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Abstract: This paper continues the theme of the recent work Chen et al. (2008) , in which fast collocation methods are introduced for solving ill-posed Fredholm integral equations of the first kind. We develop in this paper multilevel augmentation algorithms, which lead to fast solutions of the discrete equations resulting from fast collocation methods. Regularization parameter choice strategies are given for proposed methods. The theoretical analysis and numerical experiments illustrate the accuracy and efficiency of the algorithm. [Copyright &y& Elsevier]

Abstract: Data compression via the Huffman algorithm, which is a data compression technique, is the most efficient technique between single symbol data compression techniques. This algorithm is counted among statistical data compression techniques. Many efforts have been made for optimizing this technique and some algorithms have been presented, too. One of these algorithms is the ACW algorithm which is presented by Hussein Al-Bahadili et al. At first, they used the Huffman algorithm and then used the results of the Huffman algorithm as the input of their algorithm to calculate the optimum character wordlength. So, they decreased the stored characters via increasing the character wordlength for doing the compression. In this paper, we examined and criticized the ACW algorithm and presented some of its weaknesses via suitable counterexamples. At the end, it was concluded that the optimum character wordlength can never be calculated by extant techniques. [Copyright &y& Elsevier]

Abstract: In this paper, we present a dynamic programming (DP) algorithm for the multi-objective 0–1 knapsack problem (MKP) by combining two state reduction techniques. One generates a backward reduced-state DP space (BRDS) by discarding some states systematically and the other reduces further the number of states to be calculated in the BRDS using a property governing the objective relations between states. We derive the condition under which the BRDS is effective to the MKP based on the analysis of solution time and memory requirements. To the authors’ knowledge, the BRDS is applied for the first time for developing a DP algorithm. The numerical results obtained with different types of bi-objective instances show that the algorithm can find the Pareto frontier faster than the benchmark algorithm for the large size instances, for three of the four types of instances conducted in the computational experiments. The larger the size of the problem, the larger improvement over the benchmark algorithm. Also, the algorithm is more efficient for the harder types of bi-objective instances as compared with the benchmark algorithm. [Copyright &y& Elsevier]

Abstract: In this paper an attempt is made to extend some standard results in set theory on the basis of soft set relations. Antisymmetric relation and transitive closure of a soft set relation are introduced and an analogue of Warshall’s algorithm is proposed for calculating the transitive closure of a soft set relation. Ordering on a soft set is defined and some set theoretical results based on this are proved. [Copyright &y& Elsevier]

Abstract: We study an on-line machine covering problem, in which jobs arrive one by one and their processing times are known upon their arrival, and jobs are allowed to migrate between machines when a new job is added in the system. However, the total processing time of migration induced by an incoming job is bounded by a constant factor times the processing time of the incoming job. The objective is to maximize the minimum machine load. In this paper, we present an on-line algorithm with competitive ratio 6/5 for the two identical machines case with . Moreover, the presented on-line algorithm is only a local migration, that is, when one job is assigned to machine , only the jobs on machine are allowed to migrate. We also show that the provided algorithm is a best possible on-line algorithm in the sense of local migration. [Copyright &y& Elsevier]

Abstract: This paper explores the problems of generalized center conditions and integrability of resonant infinity for a complex polynomial differential system. The method is based on converting resonant infinity into an elementary singular point by a homeomorphic transformation. The calculation of generalized singular point quantities is an effective way of finding necessary conditions for integrable systems. A new recursive algorithm for computing generalized singular point quantities at the origin of the transformed system is derived. At the same time, a necessary and sufficient condition for resonant infinity to be a generalized complex center is presented. As an application of the new recursive algorithm, the generalized center conditions for resonant infinity for a class of cubic systems are discussed. To the best of our knowledge, this is the first time that the generalized center problem has been considered for resonant infinity. [Copyright &y& Elsevier]

Abstract: A novel modified differential evolution algorithm (NMDE) is proposed to solve constrained optimization problems in this paper. The NMDE algorithm modifies scale factor and crossover rate using an adaptive strategy. For any solution, if it is at a standstill, its own scale factor and crossover rate will be adjusted in terms of the information of all successful solutions. We can obtain satisfactory feasible solutions for constrained optimization problems by combining the NMDE algorithm and a common penalty function method. Experimental results show that the proposed algorithm can yield better solutions than those reported in the literature for most problems, and it can be an efficient alternative to solving constrained optimization problems. [Copyright &y& Elsevier]

Abstract: This paper concentrates on a limited-flow network in which each node and branch has a designated capacity, which will have different lower levels due to various partial and complete failures. We try to evaluate the system unreliability that the maximum flow of the network is less than or equal to the demand d without exceeding the budget B. First, a simple algorithm in terms of minimal cuts is proposed to generate all (d, B)-MCs in order to evaluate the system unreliability. A computer example is shown to illustrate the solution procedure. [Copyright &y& Elsevier]

Abstract: The scheduling problems studied in this paper concern the two-stage no-wait flowshops with parallel machines under the objective function of the minimization of the maximum completion time. A new heuristic algorithm, i.e., the minimum deviation algorithm, is developed to solve the problems. In order to evaluate the average case performance of the algorithm, we design numerical experiments to compare the effectiveness of the algorithm with that of the other approximation algorithms. Extensive simulations are conducted under different shop conditions, and the results statistically show that the minimum deviation algorithm performs well under most of the situations. [Copyright &y& Elsevier]

Let CSRnxn={A=(aij)∊Rnxn|aij=an+1−j, i,j=1,2…, n} In this paper, we mainly discuss solving the following problems. PROBLEM Io Given X, B ∊ Rnxm Find A ∊ CSRn×n such that AX = B. PROBLEM I. Given X, B ∊ Rn×m. Find A ∊ CSRn×n such that ∥AX−B∥=min.PROBLEM II. Given A` ∊ Rn×n. Find A* ∊ SE such that where ∥ · ∥ is the Frobenius norm, and SE is the solution set of Problem I or I0.The expressions of the general solution of Problems I and 10 have been derived. The sufficient and necessary conditions for the solvability of Problem I0 have been provided. The numerical algorithm to find the optimal approximate solution and some numerical experiments have been given. [Copyright &y& Elsevier]

In this paper, we combine the new trust region subproblem proposed in [1] with the nonmonotone technique to propose a new algorithm for unconstrained optimization—the nonmonotone adaptive trust region method. The local and global convergence properties of the nonmonotone adaptive trust region method are proved. Its efficiency is tested by numerical results. [Copyright &y& Elsevier]