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Evolutionary multi-objective optimization (EMO) algorithms are actively used for answering optimization problems with multiple contradictory objectives and scheming interpretable and precise real-time applications. A majority of existing EMO algorithms performs better on two or three objectives non-dominated problems; however, they meet complications in managing and maintaining a set of optimal solutions to multi-objective optimization problems. This paper proposes a search space-based multi-objective evolutionary algorithm (SSMOEA) for multi-objective optimization problems. To accomplish the potential of the search space-based method for solving multi-objective optimization problems and to reinforce the selection procedure toward the ideal direction while sustaining an extensive and uniform distribution of solutions is our key objective. To the best of our knowledge, this paper is the first attempt to propose a search space-based multi-objective evolutionary algorithm for multi-objective optimization. The experimental setup used showed that the proposed algorithm is good and competitive in comparison to the existing EMO algorithms from the viewpoint of finding a scattered and estimated solution set in multi-objective optimization problems. SSMOEA can achieve a good trade-off between search space convergence and search space diversity in the appropriate experimental setup. [ABSTRACT FROM AUTHOR]

Abstract: This paper considers the problem of finding architectures with sufficient multi-objective Pareto optimality and maximum diversity of their design-variable values. This problem has been exclusively addressed to date by Evolutionary Algorithms, which are known to be powerful, and yet, the optimality of their solutions cannot be guaranteed. This paper defines two somewhat dual Maximal Design Diversity (MDD) problems, namely, (1) Primal -MDD: maximizing a design-variable diversity metric between architectures given a margin for compromising Pareto optimality, and (2) Dual -MDD: minimizing the compromise of Pareto optimality of architectures given a lower bound for design-variable diversity. Greedy algorithms for computing both Primal and Dual -MDD are presented. For the Primal -MDD the proposed greedy algorithm is proven to be a -approximation of the optimal algorithm and an upper bound for the optimality violation is computed, with respect to the efficient frontier in the objective space. For the Dual -MDD the optimality violation of the proposed greedy algorithm is proven to be at least as good as that of the optimal algorithm when the lower bound on the distance between the solutions in the design-variable space is doubled. Finally, a real-world mixed-integer non-linear programming model with two objectives, dozens of variables and hundreds of constraints is considered as the main use case, taken from the domain of aircraft-engine design. The results validate the fidelity of the algorithm. [Copyright &y& Elsevier]

In this paper, we significantly extend the applicability of state-of-the-art ELDP (equations for linearizing discrete product terms) method by providing a new linearization to handle more complicated non-linear terms involving both of discrete and bounded continuous variables. A general class of “representable programming problems” is formally proposed for a much wider range of engineering applications. Moreover, by exploiting the logarithmic feature embedded in the discrete structure, we present an enhanced linear reformulation model which requires half an order fewer equations than the original ELDP. Computational experiments on various engineering design problems support the superior computational efficiency of the proposed linearization reformulation in solving engineering optimization problems with discrete and bounded continuous variables. [ABSTRACT FROM AUTHOR]

An edge-bicolored graph G = ( V , R ∪ B ) is called Red/Blue-split graph if there exists a partition I B and I R of V such that I B and I R are independent sets in ( V , B ) and ( V , R ) , respectively. Red/Blue-split graphs generalize several well studied graph classes including split graphs, bipartite graphs and König–Egerváry graphs. In this paper we consider the algorithmic complexity of various optimization problems like minimum edge (or vertex) deletion and maximum edge (or vertex) induced subgraph related to Red/Blue split graphs. All these problems are NP -hard and thus we look at them from algorithmic paradigms that are meant for coping with NP -hardness. We obtain various hardness as well as algorithmic results for these problems in the realm of approximation algorithms and parameterized complexity. The main tool we use to obtain all our results is polynomial time transformations between appropriate problems. On the way, we also resolve some problems related to inapproximability about certain optimization problems mentioned by Korach et al. (2006) [17] . [ABSTRACT FROM AUTHOR]

Various papers have analyzed the noisy optimization of convex functions. This analysis has been made according to several criteria used to evaluate the performance of algorithms: uniform rate, simple regret and cumulative regret. We propose an iterative optimization framework, a particular instance of which, using Hessian approximations, provably (i) reaches the same rate as Kiefer–Wolfowitz algorithm when the noise has constant variance, (ii) reaches the same rate as Evolution Strategies when the noise variance decreases quadratically as a function of the simple regret, (iii) reaches the same rate as Bernstein-races optimization algorithms when the noise variance decreases linearly as a function of the simple regret. [ABSTRACT FROM AUTHOR]

Being the unbalanced version of the famous Min s – t Cut problem, the Min k -Size s – t Cut problem asks to find a k -size s – t cut with the minimum capacity, where a k -size s – t cut means an s – t cut with its s -side having size at most k . This problem is fundamental and has extensive applications, especially in community identification in social and information networks. It is known that the Min k -Size s – t Cut problem is NP-hard and can be approximated within O ( log ⁡ n ) , where n is the number of vertices in the input graph. In this paper, we give a new approximation algorithm for the Min k -Size s – t Cut problem based on the parametric flow technique. The algorithm is very simple and has only three lines to state. Its approximation ratio is k + 1 k + 1 − k ⁎ , where k ⁎ is the size of the s -side of an optimal solution. [ABSTRACT FROM AUTHOR]

For two positive integers m , k and a connected graph G = ( V , E ) with a nonnegative vertex weight function w , the balanced m -connected k -partition problem, denoted as BC m P k , is to find a partition of V into k disjoint nonempty vertex subsets ( V 1 , V 2 , … , V k ) such that each G [ V i ] (the subgraph of G induced by V i ) is m -connected, and min 1 ≤ i ≤ k ⁡ { w ( V i ) } is maximized. The optimal value of BC m P k on graph G is denoted as β m ⁎ ( G , k ) , that is, β m ⁎ ( G , k ) = max ⁡ min 1 ≤ i ≤ k ⁡ { w ( V i ) } , where the maximum is taken over all m -connected k -partition of G . In this paper, we study the BC 2 P k problem on interval graphs, and obtain the following results. (1) For k = 2 , a 4/3-approximation algorithm is given for BC 2 P 2 on 4-connected interval graphs. (2) In the case that there exists a vertex v with weight at least W / k , where W is the total weight of the graph, we prove that the BC 2 P k problem on a 2 k -connected interval graph G can be reduced to the BC 2 P k − 1 problem on the ( 2 k − 1 ) -connected interval graph G − v . In the case that every vertex has weight at most W / k , we prove a lower bound β 2 ⁎ ( G , k ) ≥ W / ( 2 k − 1 ) for 2 k -connected interval graph G . (3) Assuming that weight w is integral, a pseudo-polynomial time algorithm is obtained. Combining this pseudo-polynomial time algorithm with the above lower bound, a fully polynomial time approximation scheme (FPTAS) is obtained for the BC 2 P k problem on 2 k -connected interval graphs. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a new ‘Parareal-algorithm’ to solve time-dependent ODEs parallel in time. The algorithm approximates the solutions later in time simultaneously with the solutions earlier in time. To approximate the solutions simultaneously, an optimization problem is constructed and solved using gradient based techniques. The accurate gradients are evaluated using adjoints. Promising results are obtained when the interval of interest is split into suffciently small subintervals. [Copyright &y& Elsevier]

Abstract: This paper describes an extremely fast polynomial time algorithm, the Near Optimal Vertex Cover Algorithm (NOVCA) that produces an optimal or near optimal vertex cover for any known undirected graph G (V, E). NOVCA constructs the vertex cover by repeatedly adding, at each step, all vertices adjacent to the vertex of minimal degree; in the case of a tie, it selects the one having the maximum sum of degrees of its neighbors. The results identifying bounds on the size of the minimum vertex cover as well as polynomial complexity of algorithm are given with experimental verification. Future research efforts will be directed at tuning the algorithm and providing proof for better approximation ratio with NOVCA compared to any other available vertex cover algorithms. [Copyright &y& Elsevier]

Abstract: Finding shortest paths is a fundamental problem in graph theory, which has a large amount of applications in many areas like computer science, operations research, network routing and network analysis. Although many exact and approximate algorithms have been proposed, it is still a time-consuming task to calculate shortest paths for large-scale networks with tremendous volume of data available in recent years. In this paper, we find that the classic Dijkstra''s algorithm can be improved by simple modification. We propose a fast algorithm which utilize the preiously-calculated results to accelerate the latter calculation. Simple optimization strategies are also proposed with consideration of characteristics of scale-free complex networks. Our experimental results show that the average running time of our algorithm is lower than the Dijkstra''s algorithm by a factor relating to the connection probability in random networks of ER model. The performance of our algorithm is significantly better than the Dijkstra''s algorithm in scale-free networks generated by the AB model. The results show that the time complexity is reduced to about O(n2.4) in scalefree complex networks. When the optimization strategies are applied, the algorithm performance is further improved slightly in scale-free networks. [Copyright &y& Elsevier]

Abstract: In this paper we show that the problem of identifying an edge of a graph such that there exists an optimal vertex cover of containing exactly one of the vertices and is NP-hard. Such an edge is called a weak edge. We then develop a polynomial time approximation algorithm for the vertex cover problem with performance guarantee , where is an upper bound on a measure related to a weak edge of a graph. A related problem of identifying an edge such that there exists an optimal vertex cover containing both vertices and is also shown to be NP-hard. Further, we discuss a new relaxation of the vertex cover problem which is used in our approximation algorithm to obtain smaller values of . We also obtain linear programming representations of the vertex cover problem on special graphs. [Copyright &y& Elsevier]

Abstract: In this paper, we deal with several reoptimization variants of the Steiner tree problem in graphs obeying a sharpened β-triangle inequality. A reoptimization algorithm exploits the knowledge of an optimal solution to a problem instance for finding good solutions for a locally modified instance. We show that, in graphs satisfying a sharpened triangle inequality (and even in graphs where edge-costs are restricted to the values 1 and for an arbitrary small ), Steiner tree reoptimization still is NP-hard for several different types of local modifications, and even APX-hard for some of them. As for the upper bounds, for some local modifications, we design linear-time -approximation algorithms, and even polynomial-time approximation schemes, whereas for metric graphs , none of these reoptimization variants is known to permit a PTAS. As a building block for some of these algorithms, we employ a 2β-approximation algorithm for the classical Steiner tree problem on such instances, which might be of independent interest since it improves over the previously best known ratio for any . [Copyright &y& Elsevier]

Abstract: Expensive optimization aims to find the global minimum of a given function within a very limited number of function evaluations. It has drawn much attention in recent years. The present expensive optimization algorithms focus their attention on metamodeling techniques, and call existing global optimization algorithms as subroutines. So it is difficult for them to keep a good balance between model approximation and global search due to their two-part property. To overcome this difficulty, we try to embed a metamodel mechanism into an efficient evolutionary algorithm, low dimensional simplex evolution (LDSE), in this paper. The proposed algorithm is referred to as the low dimensional simplex evolution extension (LDSEE). It is inherently parallel and self-contained. This renders it very easy to use. Numerical results show that our proposed algorithm is a competitive alternative for expensive optimization problems. [Copyright &y& Elsevier]

Abstract: In comparative genomics, the first step of sequence analysis is usually to decompose two or more genomes into syntenic blocks that are segments of homologous chromosomes. For the reliable recovery of syntenic blocks, noise and ambiguities in the genomic maps need to be removed first. Maximal Strip Recovery (MSR) is an optimization problem proposed by Zheng, Zhu, and Sankoff for reliably recovering syntenic blocks from genomic maps in the midst of noise and ambiguities. Given genomic maps as sequences of gene markers, the objective of MSR- is to find subsequences, one subsequence of each genomic map, such that the total length of syntenic blocks in these subsequences is maximized. For any constant , a polynomial-time -approximation for MSR- was previously known. In this paper, we show that for any , MSR- is APX-hard, even for the most basic version of the problem in which all gene markers are distinct and appear in positive orientation in each genomic map. Moreover, we provide the first explicit lower bounds on approximating MSR- for all . In particular, we show that MSR- is NP-hard to approximate within . From the other direction, we show that the previous -approximation for MSR- can be optimized into a polynomial-time algorithm even if is not a constant but is part of the input. We then extend our inapproximability results to several related problems including CMSR-, -gap-MSR-, and -gap-CMSR-. [Copyright &y& Elsevier]

Abstract: In this paper, we present a new symmetric rank-one (SR1) method for the solution of unconstrained optimization problems. The proposed method involves an algorithm in which the usual SR1 Hessian is updated a number of times in a way to be specified in some iterations, to improve the performance of the Hessian approximation. In particular, we discuss how to consider a criterion for indicating at each iteration whether it is necessary to employ extra updates. However it is well known that there are some theoretical difficulties when applying the SR1 update. Even for a current positive definite Hessian approximation, it is possible that the SR1 update may not be defined or the SR1 update may not preserve positive definiteness at some iterations. We then employ a restarting procedure that guarantees that updated matrices will be well-defined while preserving positive definiteness of updates. Numerical results support these theoretical considerations. They show that the implementation of the SR1 method using extra updating techniques improves the performance of the SR1 method substantially for a number of test problems from the literature. [Copyright &y& Elsevier]

Abstract: The vector quantization (VQ) was a powerful technique in the applications of digital image compression. The traditionally widely used method such as the Linde–Buzo–Gray (LBG) algorithm always generated local optimal codebook. Recently, particle swarm optimization (PSO) is adapted to obtain the near-global optimal codebook of vector quantization. An alternative method, called the quantum particle swarm optimization (QPSO) had been developed to improve the results of original PSO algorithm. In this paper, we applied a new swarm algorithm, honey bee mating optimization, to construct the codebook of vector quantization. The results were compared with the other three methods that are LBG, PSO–LBG and QPSO–LBG algorithms. Experimental results showed that the proposed HBMO–LBG algorithm is more reliable and the reconstructed images get higher quality than those generated from the other three methods. [ABSTRACT FROM AUTHOR]

Abstract: Borodin, Nielsen and Rackoff  introduced the class of priority algorithms as a framework for modeling deterministic greedy-like algorithms. In this paper we address the effect of randomization in greedy-like algorithms. More specifically, we consider approximation ratios within the context of randomized priority algorithms. As case studies, we prove inapproximation results for two well-studied optimization problems, namely facility location and makespan scheduling. [Copyright &y& Elsevier]

Abstract: Many real problems can be modeled to the problems with a hierarchical structure, and bilevel programming is a useful tool to solve the hierarchical optimization problems. So the bilevel programming is widely applied, and numerous methods have been proposed to solve this programming. In this paper, we propose an approximate programming algorithm to solve bilevel nonlinear programming problem. Finally, the example illustrates the feasibility of the proposed algorithm. [Copyright &y& Elsevier]

Abstract: This paper discusses optimization of quality measures over first order Delaunay triangulations. Unlike most previous work, our measures relate to edge-adjacent or vertex-adjacent triangles instead of only to single triangles. We give efficient algorithms to optimize certain measures, including measures related to the area ratio of adjacent triangles, angle between outward normals of adjacent triangles (for polyhedral terrains), and number of convex vertices. Some other measures are shown to be NP-hard. These include maximum vertex degree, number of convex edges, and number of mixed vertices. For the latter two measures we provide, for any constant , factor approximation algorithms that run in and time (when the Delaunay triangulation is given). For minimizing the maximum vertex degree, the NP-hardness proof provides an inapproximability result. Our results are presented for the class of first order Delaunay triangulations, but also apply to triangulations where for every triangle at least two edges are fixed. The approximation result on maximizing the number of convex edges is also extended to k-th order Delaunay triangulations. [Copyright &y& Elsevier]

Abstract: This paper discusses a new approach for displacement-based topology optimization of continuum. Topology optimization of continuum can be performed with the optimization of material distribution. This optimization problem will include a large number of design variables, and it may require a high computational cost, especially for computation of gradient components with respect to an objective function and determination of an appropriate updating increment. A conventional approximate optimization technique may not be effective for this problem because it is a very large-scale problem. From this viewpoint, a new optimization technique, which is based on a successive approximation algorithm, is proposed. The proposed method consists of two main processes: (1) a linear approximation for determination of an updating direction, and (2) a nonlinear approximation for determining a scale coefficient of the updating vector. The first approximation is performed using the perturbation-based finite element analysis, and the second approximation is performed using the Kriging Method. In order to investigate effectiveness of the proposed method, it is applied to some typical examples for topology optimization problem. From the numerical results, effectiveness and validity of the proposed method are discussed. [Copyright &y& Elsevier]

Abstract: In this paper we discuss the complexity and approximability of the minimum corridor connection problem where, given a rectilinear decomposition of a rectilinear polygon into “rooms”, one has to find the minimum length tree along the edges of the decomposition such that every room is incident to a vertex of the tree. We show that the problem is strongly NP-hard and give a subexponential time exact algorithm. For the special case when the room connectivity graph is k-outerplanar the algorithm running time becomes cubic. We develop a polynomial time approximation scheme for the case when all rooms are fat and have nearly the same size. When rooms are fat but are of varying size we give a polynomial time constant factor approximation algorithm. [Copyright &y& Elsevier]

Abstract: In this paper, a novel learning strategy for radial basis function networks (RBFN) is proposed. By adjusting the parameters of the hidden layer, including the RBF centers and widths, the weights of the output layer are adapted by local optimization methods. A new local optimization algorithm based on a combination of the gradient and Newton methods is introduced. The efficiency of some local optimization methods to update the weights of RBFN is studied in solving systems of nonlinear integral equations. [Copyright &y& Elsevier]

Abstract: In generalized tree alignment problem, we are given a set of biologically related sequences and we are interested in a minimum cost evolutionary tree for . In many instances of this problem partial phylogenetic tree for is known. In such instances, we would like to make use of this knowledge to restrict the tree topologies that we consider and construct a biologically relevant minimum cost evolutionary tree. So, we propose the following natural generalization of the generalized tree alignment problem, a problem known to be MAX-SNP Hard, stated as follows: Constrained Generalized Tree Alignment Problem [S. Divakaran, Algorithms and heuristics for constrained generalized alignment problem, DIMACS Technical Report 2007-21, 2007]: Given a set of related sequences and a phylogenetic forest comprising of node-disjoint phylogenetic trees that specify the topological constraints that an evolutionary tree of needs to satisfy, construct a minimum cost evolutionary tree for . In this paper, we present constant approximation algorithms for the constrained generalized tree alignment problem. For the generalized tree alignment problem, a special case of this problem, our algorithms provide a guaranteed error bound of . [Copyright &y& Elsevier]

Abstract: In this paper we consider a conic trust-region method for unconstrained optimization problems and analyze its convergence properties. We propose a convenient curvilinear search method to approximately solve the arising conic trust-region subproblem. Note that this approximate method preserves the strong convergence properties of the exact solution methods and is easy to implement. Both the linear and superlinear convergence of the method are established under commonly used conditions. Numerical experiments are conducted to show the efficiency of the new method. [Copyright &y& Elsevier]

Abstract: In this paper, a numerical research on the sensitivity of nonmonotone trust region algorithms to their parameters is presented. We compare the numerical efficiency of two classes of nonmonotone trust region (NTR) algorithms in the context of unconstrained optimization. We examine the sensitivity of the algorithms to the parameters related to the nonmonotone technique and the initial trust region radius. We show that the numerical efficiency of nonmonotone trust region algorithms can be improved by choosing appropriate parameters. Based on extensive numerical tests, some efficient ranges of these parameters for nonmonotone trust region algorithms are recommended. [Copyright &y& Elsevier]

Abstract: Gutin et al. [G. Gutin, A. Yeo, Polynomial approximation algorithms for the TSP and the QAP with a factorial domination number, Discrete Applied Mathematics 119 (1–2) (2002) 107–116] proved that, in the ATSP problem, a tour of weight not exceeding the weight of an average tour is of dominance ratio at least for all . (Tours with this property can be easily obtained.) In [N. Alon, G. Gutin, M. Krivelevich, Algorithms with large domination ratio, Journal on Algorithms 50 (2004) 118–131; G. Gutin, A. Vainshtein, A. Yeo, Domination analysis of combinatorial optimization problems, Discrete Applied Mathematics 129 (2–3) (2003) 513–520; G. Gutin, A. Yeo, Polynomial approximation algorithms for the TSP and the QAP with a factorial domination number, Discrete Applied Mathematics 119 (1–2) (2002) 107–116], algorithms with large dominance ratio were provided for Max Cut, Max -Sat, ATSP, and other problems. All these algorithms share a common property — they provide solutions of quality guaranteed to be not worse than the average solution value. In this paper we show that, in general, this property by itself does not necessarily ensure a good performance in terms of dominance. Specifically, we show that for the MaxSat problem, algorithms with this property might perform poorly in terms of dominance. [Copyright &y& Elsevier]

Abstract: This paper presents gradient type algorithms to solve frictional multi-contact problems written as quasi-optimization problems. A single loop scheme formally close to the classical conjugate gradient method is proposed with some adaptations of the iterate corrections and gradient projections. Since the convergence is difficult to prove, various tests in the field of granular media are performed with comparison with the non-linear Gauss–Seidel scheme. [Copyright &y& Elsevier]

Abstract: In this paper, we present a formulation of numerical approximations of the frictional quasi-contact problem with dry friction between a deformable body and a foundation with possibility to consider the case of two deformable bodies. We consider numerical approximations of 3D static contact problem with dry friction, using finite contact elements. Saddle-point algorithm, Lagrange incremental multipliers method and penalty functions are used to enforce finite element surface contact constrains for incremental formulation of the frictional quasi-static problem. Some typical examples in the elastic contact problems with dry friction are presented. [ABSTRACT FROM AUTHOR]