Related papers: Genetic Algorithm for the 0/1 Multidimensional Kna…
The Bilevel Optimization Problem is a hierarchical optimization problem with two agents, a leader and a follower. The leader make their own decisions first, and the followers make the best choices accordingly. The leader knows the…
Knapsack problems (KPs) are common in industry, but solving KPs is known to be NP-hard and has been tractable only at a relatively small scale. This paper examines KPs in a slightly generalized form and shows that they can be solved nearly…
In the online general knapsack problem, an algorithm is presented with an item $x=(s,v)$ of size $s$ and value $v$ and must irrevocably choose to pack such an item into the knapsack or reject it before the next item appears. The goal is to…
The development of a satisfying and rigorous mathematical understanding of the performance of neural networks is a major challenge in artificial intelligence. Against this background, we study the expressive power of neural networks through…
The disjunctively constrained knapsack problem consists in packing a subset of pairwisely compatible items in a capacity-constrained knapsack such that the total profit of the selected items is maximized while satisfying the knapsack…
The article describes an investigation of the effectiveness of genetic algorithms for multi-objective combinatorial optimization (MOCO) by presenting an application for the vehicle routing problem with soft time windows. The work is…
Constrained submodular maximization problems encompass a wide variety of applications, including personalized recommendation, team formation, and revenue maximization via viral marketing. The massive instances occurring in modern day…
In general, we can not use algebraic or enumerative methods to optimize a quality control (QC) procedure so as to detect the critical random and systematic analytical errors with stated probabilities, while the probability for false…
In the incremental knapsack problem ($\IK$), we are given a knapsack whose capacity grows weakly as a function of time. There is a time horizon of $T$ periods and the capacity of the knapsack is $B_t$ in period $t$ for $t = 1, \ldots, T$.…
We describe an implementation of a genetic algorithm on partially commutative groups and apply it to the double coset search problem on a subclass of groups. This transforms a combinatorial group theory problem to a problem of combinatorial…
We introduce and study a discrete multi-period extension of the classical knapsack problem, dubbed generalized incremental knapsack. In this setting, we are given a set of $n$ items, each associated with a non-negative weight, and $T$ time…
We show for several computational problems how classical greedy algorithms for special cases can be derived in a simple way from dynamic programs for the general case: interval scheduling (restricted to unit weights), knapsack (restricted…
Addressing a complex real-world optimization problem is a challenging task. The chance-constrained knapsack problem with correlated uniform weights plays an important role in the case where dependent stochastic components are considered. We…
A genetic algorithm (GA) is a search-based optimization technique based on the principles of Genetics and Natural Selection. We present an algorithm which enhances the classical GA with input from quantum annealers. As in a classical GA,…
Quantum algorithms are emerging tools in the design of functional materials due to their powerful solution space search capability. How to balance the high price of quantum computing resources and the growing computing needs has become an…
We study the knapsack problem with graph theoretic constraints. That is, we assume that there exists a graph structure on the set of items of knapsack and the solution also needs to satisfy certain graph theoretic properties on top of…
The genetic algorithm is an optimization procedure motivated by biological evolution and is successfully applied to optimization problems in different areas. A statistical mechanics model for its dynamics is proposed based on the…
This paper presents a cumulative multi-niching genetic algorithm (CMN GA), designed to expedite optimization problems that have computationally-expensive multimodal objective functions. By never discarding individuals from the population,…
The use of Lagrangian cuts proves effective in enhancing the lower bound of the master problem within the execution of benders-type algorithms, particularly in the context of two-stage stochastic programs. However, even the process of…
Optimization problems are ubiquitous in various industrial settings, and multi-knapsack optimization is one recurrent task faced daily by several industries. The advent of quantum computing has opened a new paradigm for computationally…