Polynomial-time approximation scheme
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New binary bat algorithm for solving 0–1 knapsack problem Open
This paper presents a novel binary bat algorithm (NBBA) to solve 0–1 knapsack problems. The proposed algorithm combines two important phases: binary bat algorithm (BBA) and local search scheme (LSS). The bat algorithm enables the bats to e…
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A Comparative Study of Meta-Heuristic Optimization Algorithms for 0 – 1 Knapsack Problem: Some Initial Results Open
In this paper, we present some initial results of several meta-heuristic optimization algorithms, namely, genetic algorithms, simulated annealing, branch and bound, dynamic programming, greedy search algorithm, and a hybrid genetic algorit…
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The Hardness of Approximation of Euclidean k-means Open
The Euclidean $k$-means problem is a classical problem that has been extensively studied in the theoretical computer science, machine learning and the computational geometry communities. In this problem, we are given a set of $n$ points in…
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Genetic Algorithm for the 0/1 Multidimensional Knapsack Problem Open
The 0/1 multidimensional knapsack problem is the 0/1 knapsack problem with m constraints which makes it difficult to solve using traditional methods like dynamic programming or branch and bound algorithms. We present a genetic algorithm fo…
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Chamberlin--Courant Rule with Approval Ballots: Approximating the MaxCover Problem with Bounded Frequencies in FPT Time Open
We consider the problem of winner determination under Chamberlin--Courant's multiwinner voting rule with approval utilities. This problem is equivalent to the well-known NP-complete MaxCover problem and, so, the best polynomial-time approx…
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Polynomial Time Approximation Scheme for Two Parallel Machines Scheduling with a Common Due Date to Maximize Early Work Open
We study the scheduling problem with a common due date on two parallel identical machines and the total early work criterion. The problem is known to be NP-hard. We prove a few dominance properties of optimal solutions of this problem. The…
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Migrating birds optimization (MBO) algorithm to solve knapsack problem Open
This study presents Migrating Birds Optimization (MBO) which is a novel meta-heuristic algorithm for the solution of knapsack problem. The knapsack problem which is classified as NP-complete problem is a combinatorial optimization problem.…
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Approximation Schemes for 0-1 Knapsack Open
We revisit the standard 0-1 knapsack problem. The latest polynomial-time approximation scheme by Rhee (2015) with approximation factor 1+eps has running time near O(n+(1/eps)^{5/2}) (ignoring polylogarithmic factors), and is randomized. We…
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Knapsack problems with position-dependent item weights or profits Open
We consider three new knapsack problems with variable weights or profits of items, where the weight or profit of an item depends on the position of the item in the sequence of items packed in the knapsack. We show how to solve the problems…
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Comparison of Dynamic Programming Algorithm and Greedy Algorithm on Integer Knapsack Problem in Freight Transportation Open
At this time the delivery of goods to be familiar because the use of delivery of goods services greatly facilitate customers. PT Post Indonesia is one of the delivery of goods. On the delivery of goods, we often encounter the selection of …
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A PTAS for <i>ℓ<sub>p</sub></i>-Low Rank Approximation Open
A number of recent works have studied algorithms for entrywise ℓp-low rank approximation, namely algorithms which given an n × d matrix A (with n ≥ d), output a rank-k matrix B minimizing ‖A – B‖pp = ∑i, j|Ai, j – Bi, j|p when p > 0; and ‖…
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Different Transfer Functions for Binary Particle Swarm Optimization with a New Encoding Scheme for Discounted {0-1} Knapsack Problem Open
The discounted {0-1} knapsack problem (DKP01) is a kind of knapsack problem with group structure and discount relationships among items. It is more challenging than the classical 0-1 knapsack problem. In this paper, we study binary particl…
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A common approximation framework for early work, late work, and resource leveling problems Open
We study the approximability of two related machine scheduling problems. In\nthe late work minimization problem, there are identical parallel machines and\nthe jobs have a common due date. The objective is to minimize the late work,\ndefin…
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Minimizing total weighted completion time on a single machine subject to non-renewable resource constraints Open
In this paper we describe new complexity
\nresults, and approximation algorithms for single ma-
\nchine scheduling problems with non-renewable resource
\nconstraints and the total weighted completion time ob-
\njective. This problem is har…
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Truthful Mechanisms for Combinatorial Allocation of Electric Power in Alternating Current Electric Systems for Smart Grid Open
Traditional studies of combinatorial auctions often only consider linear constraints. The rise of smart grid presents a new class of auctions, characterized by quadratic constraints. This article studies the complex-demand knapsack problem…
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Binary salp swarm algorithm for discounted {0-1} knapsack problem Open
While the classical knapsack problem has been the object to be solved by optimization algorithm proposals for many years, another version of this problem, discounted {0-1} knapsack problem, is gaining a lot of attention recently. The origi…
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A Subquadratic Approximation Scheme for Partition Open
The subject of this paper is the time complexity of approximating Knapsack, Subset Sum, Partition, and some other related problems. The main result is an $\widetilde{O}(n+1/\varepsilon^{5/3})$ time randomized FPTAS for Partition, which is …
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A Binary Multi-Scale Quantum Harmonic Oscillator Algorithm for 0–1 Knapsack Problem With Genetic Operator Open
The 0-1 knapsack problem is a typical discrete combinatorial optimization problem with numerous applications. In this paper, a binary multi-scale quantum harmonic oscillator algorithm (BMQHOA) with genetic operator is proposed for solving …
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Amplitude Angle Modulated Bat Algorithm With Application to Zero-One Knapsack Problem Open
Angle-modulated bat algorithm (AMBA) provides a technique that enables the bat algorithm (BA) developed for continuous problems to operate in binary spaces, which employs an angle modulation technique to generate a bit string corresponding…
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Optimal algorithms for scheduling under time-of-use tariffs Open
We consider a natural generalization of classical scheduling problems to a setting in which using a time unit for processing a job causes some time-dependent cost, the time-of-use tariff, which must be paid in addition to the standard sche…
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Provably Good Solutions to the Knapsack Problem via Neural Networks of Bounded Size Open
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 throug…
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Streaming Algorithms for Maximizing Monotone Submodular Functions under a Knapsack Constraint Open
In this paper, we consider the problem of maximizing a monotone submodular function subject to a knapsack constraint in the streaming setting. In particular, the elements arrive sequentially and at any point of time, the algorithm has acce…
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Comparison and Analysis of Algorithms for the 0/1 Knapsack Problem Open
The 0/1 knapsack problem is a typical problem in the field of operational research and combinatorial optimization, and it belongs to the NP problem. Research on the solutions of the 0/1 knapsack problem algorithm has very important practic…
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Leveraging Knapsack QAOA Approach for Optimal Electric Vehicle Charging Open
The electric vehicle (EV) industry is currently afflicted with inefficient charging systems. Considering the growing adoption of EVs, optimization strategies for efficient charging, and overcoming constraints such as a limited power supply…
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Approximation and Parameterized Complexity of Minimax Approval Voting Open
We present three results on the complexity of Minimax Approval Voting. First, we study Minimax Approval Voting parameterized by the Hamming distance d from the solution to the votes. We show Minimax Approval Voting admits no algorithm runn…
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Binary social group optimization algorithm for solving 0-1 knapsack problem Open
In this paper, we propose the binary version of the Social Group Optimization (BSGO) algorithm for solving the 0-1 knapsack problem. The standard Social Group Optimization (SGO) is used for continuous optimization problems. So a transforma…
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A PTAS for planar group Steiner tree via spanner bootstrapping and prize collecting Open
We present the first polynomial-time approximation scheme (PTAS), i.e., (1+ε)-approximation algorithm for any constant ε> 0, for the planar group Steiner tree problem (in which each group lies on a boundary of a face). This result improves…
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On Approximating (Sparse) Covering Integer Programs Open
We consider approximation algorithms for covering integer programs of the form min 〈c, x〉 over x ∊ ℤ≥0n s.t. Ax ≥ b and x ≤ d; where A ∊ ℝ≥0m×n, b ∊ ℝ≥0m, and c, d ∊ ℝ≥0n all have nonnegative entries. We refer to this problem as CIP, and t…
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Improved Approximation Algorithms for 2-Dimensional Knapsack: Packing into Multiple L-Shapes, Spirals, and More Open
In the 2-Dimensional Knapsack problem (2DK) we are given a square knapsack and a collection of n rectangular items with integer sizes and profits. Our goal is to find the most profitable subset of items that can be packed non-overlappingly…
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A New Moth-Flame Optimization Algorithm for Discounted {0-1} Knapsack Problem Open
The discounted {0–1} knapsack problem may be a kind of backpack issue with gathering structure and rebate connections among things. A moth-flame optimization algorithm has shown good searchability combined with an effective solution presen…