Rafael C. S. Schouery

Renan Fernando Franco da Silva, Vinícius Loti de Lima, Rafael C. S. Schouery et al.

Cutting and packing problems are fundamental in manufacturing and logistics, as they aim to minimize waste and improve efficiency. The Cutting Stock Problem (CSP) concerns material cutting, whereas the Bin Packing Problem (BPP) concerns packing items into bins. Since the 1960s, these problems have been widely studied because of their industrial relevance and computational complexity. Over time, exact algorithms, often based on mixed-integer programming (MIP), have become able to solve increasingly large instances, often with hundreds of items, within minutes. In 2016, Delorme et al. showed that the algorithm BELOV, combined with a modern version of CPLEX, could solve all benchmark instances available at that time within ten minutes. Motivated by this progress, they introduced two new classes of instances, AI and ANI, which proved extremely challenging for all exact solvers and have guided research on CSP and BPP over the past decade. Despite significant subsequent advances, 13 out of 500 of these instances remain unsolved by state-of-the-art algorithms within a one-hour time limit. In this paper, we show that although AI and ANI instances are particularly hard for MIP-based methods, the BPP restricted to these classes is not strongly NP-hard. We present polynomial-time algorithms for the AI class and pseudopolynomial-time algorithms for the ANI class. Our best algorithms solve all benchmark instances from these classes orders of magnitude faster than previous approaches. They are also straightforward to adapt to the Skiving Stock Problem (SSP), which can be seen as a counterpart of the CSP. Additionally, they can be used as preprocessing routines in exact methods, as their runtime is independent of the instance class, although they are guaranteed to return an optimality status only for instances belonging to the class for which they were designed.

Renan F. F. da Silva, Thiago A. de Queiroz, Rafael C. S. Schouery

The Knapsack Problem (KP) and its generalization, the Bounded Knapsack Problem (BKP), are classical NP-hard problems with numerous practical applications, and despite being introduced over 25 years ago, the solvers COMBO and BOUKNAP remain the state of the art due to their highly optimized implementations and sophisticated bounding techniques. In this work, we present RECORD (Refined Core-based Dynamic Programming), a new solver for both problems that builds upon key components of COMBO, including core- and state-based dynamic programming, weak upper bounds, and surrogate relaxation with cardinality constraints, while introducing novel strategies to overcome its limitations. In particular, we propose multiplicity reduction to limit the number of distinct item types, combined with on-the-fly item aggregation, refined fixing-by-dominance techniques, and a new divisibility bound that strengthens item fixing and symmetry breaking. These enhancements allow RECORD to preserve COMBO's near-linear-time behavior on most instances while achieving substantial speedups on more challenging cases, and computational experiments show that it consistently outperforms both COMBO and BOUKNAP on difficult benchmark sets, often by several orders of magnitude, establishing a new state-of-the-art solver for KP and BKP.

Renan F. F. da Silva, Yulle G. F. Borges, Rafael C. S. Schouery

The Colored Bin Packing Problem (CBPP) is a generalization of the Bin Packing Problem (BPP). The CBPP consists of packing a set of items, each with a weight and a color, in bins of limited capacity, minimizing the number of used bins and satisfying the constraint that two items of the same color cannot be packed side by side in the same bin. In this article, we proposed an adaptation of BPP heuristics and new heuristics for the CBPP. Moreover, we propose a set of fast neighborhood search algorithms for CBPP. These neighborhoods are applied in a meta-heuristic approach based on the Variable Neighborhood Search (VNS) and a matheuristic approach that combines linear programming with the meta-heuristics VNS and Greedy Randomized Adaptive Search (GRASP). The results indicate that our matheuristic is superior to VNS and that both approaches can find near-optimal solutions for a large number of instances, even for those with many items.

Welverton R. Silva, Rafael C. S. Schouery

One-way car-sharing systems are transportation systems that allow customers to rent cars at stations scattered around the city, use them for a short journey, and return them at any station. The maximum customers' satisfaction problem concerns the task of assigning the cars, initially located at given stations, to maximize the number of satisfied customers. We consider the problem with two stations where each customer has exactly two demands in opposite directions between both stations, and a customer is satisfied only if both their demands are fulfilled. For solving this problem, we propose mixed-integer programming (MIP) models and matheuristics based on local search. We created a benchmark of instances used to test the exact and heuristic approaches. Additionally, we proposed a preprocessing procedure to reduce the size of the instance. Our MIP models can solve to optimality 85% of the proposed instances with 1000 customers in 10 minutes, with an average gap smaller than 0.1% for all these instances. For larger instances (2500 and 5000 customers), except for some particular cases, they presented an average gap smaller than 0.8%. Also, our local-based matheuristics presented small average gaps which are better than the MIP models in some larger instances.