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Classical adjoint-based optimization approach for the optimal control of partial differential equations is known to require a large amount of CPU time and memory storage. In this article, in order to reduce these requirements, a posteriori and a priori model order reduction techniques such as POD (Proper Orthogonal Decomposition) and PGD (Proper Generalized Decomposition) are used. As a matter of fact, these techniques allows a fast access to the temporal dynamics of a solution approximated in a suitable subspace of low dimension, spanned by a set of basis functions that form a reduced basis. The costly high fidelity model is then projected onto this basis and results in a system of ordinary differential equations which can be solved in quasi-real time. A disadvantage of considering a fixed POD basis in a suboptimal control loop, is basically the dependence of such bases on a posteriori information coming from high fidelity simulations. Therefore, a non robustness of the POD basis can be expected for certain perturbations in the original parameter for which it was built. As a result, update the reduced bases with respect to each variation in the control parameter using the POD method is still costly. To get over this difficulty, we equip the usual reduced optimal control algorithm with an intermediate basis adaptation step. The first proposed approach consists in adapting the reduced basis for a new control parameter by interpolating over a set of POD bases previously computed for a range of control parameters. To achieve that, an interpolation technique based on properties of the tangent subspace of the Grassmann manifold (ITSGM) is considered. The second approach is the PGD method, which by nature, enrich a space time decomposition trying to enhance the approximation by learning from its own errors. Relaying on this property, this method is employed in the control loop as a basis corrector, in such a way the given spatial basis is adapted for the new control parameter by performing just few enrichments. These two approaches are applied in the sub-control of the two dimensional non-linear reaction-diffusion equations and Burgers equations. [ABSTRACT FROM AUTHOR]

In this paper, a robust optimization approach is used to solve the redundancy allocation problem (RAP) in series-parallel systems with component mixing where uncertainty exists in components’ reliabilities. In real world, the reliabilities of components are imprecisely estimated or the reliability of some components may vary due to some realistic factors. Therefore, we may deal with a system where there are many components with uncertain values of reliabilities. To deal with this problem, for the first time a robust optimization approach is applied to RAP with component mixing to produce a robust solution, which is relatively insensitive with respect to uncertainty in reliability of components. In addition, the advantages of the proposed robust technique are illustrated by considering a series-parallel system and finding the suitable redundancy levels and then Monte Carlo simulation is implemented to examine the quality of the robust solutions. The results indicate that applying the proposed robust RAP can be more reliable to determine system reliability in the designing phase of systems. [ABSTRACT FROM AUTHOR]

A robust congestion pricing (ROPRICE) of signal-controlled road network is considered for equilibrium network flow with uncertain travel demand. A min–max bi-level program is presented to mitigate vulnerability of area traffic control road network against growing travel demand and reduce traffic congestion. A cutting plane projection approach (CPP) is proposed to effectively solve the ROPRICE problem with global convergence. Numerical computations are performed using various test road networks and comparisons are made with recently proposed heuristics. Computational results indicate that the proposed solution scheme can substantially achieve greater system performance as compared to other alternatives. [ABSTRACT FROM AUTHOR]

We investigate a stochastic Discrete Time/Cost Trade-off Problem. This multimode project scheduling problem, requires assigning modes to activities, and scheduling the activities so that the sum of the activities cost and the expected tardiness cost is minimized. Furthermore, the derived solution should be stable. This stability property renders the schedule less sensitive to uncontrollable factors that may disrupt the project execution. To solve this problem, we propose a two-stage solution strategy. In the first stage, we implemented a simulation–optimization strategy that yields a cost-effective schedule. Next, a mixed-integer programming formulation is used to derive a schedule that is both stable and cost-effective. We report the results of computational experiments that attest to the efficacy of the proposed approach. [ABSTRACT FROM AUTHOR]

The optimized networks with “onion-like” topologies which have improved robustness to resist malicious attacks have attracted a great deal of research effort. In this paper, we investigate the synchronization behavior of dynamical scale-free onion networks. Large quantities of numerical simulations indicate that solely enhancing the network robustness can lead to the reduction of the ability to achieve synchronization. Furthermore, two important structural properties of “onion-like” topologies, the increase of average path length and the increase of assortative coefficient, are analyzed and considered to be responsible for the decease of synchronizability. The numerical results demonstrate that in system design the balance between maximizing the ability to resist attacks and improving the ability to achieve synchronization should deserve careful consideration. Current results are beneficial for us to deeply understand the dynamical properties and patterns in the complex networked systems. [ABSTRACT FROM AUTHOR]

In this paper, we consider the multi-facility Weber location problem (MFWP) with uncertain location of demand points and transportation cost parameters. Equivalent formulations of its robust counterparts for both the Euclidean and block norms and interval and ellipsoidal uncertainty sets are given as conic linear optimization problems. [ABSTRACT FROM AUTHOR]

Abstract: The robust shortest path problem is a network optimization problem that can be defined to deal with uncertainty of costs associated with the arcs of a network. Two models have been considered for the robust shortest path problem: interval data and discrete data sets. This work addresses the robust shortest path problem with a minmax regret objective function on a finite multi-scenario model. This problem consists in finding an optimal path in the sense that it has the minimum maximum deviation from the shortest one over all scenarios. With this goal some properties of the problem and of its optimal solutions are derived. These results allow to introduce three approaches, a labeling algorithm, an algorithm based on ranking loopless paths, and a hybrid algorithm which ranks loopless paths in a suitable way to apply the early elimination of useless solutions. The algorithms are tested on random networks and compared with a previous method for the same problem. The obtained computational results are reported and discussed. They show that the labeling and the hybrid approaches outperform the others. [Copyright &y& Elsevier]

Highlights: [•] Application of Kriging, RBF and RBFNN in robust parameter design. [•] These models are superior the quadratic polynomial regression model. [•] Kriging model is the most accurate model in comparison with the polynomial regression model. [•] We introduced a new approach using multi-objective optimization instead of the mean squared error. [Copyright &y& Elsevier]

Abstract: A totally optimized image watermarking methodology that manages to enhance its local behaviour by applying the Krawtchouk moments is presented through this paper. The introduced technique is making use of a simple genetic algorithm in order to optimize the set of parameters that significantly influences the locality properties alongside with the overall performance of the watermarking procedure. Herein, the watermarking process is tackled as an optimization procedure. In this context, the appropriate set of configuration parameters is being searched for ensuring high quality watermarked images and low bit error rates at the extraction stage. For this purpose, several traditional and newly introduced image quality measures are used in order to quantify the influence of the examined set of parameters, as far as the quality of the watermarked image and the accuracy of the extracted watermark are concerned. The proposed method produces watermarked images of high quality and ensures high detection rates under several non-geometric attacks, by using less prior-knowledge at the detector’s side. Extensive experiments have shown that by handling the watermarking process as an optimization problem, more robust and accurate watermarking schemes can be derived. [Copyright &y& Elsevier]

Abstract: In this paper, the robust H ∞ filter scheme for the discrete-time switched systems with interval time-varying delay and linear fractional perturbations is proposed. A convex optimization problem with some LMI constraints is formulated to design the stable switched filter which minimizes the H ∞ norm bound for filtering error system. Some nonnegative inequalities and the free weighting matrix technique are used to provide the additional degree of freedom which improves the conservativeness of the proposed results. Finally, a numerical example is illustrated to show the use of the main results. [Copyright &y& Elsevier]

Abstract: Robustness in complex networks is an ongoing research effort that seeks to improve the connectivity of networks against attacks and failures. Among other measures, algebraic connectivity has been used to characterize processes such as damped oscillation of liquids in connected pipes. Similar characterizations include the number of edges necessary to disconnect a network: the larger the algebraic connectivity, the larger the number of edges required to disconnect a network and hence, the more robust a network. In this paper, we answer the question, “Which edge can we rewire to have the largest increase in algebraic connectivity?”. Furthermore, we extend the rewiring of a single edge to rewiring multiple edges to realize the maximal increase in algebraic connectivity. The answer to this question above can provide insights to decision makers within various domains such as communication and transportation networks, who seek an efficient solution to optimize the connectivity and thus increase the robustness of their networks. Most importantly, our analytical and numerical results not only provide insights to the number of edges to rewire, but also the location in the network where these edges would effectuate the maximal increase in algebraic connectivity and therefore, enable a maximal increase in robustness. [Copyright &y& Elsevier]

Abstract: Chaos optimization algorithm (COA), which has the features of easy implementation, short execution time and robust mechanisms of escaping from the local optimum, is a promising tool for the engineering applications. The design of approaches to improve the convergence of the COA is a challenging issue. Improved mutative-scale parallel chaotic optimization algorithm (MPCOA) are proposed in this paper, and three ways of improvements for MPCOA are investigated in detail: MPCOA combined with simplex search method, MPCOA based on competitive/cooperative inter-communication, MPCOA combined with harmony search algorithm. Several simulation results are used to show the effective performance of these chaos optimization algorithms. [Copyright &y& Elsevier]

Abstract: This paper is concerned with the problem of passivity analysis for a class of Cohen–Grossberg fuzzy bidirectional associative memory (BAM) neural networks with time varying delay. By employing the delay fractioning technique and linear matrix inequality optimization approach, delay dependent passivity criteria are established that guarantees the passivity of fuzzy Cohen–Grossberg BAM neural networks with uncertainties. The passivity condition is expressed in terms of LMIs, which can be easily solved by various convex optimization algorithms. Finally, a numerical example is given to illustrate the effectiveness of the proposed result. [Copyright &y& Elsevier]

Abstract: In this paper, a robust filtering problem is considered for a class of discrete-time nonlinear systems. Based on the Lyapunov method, a design criterion of the robust filter guarantee not only the stability but also the prespecified upper bound of norm from the disturbance inputs to error state outputs. The design condition can be solved easily by efficient convex optimization algorithms. Numerical examples show the effectiveness of the proposed method. [Copyright &y& Elsevier]

Abstract: Least squares problems arise frequently in many disciplines such as image restorations. In these areas, for the given least squares problem, usually the coefficient matrix is ill-conditioned. Thus if the problem data are available with certain error, then after solving least squares problem with classical approaches we might end up with a meaningless solution. Tikhonov regularization, is one of the most widely used approaches to deal with such situations. In this paper, first we briefly describe these approaches, then the robust optimization framework which includes the errors in problem data is presented. Finally, our computational experiments on several ill-conditioned standard test problems using the regularization tools, a Matlab package for least squares problem, and the robust optimization framework, show that the latter approach may be the right choice. [Copyright &y& Elsevier]

Abstract: This paper establishes new robust delay-dependent stability and stabilization methods for a class of nonlinear discrete-time systems with time-varying delays. The parameter uncertainties are convex-bounded and the unknown nonlinearities are time-varying perturbations satisfying Lipschitz conditions in the state and delayed-state. An appropriate Lyapunov functional is constructed to exhibit the delay-dependent dynamics and compensate for the enlarged time-span. The developed methods for stability and stabilization eliminate the need for over bounding and utilize smaller number of LMI decision variables. New and less conservative solutions to the stability and stabilization problems of nonlinear discrete-time system are provided in terms of feasibility-testing of new parametrized linear matrix inequalities (LMIs). Robust feedback stabilization methods are provided based on state-measurements and by using observer-based output feedback so as to guarantee that the corresponding closed-loop system enjoys the delay-dependent robust stability with an gain smaller that a prescribed constant level. All the developed results are expressed in terms of convex optimization over LMIs and tested on representative examples. [Copyright &y& Elsevier]

Abstract: Although evolutionary algorithms (EAs) have some operators which let them explore the whole search domain, still they get trapped in local minima when multimodality of the objective function is increased. To improve the performance of EAs, many optimization techniques or operators have been introduced in recent years. However, it seems that these modified versions exploit some special properties of the classical multimodal benchmark functions, some of which have been noted in previous research and solutions to eliminate them have been proposed. In this article, we show that quite symmetric behavior of the available multimodal test functions is another example of these special properties which can be exploited by some EAs such as covariance matrix adaptation evolution strategy (CMA-ES). This method, based on its invariance properties and good optimization results for available unimodal and multimodal benchmark functions, is considered as a robust and efficient method. However, as far as black box optimization problems are considered, no special trend in the behavior of the objective function can be assumed; consequently this symmetry limits the generalization of optimization results from available multimodal benchmark functions to real world problems. To improve the performance of CMA-ES, the Elite search sub-algorithm is introduced and implemented in the basic algorithm. Importance and effect of this modification is illustrated experimentally by dissolving some test problems in the end. [Copyright &y& Elsevier]