Multi-objective single agent stochastic search in non-dominated sorting genetic algorithm

A hybrid multi-objective optimization algorithm based on genetic algorithm and stochastic local search is developed and evaluated. The single agent stochastic search local optimization algorithm has been modified in order to be suitable for multi-objective optimization where the local optimization is performed towards non-dominated points. The presented algorithm has been experimentally investigated by solving a set of well known test problems, and evaluated according to several metrics for measuring the performance of algorithms for multi-objective optimization. Results of the experimental investigation are presented and discussed

Parallel Optimization Algorithm for Competitive Facility Location

A stochastic search optimization algorithm is developed and applied to solve a bi-objective competitive facility location problem for firm expansion. Parallel versions of the developed algorithm for shared- and distributed-memory parallel computing systems are proposed and experimentally investigated by approximating the Pareto front of the competitive facility location problem of different scope. It is shown that the developed algorithm has advantages against its precursor in the sense of the precision of approximation. It is also shown that the proposed parallel versions of the algorithm have almost linear speed-up when solving competitive facility location problems of different scope reasonable for practical applications

Parallelization of random search global optimization algorithms

Global optimization problems are relevant in various fields of research and industry, such as chemistry, biology, biomedicine, operational research, etc. Normally it is easier to solve optimization problems having some specific properties of objective function such as linearity, convexity, differentiability, etc. However, there are a lot of practical problems that do not satisfy such properties or even cannot be expressed in an adequate mathematical form. Therefore, it is popular to use random search optimization methods in solving such optimization problems. The dissertation deals with investigation of random search global optimization algorithms, their parallelization and application to solve practical problems. The work is focused on modification and parallelization of particle swarm optimization and genetic algorithms. The modification of particle swarm optimization algorithm, based on reduction of the search area is proposed, and several strategies to parallelize the algorithm are investigated. The algorithm is applied to solve Multiple Gravity Assist problem using parallel computing system. A hybrid global multi-objective optimization algorithm is developed by modifying single agent stochastic search strategy, and incorporating it into multi-objective optimization genetic algorithm. Several strategies to parallelize multi-objective optimization genetic algorithm is proposed. Parallel algorithms are experimentally investigated by solving competitive facility location problem using high performance computing systems

Parallel computing in different systems

Šiame darbe apžvelgiami pagrindiniai lygiagrečių kompiuterių tipai, pasaulyje esančios lygiagrečios skaičiavimo sistemos, pagrindinės lygiagrečių skaičiavimų algoritmų savybės, jų sudarymo principai bei realizavimo standartai. Darbe tiriamas klasteris, dirbantis dviejose skirtingose operacinėse sistemose – Windows XP Service Pack 3, kurioje naudojamas Microsoft Visual Studio 6.0 C++ kompiliatorius ir Scientific Linux 5.2, kurioje naudojamas Open MPI wrapper kompiliatorius. Atlikti eksperimentai, kuriais buvo siekiama palyginti operacinių sistemų įtaka klasterio darbo našumui, vertinant skaičiavimo ir duomenų perdavimo greičius, lygiagretaus algoritmo pagreitėjimą ir efektyvumą. Eksperimentų metu buvo skaičiuojama apytikslė skaičiaus π reikšmė, generuojant atsitiktinius skaičius su skirtingu procesorių ir procesų skaičiumi bei skirtingomis kompiuteriams-darbininkams teikiamomis darbo porcijomis. Tai pat buvo atlikti pranešimų persiuntimo kompiuterių tinkle eksperimentai. Pateikti apibendrinti eksperimentų rezultatai ir išvados.The main types of parallel computers, current parallel computing systems, principles and realization standards of parallel computing algorithms are reviewed in this work. The cluster, which works with two different operating systems – Windows XP Service Pack 3 with Microsoft Visual Studio 6.0 C++ compiler and Scientific Linux 5.2 with Open MPI wrapper compilers is investigated in this work. Experiments designed to compare the influence of cluster operating systems on productivity of calculation and data transfer speeds, parallel algorithm speed-up and efficiency. During experiments an approximate value of π was calculated by generating random numbers using different number of processors and processes, different slave-node working portion. Experiments of message transfer in computer network were carried out too. Summarized experimental results and conclusions are presented.Švietimo akademijaVytauto Didžiojo universiteta

Atsitiktinės paieškos globaliojo optimizavimo algoritmų lygiagretinimas

Global optimization problems are relevant in various fields of research and industry, such as chemistry, biology, biomedicine, operational research, etc. Normally it is easier to solve optimization problems having some specific properties of objective function such as linearity, convexity, differentiability, etc. However, there are a lot of practical problems that do not satisfy such properties or even cannot be expressed in an adequate mathematical form. Therefore, it is popular to use random search optimization methods in solving such optimization problems. The dissertation deals with investigation of random search global optimization algorithms, their parallelization and application to solve practical problems. The work is focused on modification and parallelization of particle swarm optimization and genetic algorithms. The modification of particle swarm optimization algorithm, based on reduction of the search area is proposed, and several strategies to parallelize the algorithm are investigated. The algorithm is applied to solve Multiple Gravity Assist problem using parallel computing system. A hybrid global multi-objective optimization algorithm is developed by modifying single agent stochastic search strategy, and incorporating it into multi-objective optimization genetic algorithm. Several strategies to parallelize multi-objective optimization genetic algorithm is proposed. Parallel algorithms are experimentally investigated by solving competitive facility location problem using high performance computing systems

Atsitiktinių skaičių generavimo paraleliniuose stochastiniuose algoritmuose bendrajam optimizavimui metodai

Perfomance of stochastic algorithms for global optimization crucially depends on generation of random numbers. Random number generation methods may vary on features as independence of the generated random numbers, fit to the required distribution, and speed of generation. This paper reviews the main idea and several algorithms for generation of pseudo random numbers. Evaluation criteria of pseudo random numbers generators are also reviewed. Seven widely used random numbers generators (Linear Congruential Generator, Mersenne Twister, Mother At All, C++, Pascal, Matlab and Fortran) are experimentally compared evaluating the distribution of random numbers, correlation of sequences and speed of generation. In parallel computations correlation of sequences may depend on the seed of pseudo random numbers generators. Therefore several ways for construction of the seeds are compared considering correlation of generated sequences of random numbers when computations are performed in parallel computers

Genotipo įtakotos susirgimo rizikos įvertinimo metodų tyrimas

Chronic non-communicable diseases are caused by a combination of multilocus genetic risk factors. The genetic risk assessment companies, e.g. Navigenics and 23andMe, calculate a lifetime risk of a disease by the use of strong assumptions on the total impact of the multiple SNPs genotype. The object of the paper is to compare such risk assessment methods. The theoretical disease model that describes both environmental and genetic factors has been used for evaluation of assessment methods. The system of nonlinear equations for tuning model’s parameters to real statistical parameters of the disease has been developed. The Receiver Operating Characteristic curve has been used to evaluate the quality of the methods as predictive tests.  Darbe tiriamos susirgimo rizikos, apspręstos daugelio nukleotidų polimorfizmo ir aplinkos bei elgesio faktorių įvertinimo metodų savybės. Tam panaudotas stochastinis ligos rizikos modelis, sudaryta lygčių sistemą modelio parametrams priderinti prie statistinių ligos parametrų. Palyginti kelių kompanijų naudojami metodai taip pat metodai aprašyti literatūroje. Tirta prognostinio klasifikavimo paklaidų priklausomybė nuo paciento atitikimo populiacijai, kurios statistiniai duomenys naudojami

Application of multi-objective optimization to pooled experiments of next generation sequencing for detection of rare mutations.

In this paper we propose some mathematical models to plan a Next Generation Sequencing experiment to detect rare mutations in pools of patients. A mathematical optimization problem is formulated for optimal pooling, with respect to minimization of the experiment cost. Then, two different strategies to replicate patients in pools are proposed, which have the advantage to decrease the overall costs. Finally, a multi-objective optimization formulation is proposed, where the trade-off between the probability to detect a mutation and overall costs is taken into account. The proposed solutions are devised in pursuance of the following advantages: (i) the solution guarantees mutations are detectable in the experimental setting, and (ii) the cost of the NGS experiment and its biological validation using Sanger sequencing is minimized. Simulations show replicating pools can decrease overall experimental cost, thus making pooling an interesting option

Pooled testing with replication as a mass testing strategy for the COVID-19 pandemics

During the COVID-19 pandemic it is essential to test as many people as possible, in order to detect early outbreaks of the infection. Present testing solutions are based on the extraction of RNA from patients using oropharyngeal and nasopharyngeal swabs, and then testing with real-time PCR for the presence of specific RNA filaments identifying the virus. This approach is limited by the availability of reactants, trained technicians and laboratories. One of the ways to speed up the testing procedures is a group testing, where the swabs of multiple patients are grouped together and tested. In this paper we propose to use the group testing technique in conjunction with an advanced replication scheme in which each patient is allocated in two or more groups to reduce the total numbers of tests and to allow testing of even larger numbers of people. Under mild assumptions, a 13 x average reduction of tests can be achieved compared to individual testing without delay in time

A discrete competitive facility location model with minimal market share constraints and equity-based ties breaking rule

We consider a geographical region with spatially separated customers, whose demand is currently served by some pre-existing facilities owned by different firms. An entering firm wants to compete for this market locating some new facilities. Trying to guarantee a future satisfactory captured demand for each new facility, the firm imposes a constraint over its possible locations (a finite set of candidates): a new facility will be opened only if a minimal market share is captured in the short-term. To check that, it is necessary to know the exact captured demand by each new facility. It is supposed that customers follow the partially binary choice rule to satisfy its demand. If there are several new facilities with maximal attraction for a customer, we consider that the proportion of demand captured by the entering firm will be equally distributed among such facilities (equity-based rule). This ties breaking rule involves that we will deal with a nonlinear constrained discrete competitive facility location problem. Moreover, minimal attraction conditions for customers and distances approximated by intervals have been incorporated to deal with a more realistic model. To solve this nonlinear model, we first linearize the model, which allows to solve small size problems because of its complexity, and then, for bigger size problems, a heuristic algorithm is proposed, which could also be used to solve other constrained problems