Heuristics for Finding Sparse Solutions of Linear Inequalities

2021 ◽  
Author(s):  
Yichen Yang ◽  
Zhaohui Liu
Keyword(s):  
Optimization Problem ◽  
Search Algorithm ◽  
Greedy Algorithms ◽  
Linear Inequalities ◽  
Greedy Heuristic ◽  
Local Search Algorithm ◽  
The Third ◽  
Primal And Dual ◽  
Zero Norm ◽  
Sparse Solutions

In this paper, we consider the problem of finding a sparse solution, with a minimal number of nonzero components, for a set of linear inequalities. This optimization problem is combinatorial and arises in various fields such as machine learning and compressed sensing. We present three new heuristics for the problem. The first two are greedy algorithms minimizing the sum of infeasibilities in the primal and dual spaces with different selection rules. The third heuristic is a combination of the greedy heuristic in the dual space and a local search algorithm. In numerical experiments, our proposed heuristics are compared with the weighted-[Formula: see text] algorithm and DCA programming with three different non-convex approximations of the zero norm. The computational results demonstrate the efficiency of our methods.

Privacy Preserving Through Fireworks Algorithm Based Model for Image Perturbation in Big Data

2015 ◽  
Vol 6 (3) ◽  
pp. 41-58 ◽  
Author(s):  
Amine Rahmani ◽  
Abdelmalek Amine ◽  
Reda Mohamed Hamou ◽  
Mohamed Elhadi Rahmani ◽  
Hadj Ahmed Bouarara
Keyword(s):  
Big Data ◽  
Search Algorithm ◽  
Iterated Local Search ◽  
Privacy Preserving ◽  
Cloud Services ◽  
Local Search Algorithm ◽  
Medical Studies ◽  
Fireworks Algorithm ◽  
The Third ◽  
Highly Sensitive

Nowadays, Social networks and cloud services contain billions of users over the planet. Instagram, Facebook and other networks give the opportunity to share images. Users upload millions of pictures each day, including personal images. Another domain, which concerns medical studies, requires a highly sensitive medical images that retain personal details close to patients. Image perturbation have attracted a great deal of attention in the last few years. Many works concerning image ciphering and perturbing have been published. This paper deals with the problem of image perturbation for privacy preserving. The authors build three new systems that consist of hiding small details in pictures by rotating some pixels. Their models use two algorithms: the first one involves a simulation of the firework algorithm in which they place fireworks on selected pixels then represents sparks as rotation processes. The second system consists of a model of rotation based perturbation using iterated local search algorithm (ILS) with 2 optimization stages. Meanwhile, the third one consists of using the same principle of the previous system except by using the ILS algorithm with 3 optimization stages.

scholarly journals From Decimation to Local Search and Back: A New Approach to MaxSAT

2017 ◽  
Author(s):  
Shaowei Cai ◽  
Chuan Luo ◽  
Haochen Zhang
Keyword(s):  
Combinatorial Optimization ◽  
Local Search ◽  
Optimization Problem ◽  
State Of The Art ◽  
Search Algorithm ◽  
Combinatorial Optimization Problem ◽  
Np Hard ◽  
Local Search Algorithm ◽  
Maximum Satisfiability ◽  
New Approach

Maximum Satisfiability (MaxSAT) is an important NP-hard combinatorial optimization problem with many applications and MaxSAT solving has attracted much interest. This work proposes a new incomplete approach to MaxSAT. We propose a novel decimation algorithm for MaxSAT, and then combine it with a local search algorithm. Our approach works by interleaving between the decimation algorithm and the local search algorithm, with useful information passed between them. Experiments show that our solver DeciLS achieves state of the art performance on all unweighted benchmarks from the MaxSAT Evaluation 2016. Moreover, compared to SAT-based MaxSAT solvers which dominate industrial benchmarks for years, it performs better on industrial benchmarks and significantly better on application formulas from SAT Competition. We also extend this approach to (Weighted) Partial MaxSAT, and the resulting solvers significantly improve local search solvers on crafted and industrial benchmarks, and are complementary (better on WPMS crafted benchmarks) to SAT-based solvers.

Scheduling multi-component maintenance with a greedy heuristic local search algorithm

2019 ◽  
Vol 24 (1) ◽  
pp. 351-366 ◽  
Author(s):  
Seyedmohsen Hosseini ◽  
Sifat Kalam ◽  
Kash Barker ◽  
Jose E. Ramirez-Marquez
Keyword(s):  
Local Search ◽  
Search Algorithm ◽  
Greedy Heuristic ◽  
Local Search Algorithm

scholarly journals A Modified Niching Crow Search Approach to Well Placement Optimization

Energies ◽  
2021 ◽  
Vol 14 (4) ◽  
pp. 857
Author(s):  
Jahedul Islam ◽  
Md Shokor A. Rahaman ◽  
Pandian M. Vasant ◽  
Berihun Mamo Negash ◽  
Ahshanul Hoqe ◽  
...  
Keyword(s):  
Optimization Problem ◽  
Search Algorithm ◽  
Gravitational Search Algorithm ◽  
Multimodal Optimization ◽  
Test Functions ◽  
Well Placement ◽  
Suggested Approach ◽  
Placement Optimization ◽  
Well Placement Optimization ◽  
Search Approach

Well placement optimization is considered a non-convex and highly multimodal optimization problem. In this article, a modified crow search algorithm is proposed to tackle the well placement optimization problem. This article proposes modifications based on local search and niching techniques in the crow search algorithm (CSA). At first, the suggested approach is verified by experimenting with the benchmark functions. For test functions, the results of the proposed approach demonstrated a higher convergence rate and a better solution. Again, the performance of the proposed technique is evaluated with well placement optimization problem and compared with particle swarm optimization (PSO), the Gravitational Search Algorithm (GSA), and the Crow search algorithm (CSA). The outcomes of the study revealed that the niching crow search algorithm is the most efficient and effective compared to the other techniques.

scholarly journals Clustering of cancer data based on Stiefel manifold for multiple views

2021 ◽  
Vol 22 (1) ◽  
Author(s):  
Jing Tian ◽  
Jianping Zhao ◽  
Chunhou Zheng
Keyword(s):  
Optimization Problem ◽  
Nearest Neighbor ◽  
Search Algorithm ◽  
Stiefel Manifold ◽  
Omics Data ◽  
K Nearest Neighbor ◽  
Cancer Data ◽  
Clustering Problem ◽  
Multiple Datasets ◽  
Cluster Class

Abstract Background In recent years, various sequencing techniques have been used to collect biomedical omics datasets. It is usually possible to obtain multiple types of omics data from a single patient sample. Clustering of omics data plays an indispensable role in biological and medical research, and it is helpful to reveal data structures from multiple collections. Nevertheless, clustering of omics data consists of many challenges. The primary challenges in omics data analysis come from high dimension of data and small size of sample. Therefore, it is difficult to find a suitable integration method for structural analysis of multiple datasets. Results In this paper, a multi-view clustering based on Stiefel manifold method (MCSM) is proposed. The MCSM method comprises three core steps. Firstly, we established a binary optimization model for the simultaneous clustering problem. Secondly, we solved the optimization problem by linear search algorithm based on Stiefel manifold. Finally, we integrated the clustering results obtained from three omics by using k-nearest neighbor method. We applied this approach to four cancer datasets on TCGA. The result shows that our method is superior to several state-of-art methods, which depends on the hypothesis that the underlying omics cluster class is the same. Conclusion Particularly, our approach has better performance than compared approaches when the underlying clusters are inconsistent. For patients with different subtypes, both consistent and differential clusters can be identified at the same time.

Sign in / Sign up

Export Citation Format

Share Document