Cláudio Nogueira de Meneses

Global optimization by continuous grasp

We introduce a novel global optimization method called Continuous GRASP (C-GRASP) which extends Feo and Resende’s greedy randomized adaptive search procedure (GRASP) from the domain of discrete optimization to that of continuous global optimization. This stochastic local search method is simple to implement, is widely applicable, and does not make use of derivative information, thus making it a well-suited approach for solving global optimization problems. We illustrate the effectiveness of the procedure on a set of standard test problems as well as two hard global optimization problems.

Optimization techniques for string selection and comparison problems in genomics

In this article, a discussion of optimization issues occurring in the area of genomics such as string comparison and selection problems are discussed. With this objective, an important part of the existing results in this area will be discussed. The problems that are of interest in this paper include the closest string problem (CSP), closest substring problem (CSSP), farthest string problem (FSP), farthest substring problem (FSSP), and far from most string (FFMSP) problem. The paper presents a detailed view of the most important problems occurring in the area of string comparison and selection, using the Hamming distance measure is given.

A parallel multistart algorithm for the closest string problem

In this paper we describe and implement a parallel algorithm to find approximate solutions for the Closest String Problem (CSP). The CSP, also known as Motif Finding problem, has applications in Coding Theory and Computational Biology. The CSP is NP-hard which motivates us to think about heuristics to solve large instances. Several approximation algorithms have been designed for the CSP, but all of them have a poor performance guarantee. Recently some researchers have shown empirically that integer programming techniques can be successfully used to solve moderate-size instances (10-30 strings each of which is 300-800 characters long) of the CSP. However, real-world instances are larger than those tested. In this paper we show how a simple heuristic can be used to find near-optimal solutions to that problem. We implemented a parallel version of this heuristic and report computational experiments on large-scale instances. These results show the effectiveness of our approach.

A New Approach to the Non-unique Probe Selection Problem

Identification of biological agents in a sample is a relevant problem in medicine. A model to this problem consists of selecting optimal oligonucleotide probe sets for use in hybridization experiments in which target viruses or bacteria are to be identified in biological samples. In such an experiment the presence or absence of these targets is determined by observing whether selected probes bind to their corresponding sequences. The problem is to select a probe set that is able to uniquely identify targets while containing a minimal number of probes. In this paper we describe a heuristic algorithm that produced feasible solution sets that for large, real data sets contain significantly fewer probes than those obtained using other methods. A description of the problem, our approach, and the results are presented. We developed a C++ program and a GUI (Graphical User Interface) to run real and simulated instances of the problem.

A continuous GRASP to determine the relationship between drugs and adverse reactions

Adverse drag reactions (ADRs) are estimated to be one of the leading causes of death. Many national and international agencies have set up databases of ADR reports for the express purpose of determining the relationship between drugs and adverse reactions that they cause. We formulate the drug‐reaction relationship problem as a continuous optimization problem and utilize C‐GRASP, a new continuous global optimization heuristic, to approximately determine the relationship between drugs and adverse reactions. Our approach is compared against others in the literature and is shown to find better solutions.

Asynchronous Teams for probe selection problems

The selection of probe sets for hybridization experiments directly affects the efficiency and cost of the analysis. We propose the application of the Asynchronous Team (A-Team) technique to determine near-optimal probe sets. An A-Team is comprised of several different heuristic algorithms that communicate with each other via shared memories. The A-Team method has been applied successfully to several problems including the Set Covering Problem, the Traveling Salesman Problem, and the Point-to-Point Connection Problem, and lends itself well to the Probe Selection Problem. We designed and developed a C + + program to run instances of the Minimum Cost Probe Set and Maximum Distinguishing Probe Set problems. A program description and our results are presented in the paper.

Mathematical Programming Formulations for Problems in Genomics and Proteomics

Computational biology problems generally involve the determination of discrete structures over biological configurations determined by genomic or proteomic data. Such problems present great opportunities for application of mathematical programming techniques. We give an overview of formulations employed for the solution of problems in genomics and proteomics. In particular, we discuss mathematical programming formulations for string comparison and selection problems, with high applicability in biological data processing.

A Branch-and-Cut to the Point-to-Point Connection Problem on Multicast Networks

In multicast routing, one of the basic problems consists of sending data from a set of sources to a set of destinations with minimum cost. A formalization of this problem using graph theory is given by the nonfixed Point-to-Point Connection (PPC) Problem. The optimization version of this problem is known to be NP-hard, and it can be also applied in areas such as circuit switching and VLSI design. We present a branch-and-cut approach to solve the PPC. Initially we describe a 0–1 integer programming formulation. Then, we prove that some of the constraints in this formulation are facet defining inequalities. Other valid inequalities, based on partitions of the set of vertices in the graph are also investigated. The proposed branch-and-cut algorithm is based on the previously discussed inequalities. Computational results of the branch-and-cut algorithm are presented, with comparisons to existing heuristic and approximation algorithms. The results show the effectiveness of the branch-and-cut method for instances of moderate size.