A decomposition approach for multidimensional knapsacks with family-split penalties

The optimization of Multidimensional Knapsacks with Family-Split Penalties has been introduced in the literature as a variant of the more classical Multidimensional Knapsack and Multi-Knapsack problems. This problem deals with a set of items partitioned in families, and when a single item is picked to maximize the utility, then all items in its family must be picked. Items from the same family can be assigned to different knapsacks, and in this situation split penalties are paid. This problem arises in real applications in various fields. This paper proposes a new exact and fast algorithm based on a specific Combinatorial Benders Cuts scheme. An extensive experimental campaign computationally shows the validity of the proposed method and its superior performance compared to both commercial solvers and state-of-the-art approaches. The paper also addresses algorithmic flexibility and scalability issues, investigates challenging cases, and analyzes the impact of problem parameters on the algorithm behavior. Moreover, it shows the applicability of the proposed approach to a wider class of realistic problems, including fixed costs related to each knapsack utilization. Finally, further possible research directions are considered

Modelos empíricos aplicados a análise da capacidade produtiva: Aplicações em cenários de incertezas / Empirical models applied to productive capacity analysis: Applications in uncertainty scenarios

Cenários caracterizados por realidades de incerteza levam os governantes da esfera federal a procurarem repensar e desenvolver ferramentas que possam garantir vantagem competitiva quanto a utilização de seu capital humano em períodos marcados por fragilidades na política fiscal e monetária da nação. Surge, dessa forma, a necessidade de localizar o conceito de dimensionamento em uma literatura internacional, nacional e diversa, partindo de uma definição adequada ao contexto da gestão organizacional visando a garantia de economicidade para o setor público. O objetivo deste estudo teórico é fornecer uma referência quanto a métodos quantitativos de dimensionamento da força de trabalho. Sendo assim, apresenta-se três tipos de modelos algébricos, estatísticos e de otimização. Salienta-se suas similaridades e idiossincrasias, além de exemplificar suas práticas. Por fim, o conjunto de possibilidades apontadas neste artigo viabiliza métodos para compreender a realidade organizacional em uma proposição estratégica para uma gestão mais capacitada para tomadas de decisão

Applied (Meta)-Heuristic in Intelligent Systems

Engineering and business problems are becoming increasingly difficult to solve due to the new economics triggered by big data, artificial intelligence, and the internet of things. Exact algorithms and heuristics are insufficient for solving such large and unstructured problems; instead, metaheuristic algorithms have emerged as the prevailing methods. A generic metaheuristic framework guides the course of search trajectories beyond local optimality, thus overcoming the limitations of traditional computation methods. The application of modern metaheuristics ranges from unmanned aerial and ground surface vehicles, unmanned factories, resource-constrained production, and humanoids to green logistics, renewable energy, circular economy, agricultural technology, environmental protection, finance technology, and the entertainment industry. This Special Issue presents high-quality papers proposing modern metaheuristics in intelligent systems

Exact approaches for the knapsack problem with setups

We consider a generalization of the knapsack problem in which items are partitioned into classes, each characterized by a fixed cost and capacity. We study three alternative Integer Linear Programming formulations. For each formulation, we design an efficient algorithm to compute the linear programming relaxation (one of which is based on Column Generation techniques). We theoretically compare the strength of the relaxations and derive specific results for a relevant case arising in benchmark instances from the literature. Finally, we embed the algorithms above into a unified implicit enumeration scheme which is run in parallel with an improved Dynamic Programming algorithm to effectively solve the problem to proven optimality. An extensive computational analysis shows that our new exact algorithm is capable of efficiently solving all the instances of the literature and turns out to be the best algorithm for instances with a low number of classes

Exact approaches for the knapsack problem with setups

We consider a generalization of the knapsack problem in which items are partitioned into classes, each characterized by a fixed cost and capacity. We study three alternative Integer Linear Programming formulations. For each formulation, we design an efficient algorithm to compute the linear programming relaxation (one of which is based on Column Generation techniques). We theoretically compare the strength of the relaxations and derive specific results for a relevant case arising in benchmark instances from the literature. Finally, we embed the algorithms above into a unified implicit enumeration scheme which is run in parallel with an improved Dynamic Programming algorithm to effectively solve the problem to proven optimality. An extensive computational analysis shows that our new exact algorithm is capable of efficiently solving all the instances of the literature and turns out to be the best algorithm for instances with a low number of classes