A mathematical approach to solve the network reconstruction problem

The reconstruction of biochemical and genetic networks from experimental data is an important challenge in biology and medical basic research. We formalize this problem mathematically and present an exact algorithm for its solution. Our procedure yields either a complete list of all alternative network structures that explain the observed phenomena or proves that no solution exists using the given data set. This work was supported by the German Ministry of Education and Research (BMBF) through the FORSYS initiative.     

A parallel algorithm to solve the stable marriage problem

In this paper a parallel algorithm to solve the stable marriage problem is given. The worst case performance of this algorithm is stated. A theoretical analysis shows that the probability of the occurrence of this worst case is extremely small. For instance, if there are sixteen men and sixteen women involved, then the probability that the worst case occurs is only 10^–45. Possible future research is also discussed in this paper.     

A comparison of iterative methods to solve complex valued linear algebraic systems

Complex valued linear algebraic systems arise in many important applications. We present analytical and extensive numerical comparisons of some available numerical solution methods. It is advocated, in particular for large scale ill-conditioned problems, to rewrite the complex-valued system in real valued form leading to a two-by-two block system of particular form, for which it is shown that a very efficient and robust preconditioned iterative solution method can be constructed. Alternatively, in many cases it turns out that a simple preconditioner in the form of the sum of the real and the imaginary part of the matrix also works well but involves complex arithmetic.     

A note on two parallel algorithms to solve the stable marriage problem

Evidence is presented showing that the McVitie and Wilson algorithm to solve the stable marriage problem has a sequential component that is quite large on the average. Hence parallel implementations of the algorithm are likely to achieve only mediocre average case speedup. A corollary result is that an approximate solution with a few unstable pairings can be found much faster than an exact solution.     

A dual approach to solve the fuzzy linear programming problem

A concept of fuzzy objective based on the Fuzzification Principle is presented. In accordance with this concept, the Fuzzy Linear Mathematical Programming problem is easily solved. A relationship of duality among fuzzy constraints and fuzzy objectives is given. The dual problem of a Fuzzy Linear Programming problem is also defined.     

A neural network approach to solve the stable matching problem

In this paper two types of neurons, the maximum selection neuron and the maximum cut-off neuron are introduced. They are used to construct a neural network to represent and solve the stable matching problem. The neural network approach allows the matching to be processed dynamically in a distributed parallel processing environment.     

A graphical method to solve a maximin allocation problem

This note extends a simple graphical method of a solving resource allocation problem, the objective function being the sum of returns developed by Vidal to the case where the objective function is of a maximin type.     

A linearization approach to solve the natural gas cash-out bilevel problem

In this article, we discuss a particular imbalance cash-out problem arising in the natural gas supply chain. This problem was created by the liberalization laws that regulate deals between a natural gas shipping company and a pipeline operator. The problem was first modeled as a bilevel nonlinear mixed-integer problem that considers the cash-out penalization for the final imbalance occurring in the system. We extend the original problem’s upper level objective function by including additional terms accounting for the gas shipping company’s daily actions aimed at taking advantage of the price variations. Then we linearize all the constraints at both levels in an equivalent way so as to make easier their numerical solution. The results of numerical experiments are compared with those obtained by the inexact penalization method proposed by the authors in previous papers.     

A hybrid evolutionary algorithm to solve the job shop scheduling problem

This paper presents a Hybrid Evolutionary Algorithm (HEA) to solve the Job Shop Scheduling Problem (JSP). Incorporating a tabu search procedure into the framework of an evolutionary algorithm, the HEA embraces several distinguishing features such as a longest common sequence based recombination operator and a similarity-and-quality based replacement criterion for population updating. The HEA is able to easily generate the best-known solutions for 90 % of the tested difficult instances widely used in the literature, demonstrating its efficacy in terms of both solution quality and computational efficiency. In particular, the HEA identifies a better upper bound for two of these difficult instances.     

A MIP-based approach to solve the prize-collecting local access network design problem

This paper presents a new combinatorial optimization problem that can be used to model the deployment of broadband telecommunications systems in which optical fiber cables are installed between a central office and a number of end-customers. In this capacitated network design problem the installation of optical fiber cables with sufficient capacity is required to carry the traffic from the central office to the end-customers at minimum cost. In the situation motivating this research the network does not necessarily need to connect all customers (or at least not with the best available technology). Instead, some nodes are potential customers. The aim is to select the customers to be connected to the central server and to choose the cable capacities to establish these connections. The telecom company takes the strategic decision of fixing a percentage of customers that should be served, and aims for minimizing the total cost of the network providing this minimum service. For that reason the underlying problem is called the Prize-Collecting Local Access Network Design problem (PC-LAN).     

A branch-and-bound algorithm to solve the linear ordering problem for weighted tournaments

The linear ordering problem consists in finding a linear order at minimum remoteness from a weighted tournament T, the remoteness being the sum of the weights of the arcs that we must reverse in T to transform it into a linear order. This problem, also known as the search of a median order, or of a maximum acyclic subdigraph, or of a maximum consistent set, or of a minimum feedback arc set, is NP-hard; when all the weights of T are equal to 1, the linear ordering problem is the same as Slater's problem. In this paper, we describe the principles and the results of an exact method designed to solve the linear ordering problem for any weighted tournament. This method, of which the corresponding software is freely available at the URL address http://www.enst.fr/~charon/tournament/median.html, is based upon a branch-and-bound search with a Lagrangean relaxation as the evaluation function and a noising method for computing the initial bound. Other components are designed to reduce the BB-search-tree.     

How to solve a semi-infinite optimization problem

After an introduction to main ideas of semi-infinite optimization, this article surveys recent developments in theory and numerical methods for standard and generalized semi-infinite optimization problems. Particular attention is paid to connections with mathematical programs with complementarity constraints, lower level Wolfe duality, semi-smooth approaches, as well as branch and bound techniques in adaptive convexification procedures. A section on recent genericity results includes a discussion of the symmetry effect in generalized semi-infinite optimization.     

Using orthogonal discrete transforms to solve systems of linear algebraic equations

Two iterative methods with symmetric matrix inversion are proposed for solving systems of linear algebraic equations (SLAE). Orthogonal discrete transforms used for solving SLAE are robust to rounding errors, while at the same time they are fast and reduce computer memory requirements.Cherkassy Branch of Kiev Polytechnical Institute. Tomsk University. Translated from Vychislitel'naya i Prikladnaya Matematika, No. 74, pp. 17–19, 1992;     

Methods to solve multi-skill project scheduling problem

This is a summary of the author’s PhD thesis supervised by P. Martineau and E. Néron and defended on 28 November 2006 at the Université François-Rabelais de Tours. The thesis is written in French, and is available upon request from the author. This work deals with the problem of scheduling a project. The activities of this project requires skills that may not be mastered by all persons involved. First of all, the problem is defined in the introduction part. Then we propose different methods to solve it: lower bounds in part 2, different heuristics and meta-heuristics in part 3, and finally a branch-and-bound procedure in the last part.     

How to solve a design centering problem

This work considers the problem of design centering. Geometrically, this can be thought of as inscribing one shape in another. Theoretical approaches and reformulations from the literature are reviewed; many of these are inspired by the literature on generalized semi-infinite programming, a generalization of design centering. However, the motivation for this work relates more to engineering applications of robust design. Consequently, the focus is on specific forms of design spaces (inscribed shapes) and the case when the constraints of the problem may be implicitly defined, such as by the solution of a system of differential equations. This causes issues for many existing approaches, and so this work proposes two restriction-based approaches for solving robust design problems that are applicable to engineering problems. Another feasible-point method from the literature is investigated as well. The details of the numerical implementations of all these methods are discussed. The discussion of these implementations in the particular setting of robust design in engineering problems is new.     

A GRASP based on DE to solve single machine scheduling problem with SDST

When handling combinatorial optimization problems, we try to get the optimal arrangement of discrete entities so that the requirements and the constraints are satisfied. These problems become more and more important in various industrial and academic fields. So, over the past years, several techniques have been proposed to solve them. In this paper, we are interested in the single machine scheduling problem with Sequence-Dependent Setup Times, which can be solved through different approaches. We present a hybrid algorithm which combines Greedy Randomized Adaptive Search Procedure and Differential Evolution for tackling this problem. Our algorithm is tested on benchmark instances from the literature. The computational experiments prove the efficiency of this algorithm.     

Using artificial neural networks to solve the orienteering problem

In the orienteering problem, we are given a transportation network in which a start point and an end point are specified. Other points have associated scores. Given a fixed amount of time, the goal is to determine a path from start to end through a subset of locations in order to maximize the total path score. This problem has received a considerable amount of attention in the last ten years. The traveling salesman problem is a variant of the orienteering problem. This paper applies a modified, continuous Hopfield neural network to attack this NP-hard optimization problem. In it, we design an effective energy function and learning algorithm. Unlike some applications of neural networks to optimization problems, this approach is shown to perform quite well.     

An algorithm to solve the proportional network flow problem

The proportional network flow problem is a generalization of the equal flow problem on a generalized network in which the flow on arcs in given sets must all be proportional. This problem appears in several natural contexts, including processing networks and manufacturing networks. This paper describes a transformation on the underlying network that reduces the problem to the equal flow problem; this transformation is used to show that algorithms that solve the equal flow problem can be directly applied to the proportional network flow problem as well, with no increase in asymptotic running time. Additionally, computational results are presented for the proportional network flow problem demonstrating equivalent performance to the same algorithm for the equal flow problem.