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.

求解整数线性规划 (ILP) 模型通常属于 NP 难问题，为大型模型找到最佳答案是一项计算挑战。遗传算法是一系列元启发式算法，能够根据 ILP 模型的特点调整和重新设计参数和操作。另一方面，遗传算法仍然执行大量操作来解决大型模型，并行处理是解决这个问题的合适技术。本文介绍了一种基于 LP-Relaxation 的并行遗传算法，该算法使用基于群体的增量学习技术为源自数字电路行为综合的大型 ILP 模型提供可扩展的求解器。在所提出的算法中，每条染色体都提供了一个可能解的状态子空间，每一代都是基于概率向量和精英主义产生的。我们的实验验证了所提出算法在多核平台上的效率，因为它在解决混合整数规划问题方面优于之前的四种遗传算法。所提出的遗传算法使用四个 16 核 AMD Opteron 6386 SE 处理器在不到 20 分钟的时间内解决了 20 个 ILP 模型，包括多达 5183 个整数/二元决策变量。此外，结果表明，对于超过 4000 个变量的模型，所提出的并行遗传算法在 60 个 CPU 核上的加速比和效率超过 18 因为它在解决混合整数规划问题方面的性能优于之前的四种遗传算法。所提出的遗传算法使用四个 16 核 AMD Opteron 6386 SE 处理器在不到 20 分钟的时间内解决了 20 个 ILP 模型，包括多达 5183 个整数/二元决策变量。此外，结果表明，对于超过 4000 个变量的模型，所提出的并行遗传算法在 60 个 CPU 核上的加速比和效率超过 18 因为它在解决混合整数规划问题方面的性能优于之前的四种遗传算法。所提出的遗传算法使用四个 16 核 AMD Opteron 6386 SE 处理器在不到 20 分钟的时间内解决了 20 个 ILP 模型，包括多达 5183 个整数/二元决策变量。此外，结果表明，对于超过 4000 个变量的模型，所提出的并行遗传算法在 60 个 CPU 核上的加速比和效率超过 18X和\(30\%\)，分别。