A genetic algorithm for the minimum generating set problem

作者：Lozano Manuel; Laguna Manuel; Marti Rafael; Rodriguez Francisco J^*; Garcia Martinez Carlos

来源：Applied Soft Computing, 2016, 48: 254-264.

DOI：10.1016/j.asoc.2016.07.020

• Minimum generating set problem
• Genetic algorithms
• Multiple knapsack problem
• Real-parameter crossover operator

Given a set of positive integers S, the minimum generating set problem consists in finding a set of positive integers T with a minimum cardinality such that every element of S can be expressed as the sum of a subset of elements in T. It constitutes a natural problem in combinatorial number theory and is related to some real-world problems, such as planning radiation therapies.
We present a new formulation to this problem (based on the terminology for the multiple knapsack problem) that is used to design an evolutionary approach whose performance is driven by three search strategies; a novel random greedy heuristic scheme that is employed to construct initial solutions, a specialized crossover operator inspired by real-parameter crossovers and a restart mechanism that is incorporated to avoid premature convergence. Computational results for problem instances involving up to 100,000 elements show that our innovative genetic algorithm is a very attractive alternative to the existing approaches.

• 出版日期2016-11