A genetic algorithm-based decomposition approach to solve an integrated equipment-workforce-service planning problem

• We design a new genetic algorithm (GA) to solve problems with extremely large size.
• We propose a decomposition solution approach that combines GA with optimization.
• The new GA has modified crossover and mutation that incorporate gene dependency.
• The new GA enables self-evolution for guided improvements of individuals.
• We solve problems near 100 million integer variables in less than 10 seconds.

We develop a new genetic algorithm to solve an integrated Equipment-Workforce-Service Planning problem, which features extremely large scales and complex constraints. Compared with the canonical genetic algorithm, the new algorithm is innovative in four respects: (1) The new algorithm addresses epistasis of genes by decomposing the problem variables into evolutionary variables, which evolve with the genetic operators, and the optimization variables, which are derived by solving corresponding optimization problems. (2) The new algorithm introduces the concept of Capacity Threshold and calculates the Set of Efficient and Valid Equipment Assignments to preclude unpromising solution spaces, which allows the algorithm to search much narrowed but promising solution spaces in a more efficient way. (3) The new algorithm modifies the traditional genetic crossover and mutation operators to incorporate the gene dependency in the evolutionary procedure. (4) The new algorithm proposes a new genetic operator, self-evolution, to simulate the growth procedure of an individual in nature and use it for guided improvements of individuals. The new genetic algorithm design is proven very effective and robust in various numerical tests, compared to the integer programming algorithm and the canonical genetic algorithm. When the integer programming algorithm is unable to solve the large-scale problem instances or cannot provide good solutions in acceptable times, and the canonical genetic algorithm is incapable of handling the complex constraints of these instances, the new genetic algorithm obtains the optimal or close-to-optimal solutions within seconds for instances as large as 84 million integer variables and 82 thousand constraints.