In the knapsack problem, you are given a knapsack of size B ∈ Z and a set S = {a1, . . . , an} of objects with corresponding sizes and profits s(ai) ∈ Z and p(ai) ∈ Z. The goal is to find the optimal subset of objects whose total size is bounded by B and has the maximum possible total profit. This problem is also sometimes called the 0/1 knapsack problem because each object must be either in th...

The submodular knapsack set is the discrete lower level set of a submodular function. The modular case reduces to the classical linear 0-1 knapsack set. One motivation for studying the submodular knapsack polytope is to address 0-1 programming problems with uncertain coefficients. Under various assumptions, a probabilistic constraint on 0-1 variables can be modeled as a submodular knapsack set....

The submodular knapsack set is the discrete lower level set of a submodular function. The modular case reduces to the classical linear 0-1 knapsack set. One motivation for studying the submodular knapsack polytope is to address 0-1 programming problems with uncertain coefficients. Under various assumptions, a probabilistic constraint on 0-1 variables can be modeled as a submodular knapsack set....

We tackle the thief orienteering problem (ThOP), an academic multi-component that combines two classical combinatorial problems, namely Knapsack Problem and Orienteering Problem. In ThOP, a has time limit to steal items distributed in given set of cities. While traveling, collects by storing them their knapsack, which turn reduces travel speed. The as objective maximize total profit stolen item...

Worst-case execution time test generation can be hard if tested programs use complex heuristics. This is especially true in the case of the knapsack problem, which is often called “the easiest NP-complete problem”. For randomly generated test data, the expected running time of some algorithms for this problem is linear. We present an approach for generation of tests against algorithms for the k...

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...

This paper describes a new technique for solving the duration minimization in a resourceconstrained network. It is based on a transformation of the resource-constrained project scheduling problem (RCPSP) to a sequence of (multi)knapsack problem (MKP) solutions. In the first part, three deterministic approaches are summarized and their time complexity is discussed. Due to the combinatorial natur...

This paper summarizes and compares approaches to solving the knapsack problem and its known application in capital budgeting. The first approach uses deterministic methods and can be applied to small-size tasks with a single constraint. We can also apply commercial software systems such as the GAMS modelling system. However, because of NP-completeness of the problem, more complex problem instan...

This paper aims at proposing tractable algorithms to find effectively good solutions to large size chance-constrained combinatorial problems. A new robust model is introduced to deal with uncertainty in mixed-integer linear problems. It is shown to be strongly related to chance-constrained programming when considering pure 0– 1 problems. Furthermore, its tractability is highlighted. Then, an op...

The minimum cost multiple-source unsplittable flow problem is studied in this paper. A simple necessary condition to get a solution is proposed. It deals with capacities and demands and can be seen as a generalization of the well-known semi-metric condition for continuous multicommdity flows. A cutting plane algorithm is derived using a superadditive approach. The inequalities considered here a...