is asymptotically worse than the best known bounds, but gives better estimates for small values of n.

Some Computational Aspects of the Consistent Mass Finite Element Method for a (semi-)periodic Eigenvalue Problem

We consider a model eigenvalue problem (EVP) in 1D, with periodic or semi–periodic boundary conditions (BCs). The discretization of this type of EVP by consistent mass finite element methods (FEMs) leads to the generalized matrix EVP Kc = λ M c, where K and M are real, symmetric matrices, with a certain (skew–)circulant structure. In this paper we fix our attention to the use of a quadratic FE–mesh. Explicit expressions for the eigenvalues of the resulting algebraic EVP are established. This leads to an explicit form for the approximation error in terms of the mesh parameter, which confirms the theoretical error estimates, obtained in [2].

About the Multi Criteria Ranging Problem in the Fuzzy Environment

Decision making and technical decision analysis demand computer-aided techniques and therefore more and more support by formal techniques. In recent years fuzzy decision analysis and related techniques gained importance as an efficient method for planning and optimization applications in fields like production planning, financial and economical modeling and forecasting or classification. It is also known, that the hierarchical modeling of the situation is one of the most popular modeling method. It is shown, how to use the fuzzy hierarchical model in complex with other methods of Multiple Criteria Decision Making. We propose a novel approach to overcome the inherent limitations of Hierarchical Methods by exploiting multiple criteria decision making.

Quadratic Time Computable Instances of MaxMin and MinMax Area Triangulations of Convex Polygons

We consider the problems of finding two optimal triangulations of a convex polygon: MaxMin area and MinMax area. These are the triangulations that maximize the area of the smallest area triangle in a triangulation, and respectively minimize the area of the largest area triangle in a triangulation, over all possible triangulations. The problem was originally solved by Klincsek by dynamic programming in cubic time [2]. Later, Keil and Vassilev devised an algorithm that runs in O(n^2 log n) time [1]. In this paper we describe new geometric findings on the structure of MaxMin and MinMax Area triangulations of convex polygons in two dimensions and their algorithmic implications. We improve the algorithm’s running time to quadratic for large classes of convex polygons. We also present experimental results on MaxMin area triangulation.

A Method for Solving a Class of Multiple-Criteria Analysis Problems

AMS subject classification: 90C29.

Class Number Two for Real Quadratic Fields of Richaud-Degert Type

2000 Mathematics Subject Classification: Primary: 11D09, 11A55, 11C08, 11R11, 11R29; Secondary: 11R65, 11S40; 11R09.

On Special Case of Multiple Hypotheses Optimal Testing for Three Differently Distributed Random Variables

2000 Mathematics Subject Classification: 62P30.