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On The Roman Domination Stable Graphs

100%

Hajian M. , Rad N. J.

Discussiones Mathematicae Graph Theory

2017

tom 37

nr 4

859-871

A Roman dominating function (or just RDF) on a graph G = (V,E) is a function f : V → {0, 1, 2} satisfying the condition that every vertex u for which f(u) = 0 is adjacent to at least one vertex v for which f(v) = 2. The weight of an RDF f is the value f(V (G)) = Pu2V (G) f(u). The Roman domination number of a graph G, denoted by R(G), is the minimum weight of a Roman dominating function on G. A graph G is Roman domination stable if the Roman domination number of G remains unchanged under removal of any vertex. In this paper we present upper bounds for the Roman domination number in the class of Roman domination stable graphs, improving bounds posed in [V. Samodivkin, Roman domination in graphs: the class RUV R, Discrete Math. Algorithms Appl. 8 (2016) 1650049].

Coherent synthesis of heterogeneous system - an ant colony optimization approach

51%

Drabowski M.

Studia Informatica : systems and information technology

2007

tom Vol. 2(9)

9--18

The paper presents an innovative approach to solving the problems of computer system synthesis based on ant colony optimization method. We describe algorithm realizations aimed to optimize resource, selection and task scheduling, as well as the adaptation of those algorithms for coherent synthesis realization. We then present selected analytical experiments proving the correctness of the coherent synthesis concept and indicate its practical motivations.

A genetic algorithm and B&B algorithm for integrated production scheduling, preventiveand corrective maintenance to save energy

51%

Sadiqi A. , El Abbassi I. , El Barkany A. , Darcherif M. , El Biyaali A.

Management and Production Engineering Review

2020

tom Vol. 11, No. 4

138--148

The rapid global economic development of the world economy depends on the availability of substantial energy and resources, which is why in recent years a large share of non-renewable energy resources has attracted interest in energy control. In addition, inappropriate use of energy resources raises the serious problem of inadequate emissions of greenhouse effect gases, with major impact on the environment and climate. On the other hand, it is important to ensure efficient energy consumption in order to stimulate economic development and preserve the environment. As scheduling conflicts in the different workshops are closely associated with energy consumption. However, we find in the literature only a brief work strictly focused on two directions of research: the scheduling with PM and the scheduling with energy. Moreover, our objective is to combine both aspects and directions of in-depth research in a single machine. In this context, this article addresses the problem of integrated scheduling of production, preventive maintenance (PM) and corrective maintenance (CM) jobs in a single machine. The objective of this article is to minimize total energy consumption under the constraints of system robustness and stability. A common model for the integration of preventive maintenance (PM) in production scheduling is proposed, where the sequence of production tasks, as well as the preventive maintenance (PM) periods and the expected times for completion of the tasks are established simultaneously; this makes the theory put into practice more efficient. On the basis of the exact Branch and Bound method integrated on the CPLEX solver and the genetic algorithm (GA) solved in the Python software, the performance of the proposed integer binary mixed programming model is tested and evaluated. Indeed, after numerically experimenting with various parameters of the problem, the B&B algorithm works relatively satisfactorily and provides accurate results compared to the GA algorithm. A comparative study of the results proved that the model developed was sufficiently efficient.

Location of zeros of polynomials

41%

Zireh A.

Journal of Applied Analysis

2012

tom Vol. 18, nr 1

159-166

In this paper, we obtain a result concerning the location of zeros of a polynomial p(z)= αo+a1z+···+αnzn, where αi are complex coefficients and z is a complex variable. We obtain a ring shaped region containing all the zeros of a polynomial involving binomial coefficients and t,z-Fibonacci numbers. This result generalizes some well-known inequalities.