Capacitated clustering problem in computational biology: Combinatorial and statistical approach for sibling reconstruction

• Published in: Computers & operations research Vol. 39; no. 3; pp. 609 - 619
• Main Authors: Chou, Chun-An, Chaovalitwongse, Wanpracha Art, Berger-Wolf, Tanya Y., DasGupta, Bhaskar, Ashley, Mary V.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.03.2012; Elsevier; Pergamon Press Inc
• Subjects: Algorithms; Applied sciences; Biological and medical sciences; Biology; Biostatistics; Capacitated clustering problem; Clustering analysis; Combinatorial analysis; Combinatorial optimization; Computational biology; Computer science; control theory; systems; Construction; Data processing. List processing. Character string processing; Exact sciences and technology; Flows in networks. Combinatorial problems; Fundamental and applied biological sciences. Psychology; General aspects; Genetics; Integer programming; Mathematical models; Mathematical programming; Mathematics in biology. Statistical analysis. Models. Metrology. Data processing in biology (general aspects); Memory organisation. Data processing; Operational research and scientific management; Operational research. Management science; Optimization algorithms; Phases; Reconstruction; Sibling reconstruction; Software; Studies; Clustering analysis; Sibling reconstruction; Combinatorial optimization; Capacitated clustering problem; Computational biology; Cluster analysis; Local search; Statistical analysis; Similarity; Mixed integer programming; Randomized algorithm; Memory function; Population genetics; Biological computation; Perturbation method; Randomized design; Genetic algorithm; Efficiency; Greedy algorithm; Capacity constraint; Population dynamics; Metric; Large scale; Bioinformatics
• ISSN: 0305-0548; 1873-765X; 0305-0548
• DOI: 10.1016/j.cor.2011.04.017

The capacitated clustering problem (CCP) has been studied in a wide range of applications. In this study, we investigate a challenging CCP in computational biology, namely, sibling reconstruction problem (SRP). The goal of SRP is to establish the sibling relationship (i.e., groups of siblings) of a population from genetic data. The SRP has gained more and more interests from computational biologists over the past decade as it is an important and necessary keystone for studies in genetic and population biology. We propose a large-scale mixed-integer formulation of the CCP for SRP that is based on both combinatorial and statistical genetic concepts. The objective is not only to find the minimum number of sibling groups, but also to maximize the degree of similarity of individuals in the same sibling groups while each sibling group is subject to genetic constraints derived from Mendel's laws. We develop a new randomized greedy optimization algorithm to effectively and efficiently solve this SRP. The algorithm consists of two key phases: construction and enhancement. In the construction phase, a greedy approach with randomized perturbation is applied to construct multiple sibling groups iteratively. In the enhancement phase, a two-stage local search with a memory function is used to improve the solution quality with respect to the similarity measure. We demonstrate the effectiveness of the proposed algorithm using real biological data sets and compare it with state-of-the-art approaches in the literature. We also test it on larger simulated data sets. The experimental results show that the proposed algorithm provide the best reconstruction solutions.