The quadratic multiple knapsack problem (QMKP) is a well-studied problem in operations research. This problem involves selecting a subset of items that maximizes the linear and quadratic profit without exceeding a set of capacities for each knapsack. While its solution using metaheuristics has been explored, exact approaches have recently been investigated. One way to improve the performance of these exact approaches is by reducing the solution space in different instances, considering the properties of the items in the context of QMKP. In this paper, machine learning (ML) models are employed to support an exact optimization solver by predicting the inclusion of items with a certain level of confidence and classifying them. This approach reduces the solution space for exact solvers, allowing them to tackle more manageable problems. The methodological process is detailed, in which ML models are generated and the best one is selected to be used as a preprocessing approach. Finally, we conduct comparison experiments, demonstrating that using a ML model is highly beneficial for reducing computing times and achieving rapid convergence.

Determining the design of pushbacks in an open-pit mine is a key part of optimizing the economic value of the mining project and the operational feasibility of the mine. This problem requires balancing pushbacks that have good geometric properties to ensure the smooth operation of the mining equipment and so that the scheduling of extraction maximizes the economic value by providing early access to the rich parts of the deposit. However, because of the challenging nature of the problem, practical approaches for finding the best pushbacks strongly depend on the expert criteria to ensure good operational properties. This paper introduces the Advanced Geometrically Constrained Production Scheduling Problem to account for operational space constraints, modeled as truncated cones of extraction. To find the best solution for this problem, we present a parallel genetic algorithm based on a genotype–phenotype model such that the genotype symbolizes the base block of a truncated cone, and the phenotype represents the cone itself. A central computer node evaluates these solutions, collaborating with various secondary nodes that evolve a population of feasible solutions. The PGA’s efficacy was validated using comprehensive test instances from established research. The PGA solution exhibited a consistent average copper grade across periods, with its incremental phases reflecting real-world mine geometry. Moreover, the benefits of the MeanShift clustering technique were evident, suggesting effective phase-based scheduling. The PGA’s approach ensures optimal resource utilization and offers insights into potential avenues for further model enhancements and fine-tuning.

The efficient movement of raw materials within organizations is fundamental to maintaining the seamless progression of production processes. However, these logistical operations can inadvertently compromise overall company efficiency, primarily due to the substantial time invested in transporting materials. This paper introduces an innovative mathematical model specifically designed to optimize the transport of raw materials via drones across multiple workstations. This model employs a novel modification of the traditional multi-level Vehicle Routing Problem by incorporating an additional index and accounting for the drone’s energy consumption. We employ a widely-recognized solver for practical resolution and compare it with a heuristic algorithm. The resultant strategies offer promising prospects for the organization studied, introducing robust solutions for elevating the efficiency of raw material transportation.

Timber extraction is a vital process in forest harvesting, particularly in areas with high slopes where timber harvesting methods are not feasible. In such cases, logging towers employing extraction cables are often the most effective solution. This intricate task involves several phases, with the installation of the tower being one of the most critical. It significantly influences the performance and feasibility of timber extraction. Another crucial phase involves strategically positioning logging lines to minimize the installation time while maximizing the load capacity efficiency. This article presents an integer programming mathematical model for determining the optimal positioning of yarders conditioned to logging lines, the timber logging time, and the logging cycle time. Furthermore, a two-phase heuristic algorithm is introduced to address the problem. Both approaches offer a preliminary proposal for the location of logging towers and the arrangement of logging lines within a two-dimensional spatial plane, thereby streamlining the timber extraction process in challenging terrains. Finally, we compare manually generated approximate planning (referred to as the manual planning approach, MPA) with our presented approaches. Our methods outperform the MPA, and notably, our two-phase approach surpasses solvers commonly used in the industry by up to 38% in real case studies.

The quadratic multidimensional knapsack problem (QMdKP) is a combinatorial optimization problem that involves selecting a subset of items to maximize both linear and quadratic profits without exceeding the capacity constraints across multiple dimensions. Due to its NP-hard nature, this paper presents a framework that integrates machine learning to mitigate the high computational cost associated with its resolution. The proposed methodology employs a classification model to predict item inclusion in the optimal solution prior to the optimization process, effectively reducing the number of decision variables handled by the solver. Additionally, to address large-scale instances, we propose an iterated local search metaheuristic initialized via the predictive algorithm. These strategies were benchmarked against a standard solver, demonstrating their capability of finding optimal or near-optimal solutions with execution time improvements of up to 83%.