A Symbiosis Between Population Based Incremental Learning and LP-relaxation Based Parallel Genetic Algorithm for Solving Integer Linear Programming Models

Solving Integer Linear Programming (ILP) models generally lies in the category of NP-hard problems and finding the optimal answer for large models is a computational challenge. Genetic algorithms are a family of metaheuristic algorithms capable of adjusting and redesigning parameters and operations according to the characteristics of ILP models. On the other hand, still the genetic algorithm performs a lot of operations to solve large models, and parallel processing is a suitable technique to tackle this problem. This paper introduces an LP-Relaxation based parallel genetic algorithm that uses a population-based incremental learning technique to presents an expandable solver for large ILP models derived from a behavioral synthesis of digital circuits. In the proposed algorithm, each chromosome provides a state subspace of possible solutions, and each generation is produced based on a probability vector as well as elitism. Our experiments verify the efficiency of the proposed algorithm on multicore platforms, as it outperformed four previous genetic algorithms for solving mixed integer programming problems. The proposed genetic algorithm solved 20 ILP models include up to 5183 int / binary decision variables in less than 20 min using four 16-core AMD Opteron 6386 SE processors. Also, the results indicate that for models with more than 4000 variables, the speedup and the efficiency of the proposed parallel genetic algorithm on 60 CPU cores is more than 18X and 30%, respectively.