The Multiple-Choice Knapsack (MCKP) (see Pisinger 13) is another variant of KP where the picking criterion of items is more restrictive. Polynomial approximation algorithms for single-dimensional knapsack. The Multi-Dimensional Knapsack Problem (MDKP) (see Chu and Beasley 2) is one kind of KP where the constraints are multidimensional. The preliminary results demonstrate the effectiveness of the proposed solution approach. O-l knapsack problem is NP-complete but not strongly NP-com- plete. The multi-dimensional knapsack problem (MKP) is a generalization of the classical knapsack problem, a problem for allocating a resource/subset of objects. Computational experiments are carried out on the widely used benchmark instances with up to 100 items and 30 knapsack constraints. To accelerate the Bayesian optimisation guided search process, various techniques are proposed including variable domain tightening, initialisation by the Genetic Algorithm, and optimisation landscape smoothing by local search. The Multidimensional Knapsack Problem (MKP) is a well-studied, strongly NP- hard combinatorial optimization problem occurring in many different applica. The first level makes the decisions about the optimal allocation of knapsack capacities to different item groups, while the second level solves a multidimensional knapsack problem of reduced size for each item group. For the multidimensional knapsack problem with a large number of items and knapsack constraints, a two-level formulation is presented to take advantage of the global optimisation capability of the Bayesian optimisation approach, and the efficiency of integer programming solvers on small problems. Applying the idea of equality cuts to the multi-demand multidimensional knapsack problem resulted in a new class of cutting planes named anticover cover. Exact as well as heuristic methods exist for solving this type of problem. (Math Methods Oper Res 92(1):107132, 2020) presented the Rectangular Knapsack Problem (Rkp) as a crucial subproblem in the study on the Cardinality-constrained. The maximum number of items whose cost varies is governed by a parameter, which is supposed to have been statistically estimated. The multidimensional 01 knapsack problem is a combinatorial optimization problem, which is NP-hard and arises in many fields of optimization. It represents an extension of the KP where the weight of each item varies in a pre-defined interval. This paper considers the application of Bayesian optimisation to the well-known multidimensional knapsack problem which is strongly NP-hard. The Robust Knapsack Problem (RKP) is one possible way to face this lack of information.
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