The classical Quadratic Programming formulation of the well known portfolio selection problem, is cumbersome, time consuming and relies on two important assumptions: (a) the expected return is multivariate normally distributed; (b) the investor is risk averter. This paper formulates two alternative models, (i) maximin, and (ii) minimization of absolute deviation. Data from a very simple … Read more
Abstract: The SDPA (SemiDefinite Programming Algorithm) is known as efficient computer software based on primal-dual interior-point method for solving SDPs (Semidefinite Programs). In many applications, however, some SDPs become larger and larger, too large for the SDPA to solve on a single processor. In execution of the SDPA applied to large scale SDPs, the computation … Read more
Given an undirected graph G with nonnegative edges costs and nonnegative vertex penalties, the prize collecting Steiner problem in graphs (PCSPG) seeks a tree of G with minimum weight. The weight of a tree is the sum of its edge costs plus the sum of the penalties of those vertices not spanned by the tree. … Read more
Scheduling a sequence of tasks – in the acceptation of finding the execution times – is not a trivial problem when the optimization criterion is irregular as for instance in earliness-tardiness problems. This paper presents an efficient Dynamic Programming algorithm to solve the problem with general cost functions depending on the end time of the … Read more
It is with the aim of solving scheduling problems with irregular cost functions that this paper focuses on the continuous assignment problem. It consists in partitioning a d dimensional region into subregions of prescribed volumes so that the total cost is minimized. The dual problem of the continuous assignment problem is an unconstrained maximisation of … Read more
The hierarchical network problem is the problem of finding the least cost network, with nodes divided into groups, edges connecting nodes in each groups and groups ordered in a hierarchy. The idea of hierarchical networks comes from telecommunication networks where hierarchies exist. Hierarchical networks are described and a mathematical model is proposed for a two … Read more
We investigate the polyhedral structure of an integer program with a single functional constraint: the integer capacity-cover polyhedron. Such constraints arise in telecommunications planning and facility location applications, and feature the use of general integer (rather than just binary) variables. We derive a large class of facet-defining inequalities by using an augmenting technique that builds … Read more
This thesis is about mathematical optimization. Mathematical optimization involves the construction of methods to solve optimization problems, which can arise from real-life problems in applied science, when they are mathematically modeled. Examples come from electrical design, engineering, control theory, telecommunication, environment, finance, and logistics. This thesis deals especially with semidefinite optimization problems. Semidefinite programming is … Read more
Bound-constrained global optimization helps answer many practical questions in chemistry, molecular biology, economics. Most of algorithms for solution of global optimization problems are a combination of interval methods and exhuastive search. The efficiency of such algorithms is characterized by their ability to detect and eliminate sub-optimal feasible regions. This ability is increased by availability of … Read more
This paper presents a hybrid genetic algorithm for the Job Shop Scheduling problem. The chromosome representation of the problem is based on random keys. The schedules are constructed using a priority rule in which the priorities are defined by the genetic algorithm. Schedules are constructed using a procedure that generates parameterized active schedules. After a … Read more