We introduce methods to count and enumerate all maximal independent, all maximum independent sets, and all independent sets in threshold graphs and k-threshold graphs. Within threshold graphs and k-threshold graphs independent sets correspond to feasible solutions in related knapsack instances. We give several characterizations for knapsack instances and multidimensional knapsack instances whic...

A lot of current research in DNA computing has been directed towards solving hard combinatorial problems. Among them Knapsack problem is one of the most common problems which have been studied intensively in the last decade attracting both theorists and practicians. Fractional Knapsack Problem is easily solvable by greedy strategy, but 0/1 Knapsack Problem is not possible to solve in this metho...

In this paper, we discuss the adjacency structures of some classes of 0-1 polytopes including knapsack polytopes, set covering polytopes and 0-1 polytopes represented by complete sets of implicants. We show that for each class of 0-1 polytope, non-adjacency test problems are NP-complete. For equality constrained knapsack polytopes, we can solve adjacency test problems in pseudo polynomial time.

Connectedness of efficient solutions is a powerful property in multiple objective combinatorial optimization since it allows the construction of the complete efficient set using neighborhood search techniques. In this paper we show that, however, most of the classical multiple objective combinatorial optimization problems do not possess the connectedness property in general, including, among ot...

One of the combinatorial optimization problems is Knapsack problem, which aims to maximize benefit objects whose weight not exceeding capacity knapsack. This paper introduces artificial bee colony algorithm select a subset project and represented by knapsack problem put best investment plan achieve highest profits within determined costs, this one applications financial field. The result from p...

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....