DNA computing is a new computational paradigm that executes parallel computation with DNA molecules. Some researches in DNA computing have been presented to solve computational problems such as NPcomplete problems in polynomial increasing time by using its super parallel and high density power. Among them knapsack problem is one of the most common problems which have been studied intensively in...

Given a knapsack of size K, non-negative values d and ∆, and a set S of items, each item e ∈ S with size se and value ve, we define a shelf as a subset of items packed inside a bin with total items size at most ∆. Two subsequent shelves must be separated by a shelf divisor of size d. The size of a shelf is the total size of its items plus the size of the shelf divisor. The Shelf-Knapsack Proble...

The Integer Knapsack Problem with Set-up Weights (IKPSW) is a generalization of the classical Integer Knapsack Problem (IKP), where each item type has a set-up weight that is added to the knapsack if any copies of the item type are in the knapsack solution. The k-item IKPSW (kIKPSW) is also considered, where a cardinality constraint imposes a value k on the total number of items in the knapsack...

A knapsack problem is to select a set of items that maximizes the total profit selected while keeping weight no less than capacity knapsack. As generalized form with multiple knapsacks, multi-knapsack (MKP) disjointed for each To solve MKP, we propose deep reinforcement learning (DRL) based approach, which takes as input available capacities profits and weights items, normalized unselected dete...

The Set-Union Knapsack Problem (SUKP) and Budgeted Maximum Coverage (BMCP) are two closely related variant problems of the popular knapsack problem. Given a set weighted elements items with nonnegative values, where each item covers several distinct elements, these both aim to find subset that maximizes an objective function while satisfying capacity (budget) constraint. We propose efficient ef...

Difficult knapsack problems are problems that are expressly designed to be difficult. In this paper, enhanced Quantum Evolutionary Algorithms are designed and their application is presented for the solution of the DKPs. The algorithms are general enough and can be used with advantage in other subset selection problems.