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

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.