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The online bin packing problem is a well-known optimization challenge that finds application in a wide range of real-world scenarios. In the paper, we propose a novel algorithm called FuzzyPatternPack(FPP), which leverages fuzzy inference and pattern-based predictions of the distribution of item sizes in online bin packing. In comparison to traditional heuristics like BestFit(BF) and FirstFit(FF), as well as the more recent PatternPack(PaP) and ProfilePacking(PrP) algorithm based on online predictions, FPP demonstrates competitive and superior performance in solving various benchmark problems. Particularly, it excels in addressing problems with evolving distributions, making it a promising solution for real-world applications where the item sizes may change over time. This research unveils the promising potential of employing fuzzy logic to effectively address uncertainty in scheduling and planning problems. • Proposed algorithm utilizes pattern extraction and handles uncertainty effectively. • Employment of a fuzzy classification system adds flexibility in modeling ambiguity. • Superior performance and robustness were seen under evolving input distributions. [ABSTRACT FROM AUTHOR]

Highlights • A new variant of the Bin Packing Problem is introduced. • It is motivated by last mile delivery to tiny stores. • Items to be delivered belong to categories that may not be transported together in the same vehicle. • Extensive computational tests are performed on instances derived from the literature. • Results show that our VNS algorithm can effectively solve the BPCC in very short CPU times. Abstract In this paper, we address the Bin Packing Problem with Compatible Categories (BPCC), a challenging optimization problem that arises in the context of last mile distribution to nanostores in large cities, particularly in developing countries. By introducing the concept of incompatible categories of items to be delivered (i.e., types of items that cannot be transported together, such as food and cleaning products), as opposed to the item-by-item incompatibility found in previous literature, we aim to determine the best assignment of deliveries of distinct products to a homogeneous fleet of capacitated vehicles in order to minimize the number of required vehicles (bins). To solve large instances of the BPCC that are commonly found in practice, we propose an efficient variable neighborhood search (VNS) metaheuristic that relies on a simple greedy heuristic to generate initial solutions and on simple and efficient neighborhoods as well as problem-tailored shaking procedures. We perform extensive computational experiments on a very large set of 8000 instances derived from benchmark datasets. The tested instances differ in terms of number of items (ranging from 201 to 1002), bin capacities, compatibility matrices and proportion of items that belong to the different categories. We also present two new mathematical formulations for the BPCC and compare them to the item-by-item bin packing formulation (Gendreau et al., 2004) using a high performance computer (HPC). The computational experiments indicate that our VNS algorithm can effectively solve the BPCC in very short CPU times. [ABSTRACT FROM AUTHOR]

Test assembly design problems appear in the areas of psychology and education, among others. The goal of these problems is to construct one or multiple tests to evaluate the test subject. This paper studies a recent formulation of the problem known as the one-dimensional minimax bin-packing problem with bin size constraints (MINIMAX_BSC). In the MINIMAX_BSC, items are initially divided into groups and multiple tests need to be constructed using a single item from each group, while minimizing differences among the tests. We first show that the problem is NP-Hard, which remained an open question. Second, we propose three different local search neighborhoods derived from the exact resolution of special cases of the problem, and combine them into a variable neighborhood search (VNS) metaheuristic. Finally, we test the proposed algorithm using real-life-based instances. The results show that the algorithm is able to obtain optimal or near-optimal solutions for instances with up to 60 000-item pools. Consequently, the algorithm is a viable option to design large-scale tests, as well as to provide tests for online small-sized situations such as those found in e-learning platforms. [ABSTRACT FROM AUTHOR]

One- and two-dimensional packing and cutting problems occur in many commercial contexts, and it is often important to be able to get good-quality solutions quickly. Fairly simple deterministic heuristics are often used for this purpose, but such heuristics typically find excellent solutions for some problems and only mediocre ones for others. Trying several different heuristics on a problem adds to the cost. This paper describes a hyper-heuristic methodology that can generate a fast, deterministic algorithm capable of producing results comparable to that of using the best problem-specific heuristic, and sometimes even better, but without the cost of trying all the heuristics. The generated algorithm handles both one- and two-dimensional problems, including two-dimensional problems that involve irregular concave polygons. The approach is validated using a large set of 1417 such problems, including a new benchmark set of 480 problems that include concave polygons. [ABSTRACT FROM AUTHOR]