Gravity-based heuristic for set covering problems and its application in fault diagnosis

A novel algorithm named randomized binary gravita- tional search （RBGS） algorithm is proposed for the set covering problem （SCP）. It differs from previous SCP approaches because it does not work directly on the SCP matrix. In the proposed algo- rithm, the solution of SCP is viewed as multi-dimension position of objects in the binary search space. All objects in the space attract each other by the gravity force, and this force causes a global movement of all objects towards the objects with heavier masses which correspond to good solutions. Computation results show that the proposed algorithm is very competitive. In addition, the proposed aigodthm is extended for SCP to solve the fault diagno- sis problem in graph-based systems.

(S,T)-WEAK TRACTABILITY OF MULTIVARIATE LINEAR PROBLEMS IN THE AVERAGE CASE SETTING

The purpose of this article is to investigate (s, t)-weak tractability of multivariate linear problems in the average case set ting. The considered algorithms use finitely many evaluations of arbitrary linear functionals. Generally, we obtained matching necessary and sufficient conditions for (s,t)-weak tractability in terms of the corresponding non-increasing sequence of eigenvalues. Specifically, we discussed (s, t)-weak tractability of linear tensor product problems and obtained necessary and sufficient conditions in terms of the corresponding one-dimensional problem. As an example of applications, we discussed also (s,t)-weak tractability of a multivariate approximation problem.

Ontology-Based Semantic Annotation for Problem Set Archives in the Web

Aimming at the difficulty in getting semantic informarton from each problem in problem set archives, We propose a new method of ontology based semantic annotation for problem set archives, which utilizes programming knowledge domain ontology to add semantic annotations to problems in the Web. The system we developed adds semantic annotation for each problem in the form of Extensible Makeup Language. Our method overcomes the difficulty of extracting semantics from problem set archives and the efficiency of this method is demonstrated through a case study. Having semantic annotations of problems, a student can efficiently locate the problems that logically corre spond to his knowledge.

Homotopy Continuous Method for Weak Efficient Solution of Multiobjective Optimization Problem with Feasible Set Unbounded Condition

In this paper, we propose a homotopy continuous method (HCM) for solving a weak efficient solution of multiobjective optimization problem (MOP) with feasible set unbounded condition, which is arising in Economical Distributions, Engineering Decisions, Resource Allocations and other field of mathematical economics and engineering problems. Under the suitable assumption, it is proved to globally converge to a weak efficient solution of (MOP), if its x-branch has no weak infinite solution.

Binary Fruit Fly Swarm Algorithms for the Set Covering Problem

Currently,the industry is experiencing an exponential increase in dealing with binary-based combinatorial problems.In this sense,metaheuristics have been a common trend in the field in order to design approaches to solve them successfully.Thus,a well-known strategy consists in the use of algorithms based on discrete swarms transformed to perform in binary environments.Following the No Free Lunch theorem,we are interested in testing the performance of the Fruit Fly Algorithm,this is a bio-inspired metaheuristic for deducing global optimization in continuous spaces,based on the foraging behavior of the fruit fly,which usually has much better sensory perception of smell and vision than any other species.On the other hand,the Set Coverage Problem is a well-known NP-hard problem with many practical applications,including production line balancing,utility installation,and crew scheduling in railroad and mass transit companies.In this paper,we propose different binarization methods for the Fruit Fly Algorithm,using Sshaped and V-shaped transfer functions and various discretization methods to make the algorithm work in a binary search space.We are motivated with this approach,because in this way we can deliver to future researchers interested in this area,a way to be able to work with continuous metaheuristics in binary domains.This new approach was tested on benchmark instances of the Set Coverage Problem and the computational results show that the proposed algorithm is robust enough to produce good results with low computational cost.

Bi-extrapolated subgradient projection algorithm for solving multiple-sets split feasibility problem

This paper deals with a bi-extrapolated subgradient projection algorithm by intro- ducing two extrapolated factors in the iterative step to solve the multiple-sets split feasibility problem. The strategy is intend to improve the convergence. And its convergence is proved un- der some suitable conditions. Numerical results illustrate that the bi-extrapolated subgradient projection algorithm converges more quickly than the existing algorithms.

A Modified Genetic Algorithm for Maximum Independent Set Problems

genetic algorithm is proposed for maximum independent set problems. A specially designed mutation operato is adopted to search the solution space more efficienily, where adjacen relation of a graph is inte-grated. The DIMACS benchmark graphs are used to test our algorithm, and the results show that the algorithm outper-forms our previous version. Moreover two new low bounds are found for graphs in DIMACS.

EKELAND'S PRINCIPLE FOR SET-VALUED VECTOR EQUILIBRIUM PROBLEMS

In this paper, we introduce a concept of quasi C-lower semicontinuity for setvalued mapping and provide a vector version of Ekeland＇s theorem related to set-valued vector equilibrium problems. As applications, we derive an existence theorem of weakly efficient solution for set-valued vector equilibrium problems without the assumption of convexity of the constraint set and the assumptions of convexity and monotonicity of the set-valued mapping. We also obtain an existence theorem of ε-approximate solution for set-valued vector equilibrium problems without the assumptions of compactness and convexity of the constraint set.

Applying Surface-Based DNA Computing for Solving the Dominating Set Problem

The surface-based DNA computing is one of the methods of DNA computing which uses DNA strands immobilized on a solid surface. In this paper, we applied surface-based DNA computing for solving the dominating set problem. At first step, surface-based DNA solution space was constructed by using appropriate DNA strands. Then, by application of a DNA parallel algorithm, dominating set problem was resolved in polynomial time.

Solving the independent set problem by sticker based DNA computers

In this paper, the sticker based DNA computing was used for solving the independent set problem. At first, solution space was constructed by using appropriate DNA memory complexes. We defined a new operation called “divide” and applied it in construction of solution space. Then, by application of a sticker based parallel algorithm using biological operations, independent set problem was resolved in polynomial time.

Upper and Lower Semicontinuity of Solution Sets for Parametric Generalized Vector Quasi-equilibrium Problems

In this paper, two kinds of parametric generalized vector quasi-equilibrium problems are introduced and the relations between them are studied. The upper and lower semicontinuity of their solution sets to parameters are investigated.

Asymptotic Solution to Scattering Problem on a Set of Small Particles and Application to Creating the Materials with a Peculiar Refractive Index

The asymptotic solution to the scattering problem on a set of small particles, supplemented into homogeneous material, is used for modeling the materials with the desired refractive index. The consideration concerns the case of acoustic scalar scattering and the solution to initial scattering problem is built using an asymptotic approach. The closed form solution is reduced for the scattering problem. This is significant advantage of approach because there is no need to solve the respective system of boundary integral equations. High accuracy of solving the scattering problem is achieved by choosing the optimal parameters of the domain with small particles. The approach allows obtaining an explicit formula for the refractive index of the resulting inhomogeneous material. The numerical calculations show the possibility to get the specific values of refractive index including its negative values.

Continuity of Solution Mappings for Parametric Set Optimization Problems under Partial Order Relations

This paper mainly investigates the semicontinuity of solution mappings for set optimization problems under a partial order set relation instead of upper and lower set less order relations. To this end, we propose two types of monotonicity definition for the set-valued mapping introduced by two nonlinear scalarization functions which are presented by these partial order relations. Then, we give some sufficient conditions for the semicontinuity and closedness of solution mappings for parametric set optimization problems. The results presented in this paper are new and extend the main results given by some authors in the literature.

On“Word-to-Word”Translation Method Problem Caused by thinking Set in Translation

The so-called thinking set is a stable standard thinking set not only allowing us to figure out the politics of the whole situation and then settle the matter, yet also hindering us from employing a new method which is far more practical when the surrounding are changed. This is espcially typical in translation practise, espcially on"Word-to-Word"translation method. In this essay,some exampls will be picked and analyzed. After the analysis, some suggestion will be provided to avoid the similar problems in future.

Modeling of the Saltwater Intrusion Using the Level Set Method. Application to Henry’s Problem

The salt intrusion phenomenon is caused by overexploitation of aquifers in coastal areas. This physical phenomenon has been the subject of numerous studies and numerous methods have been proposed, with the aim of protecting the quality of the water in these aquifers. This work proposes a two-dimensional saline intrusion model using the sharp interface approach and the level set method. It consists of a parabolic equation modeling the underground flow and a hyperbolic Equation (the level set equation) which makes it possible to track the evolution of the interface. High-order numerical schemes such as the space scheme WENO5 and the third-order time scheme TVD-RK were used for the numerical resolution of the hyperbolic equation. To limit the tightening of the contour curves of the level set function, the redistanciation or reinitialization algorithm proposed by Sussma et al. (1994) was used. To ensure the effectiveness and reliability of the proposed method, two tests relating to the standard Henry problem and the modified Henry problem were performed. Recall that Henry’s problem uses the variable density modeling approach in a confined and homogeneous aquifer. By comparing the results obtained by the level set method with reinitialization (LSMR) and those obtained by Henry (1964), and by Simpson and Clement (2004), we see in the two test cases that the level set method reproduces well the toe, the tip and the behaviour of the interface. These results correspond to the results obtained by Abarca for Henry’s problem with constant dispersion coefficients. The results obtained with LSMR, reproduced the interface with a slight spacing compared to those obtained by Henry. According to Abarca (2006), this spacing is due to the absence of the longitudinal and transversal dispersion coefficients in the model.

Solving Two-Dimensional Moving-Boundary Problems with Meshless and Level Set Method

During the past decade, increasing attention has been given to the development of meshless methods using radial basis functions for the numerical solution of Partial Differential Equations （PDEs）. A level set method is a promising design tool for tracking, modelling and simulating the motion of free boundaries in fluid mechanics, combustion, computer animation and image processing. In the conventional level set methods, the level set equation is solved to evolve the interface using a capturing Eulerian approach. The solving procedure requires an appropriate choice of the upwind schemes, reinitialization, etc. Our goal is to include Multiquadric Radial Basis Functions （MQ RBFs） into the level set method to construct a more efficient approach and stabilize the solution process with the adaptive greedy algorithm. This paper presents an alternative approach to the conventional level set methods for solving moving-boundary problems. The solution was compared to the solution calculated by the exact explicit lime integration scheme. The examples show that MQ RBFs and adaptive greedy algorithm is a very promising calculation scheme.

Well-Posedness for Tightly Proper Efficiency in Set-Valued Optimization Problem

In this paper, a characterization of tightly properly efficient solutions of set-valued optimization problem is obtained. The concept of the well-posedness for a special scalar problem is linked with the tightly properly efficient solutions of set-valued optimization problem.

Completely Generalized Strongly Set-valued Nonlinear Quasi-complementarity Problems

In this paper,we study a class of completely generalized strongly set-valued nonlinearquasi-complementarity problems and discuss the existence of solutions for this kind of quasi-complementariy problems without compactness and the convergence of iterative sequencesgenerated by the algorithms.