Related papers: The {0,1}-knapsack problem with qualitative levels
Benchmark instances for the unbounded knapsack problem are typically generated according to specific criteria within a given constant range $R$, and these instances can be referred to as the unbounded knapsack problem with bounded…
The problem of ranking can be described as follows. We have a set of combinatorial objects $S$, such as, say, the k-subsets of n things, and we can imagine that they have been arranged in some list, say lexicographically, and we want to…
In this paper we consider the discounted 0-1 knapsack problem (DKP), which is an extension of the classical knapsack problem where a set of items is decomposed into groups of three items. At most one item can be chosen from each group and…
Here we present two novel contributions for achieving quantum advantage in solving difficult optimisation problems, both in theory and foreseeable practice. (1) We introduce the "Quantum Tree Generator", an approach to generate in…
Evolutionary algorithms are bio-inspired algorithms that can easily adapt to changing environments. Recent results in the area of runtime analysis have pointed out that algorithms such as the (1+1)~EA and Global SEMO can efficiently…
Factors are categorical variables, and the values which these variables assume are called levels. In this paper, we consider the variable selection problem where the set of potential predictors contains both factors and numerical variables.…
We propose a theoretical framework to capture incremental solutions to cardinality constrained maximization problems. The defining characteristic of our framework is that the cardinality/support of the solution is bounded by a value…
Gradual semantics within abstract argumentation associate a numeric score with every argument in a system, which represents the level of acceptability of this argument, and from which a preference ordering over arguments can be derived.…
We provide an exact algorithm to solve the log-linear continuous (fractional) knapsack problem. The algorithm is based on two lemmas that follow from the application of weak duality theorem and complementary slackness theorem to the linear…
Given a sample covariance matrix, we solve a maximum likelihood problem penalized by the number of nonzero coefficients in the inverse covariance matrix. Our objective is to find a sparse representation of the sample data and to highlight…
We consider AC electrical systems where each electrical device has a power demand expressed as a complex number, and there is a limit on the magnitude of total power supply. Motivated by this scenario, we introduce the complex-demand…
Knapsack and Subset Sum are fundamental NP-hard problems in combinatorial optimization. Recently there has been a growing interest in understanding the best possible pseudopolynomial running times for these problems with respect to various…
Given subsets of uncertain values, we study the problem of identifying the subset of minimum total value (sum of the uncertain values) by querying as few values as possible. This set selection problem falls into the field of explorable…
We consider the maximization problem of monotone submodular functions under an uncertain knapsack constraint. Specifically, the problem is discussed in the situation that the knapsack capacity is not given explicitly and can be accessed…
Combining quantum computers with classical compute power has become a standard means for developing algorithms that are eventually supposed to beat any purely classical alternatives. While in-principle advantages for solution quality or…
This paper introduces a family of learning-augmented algorithms for online knapsack problems that achieve near Pareto-optimal consistency-robustness trade-offs through a simple combination of trusted learning-augmented and worst-case…
We propose a stochastic variance reduced optimization algorithm for solving sparse learning problems with cardinality constraints. Sufficient conditions are provided, under which the proposed algorithm enjoys strong linear convergence…
We consider the problem of probably approximately correct (PAC) ranking $n$ items by adaptively eliciting subset-wise preference feedback. At each round, the learner chooses a subset of $k$ items and observes stochastic feedback indicating…
In this paper, we obtain a number of new simple pseudo-polynomial time algorithms on the well-known knapsack problem, focusing on the running time dependency on the number of items $n$, the maximum item weight $w_\mathrm{max}$, and the…
We study the ranking problem in generalized linear bandits. At each time, the learning agent selects an ordered list of items and observes stochastic outcomes. In recommendation systems, displaying an ordered list of the most attractive…