Biomedical subjects

Kalyanmoy Deb

Publications and source records attributed to Kalyanmoy Deb.

5 recordsLinked to original sources

PubMed2006

Introducing robustness in multi-objective optimization.

In optimization studies including multi-objective optimization, the main focus is placed on finding the global optimum or global Pareto-optimal solutions, representing the best possible objective values. However, in practice, users may not always be interested in finding the so-called global best solutions, particularly when these solutions are quite sensitive to the variable perturbations which cannot be avoided in practice. In such cases, practitioners are interested in finding the robust solutions which are less sensitive to small perturbations in variables. Although robust optimization is dealt with in detail in single-objective evolutionary optimization studies, in this paper, we present two different robust multi-objective optimization procedures, where the emphasis is to find a robust frontier, instead of the global Pareto-optimal frontier in a problem. The first procedure is a straightforward extension of a technique used for single-objective optimization and the second procedure is a more practical approach enabling a user to set the extent of robustness desired in a problem. To demonstrate the differences between global and robust multi-objective optimization principles and the differences between the two robust optimization procedures suggested here, we develop a number of constrained and unconstrained test problems having two and three objectives and show simulation results using an evolutionary multi-objective optimization (EMO) algorithm. Finally, we also apply both robust optimization methodologies to an engineering design problem.

Algorithms↗

PubMed2005

Evaluating the epsilon-domination based multi-objective evolutionary algorithm for a quick computation of Pareto-optimal solutions.

Since the suggestion of a computing procedure of multiple Pareto-optimal solutions in multi-objective optimization problems in the early Nineties, researchers have been on the look out for a procedure which is computationally fast and simultaneously capable of finding a well-converged and well-distributed set of solutions. Most multi-objective evolutionary algorithms (MOEAs) developed in the past decade are either good for achieving a well-distributed solutions at the expense of a large computational effort or computationally fast at the expense of achieving a not-so-good distribution of solutions. For example, although the Strength Pareto Evolutionary Algorithm or SPEA (Zitzler and Thiele, 1999) produces a much better distribution compared to the elitist non-dominated sorting GA or NSGA-II (Deb et al., 2002a), the computational time needed to run SPEA is much greater. In this paper, we evaluate a recently-proposed steady-state MOEA (Deb et al., 2003) which was developed based on the epsilon-dominance concept introduced earlier(Laumanns et al., 2002) and using efficient parent and archive update strategies for achieving a well-distributed and well-converged set of solutions quickly. Based on an extensive comparative study with four other state-of-the-art MOEAs on a number of two, three, and four objective test problems, it is observed that the steady-state MOEA is a good compromise in terms of convergence near to the Pareto-optimal front, diversity of solutions, and computational time. Moreover, the epsilon-MOEA is a step closer towards making MOEAs pragmatic, particularly allowing a decision-maker to control the achievable accuracy in the obtained Pareto-optimal solutions.

Algorithms↗

PubMed2003

Reliable classification of two-class cancer data using evolutionary algorithms.

In the area of bioinformatics, the identification of gene subsets responsible for classifying available disease samples to two or more of its variants is an important task. Such problems have been solved in the past by means of unsupervised learning methods (hierarchical clustering, self-organizing maps, k-mean clustering, etc.) and supervised learning methods (weighted voting approach, k-nearest neighbor method, support vector machine method, etc.). Such problems can also be posed as optimization problems of minimizing gene subset size to achieve reliable and accurate classification. The main difficulties in solving the resulting optimization problem are the availability of only a few samples compared to the number of genes in the samples and the exorbitantly large search space of solutions. Although there exist a few applications of evolutionary algorithms (EAs) for this task, here we treat the problem as a multiobjective optimization problem of minimizing the gene subset size and minimizing the number of misclassified samples. Moreover, for a more reliable classification, we consider multiple training sets in evaluating a classifier. Contrary to the past studies, the use of a multiobjective EA (NSGA-II) has enabled us to discover a smaller gene subset size (such as four or five) to correctly classify 100% or near 100% samples for three cancer samples (Leukemia, Lymphoma, and Colon). We have also extended the NSGA-II to obtain multiple non-dominated solutions discovering as much as 352 different three-gene combinations providing a 100% correct classification to the Leukemia data. In order to have further confidence in the identification task, we have also introduced a prediction strength threshold for determining a sample's belonging to one class or the other. All simulation results show consistent gene subset identifications on three disease samples and exhibit the flexibilities and efficacies in using a multiobjective EA for the gene subset identification task.

Algorithms↗

PubMed2002

Combining convergence and diversity in evolutionary multiobjective optimization.

Over the past few years, the research on evolutionary algorithms has demonstrated their niche in solving multiobjective optimization problems, where the goal is to find a number of Pareto-optimal solutions in a single simulation run. Many studies have depicted different ways evolutionary algorithms can progress towards the Pareto-optimal set with a widely spread distribution of solutions. However, none of the multiobjective evolutionary algorithms (MOEAs) has a proof of convergence to the true Pareto-optimal solutions with a wide diversity among the solutions. In this paper, we discuss why a number of earlier MOEAs do not have such properties. Based on the concept of epsilon-dominance, new archiving strategies are proposed that overcome this fundamental problem and provably lead to MOEAs that have both the desired convergence and distribution properties. A number of modifications to the baseline algorithm are also suggested. The concept of epsilon-dominance introduced in this paper is practical and should make the proposed algorithms useful to researchers and practitioners alike.

Algorithms↗

PubMed2002

A computationally efficient evolutionary algorithm for real-parameter optimization.

Due to increasing interest in solving real-world optimization problems using evolutionary algorithms (EAs), researchers have recently developed a number of real-parameter genetic algorithms (GAs). In these studies, the main research effort is spent on developing an efficient recombination operator. Such recombination operators use probability distributions around the parent solutions to create an offspring. Some operators emphasize solutions at the center of mass of parents and some around the parents. In this paper, we propose a generic parent-centric recombination operator (PCX) and a steady-state, elite-preserving, scalable, and computationally fast population-alteration model (we call the G3 model). The performance of the G3 model with the PCX operator is investigated on three commonly used test problems and is compared with a number of evolutionary and classical optimization algorithms including other real-parameter GAs with the unimodal normal distribution crossover (UNDX) and the simplex crossover (SPX) operators, the correlated self-adaptive evolution strategy, the covariance matrix adaptation evolution strategy (CMA-ES), the differential evolution technique, and the quasi-Newton method. The proposed approach is found to consistently and reliably perform better than all other methods used in the study. A scale-up study with problem sizes up to 500 variables shows a polynomial computational complexity of the proposed approach. This extensive study clearly demonstrates the power of the proposed technique in tackling real-parameter optimization problems.

Algorithms↗