A Heuristic Approach to the Consecutive Ones Submatrix Problem

أعطيت مصفوفة (0،1)، تم اقتراح مسألة المصفوفة الجزئية ذات الواحدات المتعاقبة والتي تهدف إلى إيجاد تبديل للأعمدة التي تزيد من عدد الأعمدة التي تحتوي معًا على قالب واحد فقط من الواحدات المتعاقبة في كل صف. سيتم اقتراح اسلوب الاستدلال لحل المسألة. كما سيتم دراسة مسألة تقليل القوالب المتتالية ذات الصلة بمسألة المصفوفة الجزئية ذات الواحدات المتعاقبة. تم اقتراح اجراء جديد لتحسين طريقة إدراج العمود. يتم بعد ذلك تقييم مصفوفات العالم الحقيقي ومصفوفات متولدة عشوائيًا من مسألة غطاء المجموعة و تعرض النتائج الحسابية.Given a matrix, the Consecutive Ones Submatrix (C1S) problem which aims to find the permutation of columns that maximizes the number of columns having together only one block of consecutive ones in each row is considered here. A heuristic approach will be suggested to solve the problem. Also, the Consecutive Blocks Minimization (CBM) problem which is related to the consecutive ones submatrix will be considered. The new procedure is proposed to improve the column insertion approach. Then real world and random matrices from the set covering problem will be evaluated and computational results will be highlighted

Asymmetric image encryption scheme based on Massey Omura scheme

Asymmetric image encryption schemes have shown high resistance against modern cryptanalysis. Massey Omura scheme is one of the popular asymmetric key cryptosystems based on the hard mathematical problem which is discrete logarithm problem. This system is more secure and efficient since there is no exchange of keys during the protocols of encryption and decryption. Thus, this work tried to use this fact to propose a secure asymmetric image encryption scheme. In this scheme the sender and receiver agree on public parameters, then the scheme begin deal with image using Massey Omura scheme to encrypt it by the sender and then decrypted it by the receiver. The proposed scheme tested using peak signal to noise ratio, and unified average changing intensity to prove that it is fast and has high security

An Evolutionary Approach to Solving the Maximum Size Consecutive Ones Submatrix and Related Problems

The Consecutive Ones Submatrix (C1S) has a vital role in real world applications. Consequently, there are continuous concern and demand to solve this problem via efficient algorithms. These algorithms are judged on the basis of their robustness, ease of use, and their computational time. The main aim of this thesis is to convert a Pure Integer Linear Programming (ILP) with (0, 1)−matrix into Mixed Integer Linear Programming (MILP) by finding the C1S submatrix. Given a (0, 1)−matrix, we consider the C1S problem which aims to maximize the number of columns having only one block of consecutive 1’s in each row by permuting them. We suggest an evolutionary approach to solve the problem. The Genetic Algorithm (GA) is the one proposed here to rearrange the columns of the matrix by pushing them in large blocks of 1’s. We also consider the Consecutive Blocks Minimization (CBM) problem which is related to C1S. A new procedure is proposed to improve the C1S submatrix, which is the column insertion approach. Moreover, preprocessing by minimum degree ordering is also used. On the other hand, we suggest another approach to solve the C1S. It is using the MVEE problem. To pave the way we first solve the problem. Given a set of points C = {x 1 ,x 2 ,...,x m } ⊆ R^n , what is the minimum volume ellipsoid that encloses it? Equally interestingly, one may ask: What is the maximum volume ellipsoid that can be embedded in the set of points without containing any? These problems have a number of applications beside being interesting in their own right. If one requires that at least k of m points, k < m be enclosed in the minimum volume ellipsoid, then the problem becomes more difficult but has the potential, once solved, to detect outliers among the n points. We suggest an evolutionary-type approach for their solution. We will also highlight application areas and include computational results

Solving partial differential equations with hybridized physic-informed neural network and optimization approach: Incorporating genetic algorithms and L-BFGS for improved accuracy

Partial differential equations (PDEs) are essential mathematical models for describing a wide range of physical phenomena. Numerically, Physic-Informed Neural Networks (PINNs), a variant of artificial neural networks, present a promising method for solving PDEs. However, due to limitation in accuracy and stability, various adaptive PINN variants have been proposed. We have designed a novel approach that adopted self-adaptive PINN (SA-PINN) with two optimization techniques: the genetic algorithm (GA) and the limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm. Self-adaptive PINN modifies the weights in the loss function to be fully trainable, enabling the ANN to learn and stabilize the PINN in approximating the difficult regions of the solution. GA initializes the population of ANN trainable parameters to optimize the training process with less number of iterations, while L-BFGS is used to find the best solution accurately. Our proposed approach, named SA-PINN-GA-LBFGS, is tested on solving several benchmark PDE problems including elliptic, parabolic, and hyperbolic types. We compare our results with state-of-the-art methods, demonstrating that SA-PINN-GA-LBFGS provides higher accuracy and greater efficiency