A novel solution approach with ML-based pseudo-cuts for the Flight and Maintenance Planning problem

Abstract

This paper deals with the long-term Military Flight and Maintenance Planning problem. In order to solve this problem efficiently, we propose a new solution approach based on a new Mixed Integer Program and the use of both valid cuts generated on the basis of initial conditions and learned cuts based on the prediction of certain characteristics of optimal or near-optimal solutions. These learned cuts are generated by training a Machine Learning model on the input data and results of 5000 instances. This approach helps to reduce the solution time with little losses in optimality and feasibility in comparison with alternative matheuristic methods. The obtained experimental results show the benefit of a new way of adding learned cuts to problems based on predicting specific characteristics of solutions.

Machine Learning-Guided Dual Heuristics and New Lower Bounds for the Refueling and Maintenance Planning Problem of Nuclear Power Plants

“…Considering bi-objective extension, implied by robust optimization considerations [38] or stability costs [24], we can compute dual bound-sets using computations of dual bounds from this paper using scalarization or epsilon-constraint methods. Lastly, we mention as a perspective that the results of Section 5 are valid for a general class of 2-stage stochastic problems, optimizing strategical problems like maintenance planning conjointly with an operational level as in [3].…”

“…Constraints (2) are required with definition of variables d. Constraints (3) and (4) model CT13 time windows constraints: outage (i, k) is operated between weeks To i,k and Ta i,k . Constraints (5) model CT1 demand constraints.…”

“…Usually, hybrid algorithms compute primal solutions of optimization problems as in [3], rare works use such hybridization to improve dual bounds. Using dual heuristics for Mixed Integer Linear Programming (MILP) is mentioned in [4]: "In linear programming based branch-and-bound algorithms, many heuristics have been developed to improve primal solutions, but on the dual side we rely solely on cutting planes to improve dual bounds".…”

Equipment maintenance task prediction model analysis based on BAS-PSO hybrid optimization algorithm

“…It is derived from the study on the predation behavior of birds and belongs to a kind of swarm intelligence optimization algorithm. It has the advantages of fast search speed, high efficiency and simple algorithm, but for discrete optimization problems, it is easy to fall into local optimum Peschiera et al (2020). Therefore, the performance of traditional particle swarm optimization algorithm can be improved by introducing inertia weight, designing different topology structures or combining with other optimization algorithms.…”

The Unit Re-Balancing Problem

“…For vehicle routing problems dealing with specialized technicians, balancing issues in the workload of technicians were modeled in [19] and solved with a bi-objective optimization model [20]. In a military context, planning flights and maintenance of military aircrafts is considered in [21], where flights must be balanced to keep aircrafts intact as long as possible and maintenance operations must be balanced to keep the squadron available at all times. The authors improved programming model by training a Machine Learning model on a large set of past real-world instances.…”