Multi-objective evolutionary algorithm for optimizing maintenance scheduling

The goal of the CIMPLO project is to provide industry with a tool for optimizing maintenance activities. When optimizing the maintenance operations, multiple objectives are required to be optimized, such as the processing time, processing cost and production safety, which leads us to a multi-objective optimization problem (MOP).

Due to the complexity of MOPs, the commonly used optimization techniques like enumerative and deterministic search techniques, are unsuitable. On the contrary, population-based meta-heuristics such as evolutionary algorithms (EAs) are commonly employed to this task because of their ability to approximate the entire Pareto front in a single run. Depending on the employed selection mechanism, most multi-objective evolutionary algorithms (MOEAs) can be classified into three categories:

(1) Pareto dominance-based MOEAs use the Pareto dominance relation as a first ranking criterion and use a second ranking criterion to promote diversity.

(2) Indicator-based MOEAs use indicators to capture both convergence and diversity in a single value.

(3) Decomposition-based MOEAs transform the original MOP into simpler, single-objective sub-problems by means of scalarizations with different weights, therefore they can converge to a well diversified set.

To solve our problem of optimizing the maintenance operations, we propose a new indicator-based MOEA, i.e., diversity-Indicator based multi-objective evolutionary algorithm (DI-MOEA) [1]. DI-MOEA adopts a hybrid selection scheme:

• The (μ + μ) generational selection operator is used when the parent population can be layered into multiple dominance ranks. The intention is to accelerate convergence until all solutions are non-dominated.
• The (μ + 1) steady state selection operator is adopted in the case that all solutions in the parent population are mutually non-dominated and the diversity is the main selection criterion to achieve a uniform distribution of the solutions on the Pareto front.

DI-MOEA employs non-dominated sorting as the first ranking criterion; the diversity indicator, i.e., the Euclidean distance based geometric mean gap indicator, as the second, diversity-based ranking criterion to guide the search.

DI-MOEA is invariant to the shape of the Pareto front and can achieve evenly spread Pareto front approximations. It has shown to be competitive to other MOEAs on common multi-objective benchmark problems and has been applied to solve our maintenance scheduling optimization problem [2].

References:

[1] Wang, Y., Emmerich, M., Deutz, A. and Bäck, T., 2019, March. Diversity-Indicator Based Multi-Objective Evolutionary Algorithm: DI-MOEA. In International Conference on Evolutionary Multi-Criterion Optimization (pp. 346-358). Springer, Cham.

[2] Wang, Y., Limmer, S., Olhofer, M., Emmerich, M.T. and Bäck, T., 2019, June. Vehicle Fleet Maintenance Scheduling Optimization by Multi-objective Evolutionary Algorithms. In 2019 IEEE Congress on Evolutionary Computation (CEC) (pp. 442-449). IEEE.