A dynamic knapsack set is a natural generalization of the 0-1 knapsack set with a continuous variable studied recently. For dynamic knapsack sets a large family of facet-defining inequalities, called dynamic knapsack inequalities, are derived by fixing variables to one and then lifting. Surprisingly such inequalities have the simultaneous lifting property, and for small instances provide a sign...

Many problems in business and engineering can be modeled as 0-1 knapsack problems. However, the 0-1 knapsack problem is one of the classical NP-hard problems. Therefore, it is valuable to develop effective and efficient algorithms for solving 0-1 knapsack problems. Aiming at the drawbacks of the selection operator in the traditional differential evolution (DE), we present a novel discrete diffe...

This paper introduces tight upper bounds for the daily photograph scheduling problem of earth observation satellites. These bounds, which were unavailable until now, allow us to assess the quality of the heuristic solutions obtained previously. These bounds are obtained with a partition-based approach following the “divide and pas conquer” principle. Dynamic programming and tabu search are conj...

We consider a problem commonly faced in industry, involving annual selection of plant capital investments. A typical approach to such a problem uses a multi-knapsack formulation, which takes as input the available budget in each year, the stream of liabilities induced by selecting each project, and the profit, i.e., net present value, of each project. The goal is to select the portfolio of proj...

We consider the following zero-sum game related to the knapsack problem. Given an instance of the knapsack problem, Alice chooses a knapsack solution and Bob chooses a cardinality k with knowing Alice’s solution. Then, Alice obtains a payoff equal to the ratio of the profit of the best k items in her solution to that of the best solution of size at most k. For α > 0, a knapsack solution is call...

We consider a variant of the knapsack problem, where items are available with different possible weights. Using a separate budget for these item improvements, the question is: Which items should be improved to which degree such that the resulting classic knapsack problem yields maximum profit? We present a detailed analysis for several cases of improvable knapsack problems, presenting constant ...

In 1978 Merkle and Hellman [11] proposed public key cryptosystems based on the knapsack problem. The simplest of these cryptosystems, the basic knapsack cryptosystem, works as follows. The public information is a set of nonnegative integers { a i : 1 ≤ i ≤ n } which are called knapsack weights. Messages are encrypted by first being broken into blocks (x 1 , ... ,x n ) of n binary digits. A bloc...