Antônio Augusto Chaves

Natalia A. Santos, Marlon Jeske, Antonio A. Chaves

This paper addresses the Quadratic Multiple Constraints Variable-Sized Bin Packing Problem (QMC-VSBPP), a challenging combinatorial optimization problem that generalizes the classical bin packing problem by incorporating multiple capacity dimensions, heterogeneous bin types, and quadratic interaction costs between items. We propose two complementary methods that advance the current state-of-the-art. First, a linearized mathematical model is introduced to eliminate quadratic terms, enabling the use of exact solvers such as Gurobi to compute strong lower bounds, reported here for the first time for this problem. Second, we develop RKO-ACO, a continuous-domain Ant Colony Optimization algorithm within the Random-Key Optimizer framework, enhanced with adaptive Q-learning parameter control and efficient local search. Extensive computational experiments on benchmark instances show that the proposed linearized model produces significantly tighter lower bounds than the original quadratic model, while RKO-ACO consistently matches or improves upon all best-known solutions in the literature, establishing new upper bounds for large-scale instances. These results provide new reference values for future studies and demonstrate the effectiveness of evolutionary and random-key approaches for solving complex quadratic packing problems. Source code and data available at https://github.com/nataliaalves03/RKO-ACO

Antonio A. Chaves, Mauricio G. C. Resende, Carise E. Schmidt et al.

Mixed-Integer Programs (MIPs) are NP-hard optimization models that arise in a broad range of decision-making applications, including finance, logistics, energy systems, and network design. Although modern commercial solvers have achieved remarkable progress and perform effectively on many small- and medium-sized instances, their performance often degrades when confronted with large-cale or highly constrained formulations. This paper explores the use of the Random-Key Optimizer (RKO) framework as a flexible, metaheuristic alternative for computing high-quality solutions to MIPs through the design of problem-specific decoders. The proposed approach separates the search process from feasibility enforcement by operating in a continuous random-key space while mapping candidate solutions to feasible integer solutions via efficient decoding procedures. We evaluate the methodology on two representative and structurally distinct benchmark problems: the mean-variance Markowitz portfolio optimization problem with buy-in and cardinality constraints, and the Time-Dependent Traveling Salesman Problem. For each formulation, tailored decoders are developed to reduce the effective search space, promote feasibility, and accelerate convergence. Computational experiments demonstrate that RKO consistently produces competitive, and in several cases superior, solutions compared to a state-of-the-art commercial MIP solver, both in terms of solution quality and computational time. These results highlight the potential of RKO as a scalable and versatile heuristic framework for tackling challenging large-scale MIPs.

Antonio A. Chaves, Mauricio G. C. Resende, Martin J. A. Schuetz et al.

This paper introduces the Random-Key Optimizer (RKO), a versatile and efficient stochastic local search method tailored for combinatorial optimization problems. Using the random-key concept, RKO encodes solutions as vectors of random keys that are subsequently decoded into feasible solutions via problem-specific decoders. The RKO framework is able to combine a plethora of classic metaheuristics, each capable of operating independently or in parallel, with solution sharing facilitated through an elite solution pool. This modular approach allows for the adaptation of various metaheuristics, including simulated annealing, iterated local search, and greedy randomized adaptive search procedures, among others. The efficacy of the RKO framework, implemented in C++ and publicly available (Github public repository: github.com/RKO-solver), is demonstrated through its application to three NP-hard combinatorial optimization problems: the alpha-neighborhood p-median problem, the tree of hubs location problem, and the node-capacitated graph partitioning problem. The results highlight the framework's ability to produce high-quality solutions across diverse problem domains, underscoring its potential as a robust tool for combinatorial optimization.

Bruno Salezze Vieira, Eduardo Machado Silva, Antonio Augusto Chaves

Efficient surgery room scheduling is essential for hospital efficiency, patient satisfaction, and resource utilization. This study addresses this challenge by introducing a novel concept of Random-Key Optimizer (RKO), rigorously tested on literature and new, real-world inspired instances. Our combinatorial optimization problem incorporates multi-room scheduling, equipment scheduling, and complex availability constraints for rooms, patients, and surgeons, facilitating rescheduling and enhancing operational flexibility. The RKO approach represents solutions as points in a continuous space, which are then mapped in the problem solution space via a deterministic function known as a decoder. The core idea is to operate metaheuristics and heuristics in the random-key space, unaware of the original solution space. We design the Biased Random-Key Genetic Algorithm with $Q$-Learning, Simulated Annealing, and Iterated Local Search for use within an RKO framework, employing a single decoder function. The proposed metaheuristics are complemented by lower-bound formulations, providing optimal gaps for evaluating the effectiveness of the heuristic results. Our results demonstrate significant lower and upper bounds improvements for the literature instances, notably proving one optimal result. Furthermore, the best-proposed metaheuristic efficiently generates schedules for the newly introduced instances, even in highly constrained scenarios. This research offers valuable insights and practical solutions for improving surgery scheduling processes, offering tangible benefits to hospitals by optimising resource allocation, reducing patient wait times, and enhancing overall operational efficiency.