A Parallelized Method for Solving Large Scale Integer Linear Optimization Problems using Cut-and-Solve with Applications to cGWAS

The commercial solver CPLEX has been one of the top solvers of mixed-integer and purely integer linear problems for some time. Its method of solving, Branch-and-Cut, has been shown to be highly effective, but has its limits in terms of input sizes which are tractable, and cannot be effectively parallelized beyond a small number. Here we present a different method of solution, Cut-and-Solve, which utilizes the power of CPLEX to effectively parallelize any mixed-integer or integer linear problem. We have utilized Cut-and-Solve in a novel way to offer optimal solution guarantees more quickly. We will show comparisons of Cut-and-Solve to CPLEX and show that it has definite promise as a solver of these types of problems. It offers a less memory intensive solution and one with power equal to the limitations only of the hardware it can be parallelized on. This method does not perform better than CPLEX at the level of parallelization tested here, but with some minor adjustments has the potential to solve previously intractable problems. Importantly, our current implementation shows an effective use as an anytime solver

A Parallelized Implementation of Cut-and-Solve and a Streamlined Mixed-Integer Linear Programming Model for Finding Genetic Patterns Optimally Associated with Complex Diseases

With the advent of genetic sequencing, there was much hope of finding the inherited elements underlying complex diseases, such as late-onset Alzheimer’s disease (AD), but it has been a challenge to fully uncover the necessary information hidden in the data. A likely contributor to this failure is the fact that the pathogenesis of most complex diseases does not involve single markers working alone, but patterns of genetic markers interacting additively or epistatically. But as we move upwards beyond patterns of size two, it quickly becomes computationally infeasible to examine all combinations in the solution space. A common solution to solving this type of combinatorial optimization problem is to model it as a mixed-integer linear program (MIP) and solve it using the algorithm branch-and-cut, implemented by a commercial solver. However, with the trend of using increasing numbers of computing cores to increase computational power, there is a need for a different approach to solving MIPs that can utilize parallel environments. Here we show how a parallelized implementation of an alternative algorithm, cut-and-solve, can be used to solve this genetics problem faster than CPLEX, one of the leading commercial MIP solvers