Renan F. F. da Silva

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.