Álvaro García-Sánchez

This paper proposes the concept of biased-randomized transformers, a novel methodology that combines biased-randomized techniques and transformer-based deep learning for ‘agile’ optimization (i.e., real-time optimization that is carried out iteratively in dynamic systems). On the one hand, biased-randomization techniques have been used in the past to inject controlled randomness into greedy heuristics, thus converting them into probabilistic algorithms capable of generating thousands of good-quality solutions while preserving heuristic logic. On the other hand, transformer models can capture complex patterns across thousands of variables. Once trained, these models can be seen as data-driven heuristics able to provide fast solutions to new instances and adapt to changing inputs. The combination of biased-randomization techniques with trained transformers allows for a fast exploration and selection of the high-quality solutions to NP-hard combinatorial optimization problems. The paper includes two case studies that illustrate the potential of these biased-randomized transformers.

In manual picker-to-part systems, the order-picking process involves a set of interrelated decisions, including order batching, assignment, sequencing, and picker routing (OBASR). In this study, a comprehensive mixed-integer linear programming (MILP) model is formulated to address the joint order batching, assignment, sequencing, and picker routing problem under time-window due date constraints (JOBASRTWD) in an offline system, aiming to maximize customer service level by minimizing the earliness and tardiness of customer orders. Finding solutions is challenging because the fully integrated formulation of batching, assignment, sequencing, and routing decisions substantially increases the search space. To obtain a high-quality solution in a reasonable time, this work proposes an efficient hybrid algorithm, namely H-GAVND, based on a hybrid-coded genetic algorithm (GA) and variable neighbourhood descent (VND). The H-GAVND algorithm simultaneously searches for near-optimal solutions to all OBASR decisions. Various simulation experiments are performed across different sizes and with different instances to validate the proposed mathematical model and assess the performance of the hybrid algorithm. The proposed mathematical model effectively solves small-scale instances using the CPLEX solver, while on a real-world scale, the H-GAVND outperforms. Moreover, the performance of the proposed method is evaluated against a population-based metaheuristic, GA, and a solution-based local search approach, VND. The results indicate that the H-GAVND algorithm outperforms the standalone GA and VND approaches, owing to the effective combination of the global exploration capability of the population-based algorithm and the strong intensification of the solution-based local search method.

This study investigates the application of Reinforcement Learning (RL) to optimize intraday operations of hydropower reservoirs. Unlike previous approaches that focus on long-term planning with coarse temporal resolutions and discretized state-action spaces, we propose an RL framework tailored to the Hydropower Reservoirs Intraday Economic Optimization problem. This framework manages continuous state-action spaces while accounting for fine-grained temporal dynamics, including dam-to-turbine delays, gate movement constraints, and power group operations. Our methodology evaluates three distinct action space formulations (continuous, discrete, and adjustments) implemented using modern RL algorithms (A2C, PPO, and SAC). We compare them against both a greedy baseline and Mixed-Integer Linear Programming (MILP) solutions. Experiments on real-world data from a two-reservoir system and a simulated six-reservoir system demonstrate that while MILP achieves superior performance in the smaller system, its performance degrades significantly when scaled to six reservoirs. In contrast, RL agents, particularly those using discrete action spaces and trained with PPO, maintain consistent performance across both configurations, achieving considerable improvements with less than one second of execution time. These results suggest that RL offers a scalable alternative to traditional optimization methods for hydropower operations, particularly in scenarios requiring real-time decision making or involving larger systems.