We develop sharp bounds on turnpike theorems for the unbounded knapsack problem. Turnpike theorems specify when it is optimal to load at least one unit of the best item (i.e., the one with the highest “bang-for-buck” ratio) and, thus can be used for problem preprocessing. The successive application of the turnpike theorems can drastically reduce the size of the knapsack problems to be solved. T...

Chance-constrained programming is a relevant model for many concrete problems. However, it is known to be very hard to tackle directly. In this paper, the chance-constrained knapsack problem (CKP) is addressed. Relying on the recent advances in robust optimization, a tractable combinatorial algorithm is proposed to solve CKP. It always provides feasible solutions for CKP. Moreover, for two spec...

While the 1980s were focused on the solution of large sized \easy" knapsack problems , this decade has brought several new algorithms, which are able to solve \hard" large sized instances. We will give an overview of the recent techniques for solving hard knapsack problems, with special emphasis on the addition of cardinality constraints , dynamic programming, and rudimentary divisibility. Comp...

The (offline) maximization (resp., minimization) knapsack problem is given a set of items with weights and sizes, and the capacity of a knapsack, to maximize (resp., minimize) the total weight of selected items under the constraint that the total size of the selected items is at most (resp., at least) the capacity of the knapsack. In this paper, we study online maximization and minimization kna...

A general-purpose parallel three-list six-table algorithm that can solve a number of knapsack-like NP-complete problems is developed in this paper. This kind of problems includes knapsack problem, exact satisfiability problem, set covering problem, etc. Running on an EREW PRAM model, The proposed parallel algorithm can find a solution of these problems of size n in O(2) time, with O(2) space an...

Cuckoo search (CS) is a novel biologically inspired algorithm and has been widely applied to many fields. Although some binary-coded CS variants are developed to solve 0-1 knapsack problems, the search accuracy and the convergence speed are still needed to further improve. According to the analysis of the shortcomings of the standard CS and the advantage of the global harmony search (GHS), a no...

The optimization of Multidimensional Knapsacks with Family-Split Penalties has been introduced in the literature as a variant more classical Knapsack and Multi-Knapsack problems. This problem deals set items partitioned families, when single item is picked to maximize utility, then all its family must be picked. Items from same can assigned different knapsacks, this situation split penalties ar...

This paper deals with three particular models of the bi-criteria {0,1}-knapsack problem: equal weighted items, constant sum of the criteria coe¢cients, and the combination of the two previous models. The con...guration of the Pareto frontier is presented and studied. Several properties on the number and the composition of the e¢cient solutions are devised. The connectedness of the e¢cient solut...