Efficient Haplotype Inference with Pseudo-boolean Optimization

Mutation in DNA is the principal cause for differences among human beings, and Single Nucleotide Polymorphisms (SNPs) are the most common mutations. Hence, a fundamental task is to complete a map of haplotypes (which identify SNPs) in the human population. Associated with this effort, a key computational problem is the inference of haplotype data from genotype data, since in practice genotype data rather than haplotype data is usually obtained. Different haplotype inference approaches have been proposed, including the utilization of statistical methods and the utilization of the pure parsimony criterion. The problem of haplotype inference by pure parsimony (HIPP) is interesting not only because of its application to haplotype inference, but also because it is a challenging NP-hard problem, being APX-hard. Recent work has shown that a SAT-based approach is the most efficient approach for the problem of haplotype inference by pure parsimony (HIPP), being several orders of magnitude faster than existing integer linear programming and branch and bound solutions. This paper provides a detailed description of SHIPs, a SAT-based approach for the HIPP problem, and presents comprehensive experimental results comparing SHIPs with all other exact approaches for the HIPP problem. These results confirm that SHIPs is currently the most effective approach for the HIPP problem.

Haplotype inference by pure parsimony (HIPP) is a well-known paradigm for haplotype inference. In order to assess the biological significance of this paradigm, we generalize the problem of HIPP to the problem of finding all optimal solutions, which we call complete HIPP. We study intrinsic haplotype features, such as backbone haplotypes and fat genotypes as well as equal columns and decomposability. We explicitly exploit these features in three computational approaches which are based on integer linear programming, depth-first branch-and-bound, and a hybrid algorithm that draws on the diverse strengths of the first two approaches. Our experimental analysis shows that our optimized algorithms are significantly superior to the baseline algorithms, often with orders of magnitude faster running time. Finally, our experiments provide some useful insights to the intrinsic features of this interesting problem.KeywordsProblem InstanceInteger Linear ProgramUnique HaplotypeBaseline AlgorithmInternational HapMap ProjectThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Haplotype inference by pure parsimony (HIPP) is known to be NP-Hard. Despite this, many algorithms successfully solve HIPP instances on simulated and real data. In this paper, we explore the connection between algebraic rank and the HIPP problem, to help identify easy and hard instances of the problem. The rank of the input matrix is known to be a lower bound on the size an optimal HIPP solution. We show that this bound is almost surely tight for data generated by randomly pairing p haplotypes derived from a perfect phylogeny when the number of distinct population members is more than (1 + epsilon/2)p log p (for some positive epsilon). Moreover, with only a constant multiple more population members, and a common mutation, we can almost surely recover an optimal set of haplotypes in polynomial time. We examine the algebraic effect of allowing recombination, and bound the effect recombination has on rank. In the process, we prove a stronger version of the standard haplotype lower bound. We also give a complete classification of the rank of a haplotype matrix derived from a galled tree. This classification identifies a set of problem instances with recombination when the rank lower bound is also tight for the HIPP problem.

Haplotype inference is a challenging problem in bioinformatics that consists in inferring the basic genetic constitution of diploid organisms on the basis of their genotype. This piece of information allows researchers to perform association studies for the genetic variants involved in diseases and the individual responses to therapeutic agents. A notable approach to the problem is to encode it as a combinatorial problem (under certain hypotheses, such as the pure parsimony) and to solve it using off-the-shelf combinatorial optimization techniques. In this paper, we present and discuss an approach based on hybridization of two meta-heuristics, one being a population based learning algorithm and the other a local search. We test our approach by solving instances from common Haplotype inference benchmarks. Results show that this approach achieves an improvement on solution quality with respect to the application of a single 'pure' algorithm.

Solving Integer Linear Programming (ILP) models generally lies in the category of NP-hard problems. Therefore, as the size of ILP models grows, the efficiency of exact algorithms for solving the models reduced significantly and for large models it is not possible to have the result. Genetic Algorithm (GA) is a metaheuristic method capable of adjusting and redesigning parameters and operations according to the characteristics of ILP models. Still GA has huge search space for large models and parallelization is a suitable technique to tackle this problem. This paper presents a scalable parallel GA to solve large ILP models derived from behavioral synthesis of digital circuits. We show that although models have non-binary variables, only binary variables are sufficient for coding chromosomes. We also use ”unknown” values for some genes to decrease the likelihood of inconsistency in the encoded constraints. Our experiments verify the efficiency and scalability of the proposed algorithm on multicore platforms. The proposed method outperforms IBM ILOG CPLEX 12.6 and MI-LXPM algorithm where the ILP models include 550 to 2258 int / binary decision variables. Also, the results indicate that the saturation point of using parallel processing elements for solving the large ILP models is at least 60.

An Optimal Cross-Layer Scheduling for Periodic WSN Applications

We present new integer linear programming (ILP) models for NP-hard optimisation problems in instances of the Stable Marriage problem with Ties and Incomplete lists (SMTI) and its many-to-one generalisation, the Hospitals/Residents problem with Ties (HRT). These models can be used to efficiently solve these optimisation problems when applied to (i) instances derived from real-world applications, and (ii) larger instances that are randomly-generated. In the case of SMTI, we consider instances arising from the pairing of children with adoptive families, where preferences are obtained from a quality measure of each possible pairing of child to family. In this case, we seek a maximum weight stable matching. We present new algorithms for preprocessing instances of SMTI with ties on both sides, as well as new ILP models. Algorithms based on existing state-of-the-art models only solve 6 of our 22 real-world instances within an hour per instance, and our new models incorporating dummy variables and constraint merging, together with preprocessing and a warm start, solve all 22 instances within a mean runtime of a minute. For HRT, we consider instances derived from the problem of assigning junior doctors to foundation posts in Scottish hospitals. Here, we seek a maximum size stable matching. We show how to extend our models for SMTI to HRT and reduce the average running time for real-world HRT instances by two orders of magnitude. We also show that our models outperform by a wide margin all known state-of-the-art models on larger randomly-generated instances of SMTI and HRT.

This paper focus on the routing, modulation level and spectrum allocation (RMLSA) problem in the next generation datacentre networks, which own the advantages of both Elastic Optical Networks (EON) and Software Defined Networking (SDN). We proposes an Integer Linear Programming (ILP) model for this problem. Simulation results show the ILP model achieves an outstanding load balancing performance.

In this paper, we propose an integer linear programming (ILP) model for static elevator operation problems. The proposed model is based on hall- and car-calls which correspond to pickup and delivery requests in pickup-and-delivery problems (PDPs), thus is similar to ILP models for PDPs. The primary difference between those models and the proposed model is the prevention of the reverse run, which means that an elevator with a passenger is moved to the direction opposite to that of the passenger. In computer illustrations, the proposed model is roughly investigated by being compared with a trip-based ILP model which has been proposed by the authors.

This paper addresses the problem of minimizing spectrum usage for shared-path protection with joint failure probability constraint in flexible bandwidth optical networks. To achieve this goal, we propose an integer linear programming (ILP) model for shared-path protection and a heuristic spectrum-aware shared protection (SASP) algorithm that considers joint failure probability. Simulation results show that the ILP model minimizes the total usage of frequency slots and average hops, but leads to high average joint failure probability. Moreover, the SASP algorithm achieves better trade-off between total usage of frequency slots and average joint failure probability compared to the ILP model and a conventional shared-path protection (CSPP) algorithm. As expected, in a 14-nodes network, the SASP algorithm performs better with respect to total spectrum usage and average hops, but results in much larger average joint failure probability compared to the CSPP algorithm.

Production Lot Sizes on a Single Imperfect Machine: FPTAS vs ILP models

In this work, we propose an integer linear programming (ILP) model to schedule a set of weakly-hard real-time tasks on a heterogeneous multiprocessor system to minimize energy consumption with the predictable performance. The ILP model provides an optimal solution in terms of energy consumption by selecting the appropriate frequency for each task with (m,k) weakly-hard deadline constraint.

Efficient and scalable provisioning of always-on multicast streaming services

The weighted independent domination problem: Integer linear programming models and metaheuristic approaches

To analyze the function of DNA, researchers have to obtain each haplotype, the genetic constitution of an individual chromosome, of an individual for analysis. Due to the significant efforts required in collecting haplotypes, the descriptions of one conflated pair of haplotypes called genotypes are usually collected. Since the genotype data contains insufficient information to identify the combination of DNA sequence in each copy of a chromosome, one has to solve the population haplotype inference problem by pure parsimony criterion which uses the minimum number of haplotypes to infer the haplotype data from genotype data for a population. Previous researches use mathematical programming methods such as integer programming and semidefinite programming models to solve the population haplotype inference problem. However, no computational experiment has ever been conducted to evaluate the algorithmic effectiveness. This paper thus conducts the first computational experiments on four haplotyping algorithms, including our new greedy heuristic and three pervious haplotyping algorithms.