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Highlights • A Quick Inclusion-Exclusion (QIE) technique is proposed. • The proposed QIE is for multi-state flow network reliability problems. • The proposed QIE is easy to code and only needs one comparision in each (intersection) term. • The proposed QIE is simpler than the traditional IE. • The proposed QIE is faster than the RSDP which is the most popular sum-of-disjoint product method. Abstract The reliability of modern information systems modeled as multi-state flow networks (MFNs) is a crucial concern the planning, design and control of these systems. The inclusion-exclusion technique (IET) is a popular tool for assessing MFN reliability because it is simple and easily understood. However, it is less efficient than other methods, like the sum-of-disjoint product method (SDP), for example. This paper proposes a new IET, called the Quick Inclusion-Exclusion technique (QIE) to increase the efficiency of the IET and reduce the amount of memory required in MFNs. The correctness and the time complexity of QIE is analyzed and proven. An MFN reliability example is implemented to illustrate the proposed QIE. In order to demonstrate its performance, the proposed QIE is compared with the most popular SDP, the recursive SDP (RSDP) in 20 benchmark networks taken from the literature. Numerical examples demonstrate that the proposed QIE outperforms RSDP in terms of both efficiency and memory use. This result differs significantly from those obtained by traditional methods. [ABSTRACT FROM AUTHOR]

Purpose – The bottleneck of current DNA computing paradigms based on brute-force search strategy is that initial solution space grows exponentially with problem size, thus only trivial instances of NP-complete problem can be solved. The purpose of this paper is to present a novel molecular program based on sticker models for solving dominating set problems. Design/methodology/approach – The authors do not synthesize the initial solution pool containing every possible candidate solution as previously reported algorithm. Instead, solutions DNA molecules to the problem of interest are constructed during the course of computation. Findings – It is shown that "exponential explosions" inherent in current DNA computing paradigms may be overcome in this way. Originality/value – The paper proposes an error-resistant DNA algorithm based on sticker model for solving minimum dominating problems. [ABSTRACT FROM AUTHOR]

The minimum weighted vertex cover (MWVC) problem, an extension of the classical minimum vertex cover (MVC) problem, is an important NP-complete combinatorial optimization problem with a wide range of applications. The objective of this paper is to design an efficient local search algorithm to solve the MWVC problem. First, the weighted edge strategy is proposed to define the dynamic scoring strategy so that our algorithm can find different possible optimal solutions. Second, the weighted configuration checking (WCC) strategy is proposed to overcome the cycling problem in local search. By combining the WCC strategy with the scoring strategy, we design the vertex selection strategy to determine the vertex to be selected as a candidate solution component. Based on these strategies, a novel local search framework, namely diversion local search based on weighted configuration checking (DLSWCC), is presented. DLSWCC is evaluated against several state-of-the-art algorithms on various benchmark instances. Experimental results show that DLSWCC outperforms its competitors in terms of both solution quality and computational efficiency in most classical instances. Specifically, DLSWCC can obtain 22 new upper bounds of 71 moderate-scale problem instances, 5 new upper bounds of 15 large-scale problem instances, and 56 new upper bounds of 56 massive graph instances. [ABSTRACT FROM AUTHOR]

According to the literature, a linear optimization problem subjected to a system of bipolar fuzzy relational equations with max-Łukasiewicz composition can be translated into a 0–1 integer linear programming problem and solved using integer optimization techniques. However, the technique of integer optimization may involve hight computation complexity. To improve computational efficiency for solving such an optimization problem, this paper proves that each component of an optimal solution obtained from such an optimization problem can either be the corresponding component’s lower bound or upper bound value. Because of this characteristic, a simple value matrix with some simplified rules can be proposed to reduce the problem size first. A simple solution procedure is then presented for determining optimal solutions without translating such an optimization problem into a 0–1 integer linear programming problem. Two examples are provided to illustrate the simplicity and efficiency of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Abstract: The k-covers problem (kCP) asks us to compute a minimum cardinality set of strings of given length k >1 that covers a given string. It was shown in a recent paper, by reduction to 3-SAT, that the k-covers problem is NP-complete. In this paper we introduce a new problem, that we call the k-bounded relaxed vertex cover problem (RVCP k ), which we show is equivalent to k-bounded set cover (SCP k ). We show further that kCP is a special case of RVCP k restricted to certain classes G x ,k of graphs that represent all strings x . Thus a minimum k-cover can be approximated to within a factor k in polynomial time. We discuss approximate solutions of kCP, and we state a number of conjectures and open problems related to kCP and G x ,k . [Copyright &y& Elsevier]

This paper introduces a hierarchical clustering algorithm in networks based upon a first divisive stage to break the graph and a second linking stage which is used to join nodes. As a particular case, this algorithm is applied to the specific problem of community detection in social networks, where a betweenness measure is considered for the divisive criterion and a similarity measure associated to data is used for the linking criterion. We show that this algorithm is very flexible as well as quite competitive (from both a performance and a computational complexity point of view) in relation with a set of state-of-the-art algorithms. Furthermore, the output given by the proposed algorithm allows to show in a dynamic and interpretable way the evolution of how the groups are split in the network. [ABSTRACT FROM AUTHOR]

This paper deals with the update step of Gaussian MAP filtering. In this framework, we seek a Gaussian approximation to the posterior probability density function (PDF) whose mean is given by the maximum a posteriori (MAP) estimator. We propose two novel optimization algorithms which are quite suitable for finding the MAP estimate although they can also be used to solve general optimization problems. These are based on the design of a sequence of PDFs that become increasingly concentrated around the MAP estimate. The resulting algorithms are referred to as Kalman optimization (KO) methods. We also provide the important relations between these KO methods and their conventional optimization algorithms (COAs) counterparts, i.e., Newton's and Levenberg-Marquardt algorithms. Our simulations indicate that KO methods are more robust than their COA equivalents. [ABSTRACT FROM AUTHOR]

Abstract: In recent years, many different variants of the particle swarm optimizer (PSO) for solving optimization problems have been proposed. However, PSO has an inherent drawback in handling constrained problems, mainly because of its complexity and dependency on parameters. Furthermore, one PSO variant may perform well for some test problems but not obtain good results for others. In this paper, our purpose is to develop a new PSO algorithm that can efficiently solve a variety of constrained optimization problems. It considers a mix of different PSO variants each of which evolves with a different number of individuals from the current population. In each generation, the algorithm assigns more individuals to the better-performing variants and fewer to the worse-performing ones. Also, a new PSO variant is developed for use in the proposed algorithm to maintain a better balance between its local and global PSO versions. A new methodology for adapting PSO parameters is presented and the proposed self-adaptive PSO algorithm tested and analyzed on two sets of test problems, namely the CEC2006 and CEC2010 constrained optimization problems. Based on the results, the proposed algorithm shows significantly better performance than the same global and local PSO variants as well as other-state-of-the-art algorithms. Although, based on our analysis, it cannot guarantee an optimal solution for any unknown problem, it is expected to be able to solve a wide variety of practical problems. [Copyright &y& Elsevier]

Abstract: Swapped Networks (SNs) are a family of two-level interconnection networks, suitable for constructing large parallel and distributed systems. In this paper, the Minimum Dominating Set (MDS) problem and the Minimum Connected Dominating Set (MCDS) problem in SNs are investigated based on the connectivity rule of SNs. We prove the two problems in SNs are -hard, and present two efficient algorithms for building dominating sets and connected dominating sets in SNs. The proposed algorithms use as input a given (connected) dominating set of the factor network, and yield a good approximation of an MDS or MCDS for the SN provided that the input is a good approximation of an MDS or MCDS for the factor network. We also derive several non-trivial bounds on the (connected) domination parameters of SNs. We believe this work is of theoretical interest in graph theory since SNs form a family of graphs. It may also motivate further research on dominating problems in SNs with their potential applications. [Copyright &y& Elsevier]

Abstract: Assume that there exists a collection C of subsets of a finite set S, and a positive integer K ⩽∣S∣, and we need to know whether there is a subset S′⊆ S with ∣S′∣⩽ K such that S′ contains at least one element of each subset in C. In other words, S′ is the subset that intersects every subset in C and is called the hitting-set. In this paper, a DNA-based algorithm is proposed to solve the small hitting-set problem. A small hitting-set is a hitting-set with the smallest K value, i.e., the hitting-set with the smallest number of elements. Furthermore, another algorithm is introduced to find the number of ones from 2 n combinations and minimum numbers of ones represents the small hitting-set since K is expected to be as small as possible. The complexity of the proposed DNA-based algorithm is discussed, in terms of time complexity, volume complexity, numbers of test tube used and the longest library strand in solution space. Finally, the simulated experiment is applied to verify the correctness of our proposed DNA-based algorithm, in order to solve the well-known hitting-set problem. [Copyright &y& Elsevier]