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In this paper we solve a constrained optimal control problem related to the location of the wastewater outfalls in a sewage disposal system. This is a problem where the control is the position and the constraints are non-convex and pointwise, which makes difficult its resolution. We discretize the problem by means of a characteristics-Galerkin method and we use three algorithms for the numerical resolution of the discretized optimization problem: an interior point algorithm, the Nelder-Mead simplex method and a duality method. Finally, we compare the numerical results obtained by applying the described methods for a realistic problem posed in the ría of Vigo (Galicia, Spain). [ABSTRACT FROM AUTHOR]

The paper describes a new preference method and its use in multiobjective optimization. These preferences are developed with a goal to reduce the cognitive overload associated with the relative importance of a certain criterion within a multiobjective design environment involving large numbers of objectives. Their successful integration with several genetic-algorithm-based design search and optimization techniques (weighted sums, weighted Pareto, weighted coevolutionary methods, and weighted scenarios) are described and theoretical results relating to complexity and sensitivity of the algorithm are presented and discussed. Its usefulness has been demonstrated in a real-world project of conceptual airframe design (a joint project with British Aerospace Systems). [ABSTRACT FROM AUTHOR]

In this paper, a functional inequality constrained optimization problem is studied using a discretization method and an adaptive scheme. The problem is discretized by partitioning the interval of the independent parameter. Two methods are investigated as to how to treat the discretized optimization problem. The discretization problem is firstly converted into an optimization problem with a single nonsmooth equality constraint. Since the obtained equality constraint is nonsmooth and does not satisfy the usual constraint qualification condition, relaxation and smoothing techniques are used to approximate the equality constraint via a smooth inequality constraint. This leads to a sequence of approximate smooth optimization problems with one constraint. An adaptive scheme is incorporated into the method to facilitate the computation of the sum in the inequality constraint The second method is to apply an adaptive scheme directly to the discretization problem. Thus a sequence of optimization problems with a small number of inequality constraints are obtained. Convergence analysis for both methods is established. Numerical examples show that each of the two proposed methods has its own advantages and disadvantages over the other. [ABSTRACT FROM AUTHOR]

This paper presents a parallel computation approach for the efficient solution of very large multistage linear and nonlinear network problems with random parameters. These problems result from particular instances of models for the robust optimization of network problems with uncertainty in the values of the right-hand side and the objective function coefficients. The methodology considered here models the uncertainty using scenarios to characterize the random parameters. A scenario tree is generated and, through the use of full-recourse techniques, an implementable solution is obtained for each group of scenarios at each stage along the planning horizon. As a consequence of the size of the resulting problems, and the special structure of their constraints, these models are particularly well-suited for the application of decomposition techniques, and the solution of the corresponding subproblems in a parallel computation environment. An augmented Lagrangian decomposition algorithm has been implemented on a distributed computation environment, and a static load balancing approach has been chosen for the parallelization scheme, given the subproblem structure of the model. Large problems - 9000 scenarios and 14 stages with a deterministic equivalent nonlinear model having 166000 constraints and 230000 variables - are solved in 45 minutes on a cluster of four small (11 Mflops) workstations. An extensive set of computational experiments is reported; the numerical results and running times obtained for our test set, composed of large-scale real-life problems, confirm the efficiency of this procedure. [ABSTRACT FROM AUTHOR]

Classical gradient methods and evolutionary algorithms represent two very different classes of optimization techniques that seem to have very different properties. This paper discusses some aspects of some "obvious" differences and explores to what extent a hybrid method, the evolutionary-gradient-search procedure, can be used beneficially in the field of continuous parameter optimization. Simulation experiments show that on some test functions, the hybrid method yields faster convergence than pure evolution strategies, but that on other test functions, the procedure exhibits the same deficiencies as steepest-descent methods. [ABSTRACT FROM AUTHOR]

The paper presents a means of attempting to account for overhead, as well as function evaluations, in evaluating unconstrained optimization techniques. Criteria are established which compare techniques on classes of algorithms. While not completely machine independent, and certainly not programmer independent, the new method eliminates much of the machine dependency of earlier criteria. The criteria are applied to three known and one new quasi-Newton algorithm, with interesting results. [ABSTRACT FROM AUTHOR]

The sequential decision problem considered in this paper consists of finding an optimal policy for increasing the capacity of a multiterminal network with requirements increasing over a planning period and arcs subject to failure. This problem is formulated as a shortest-route problem in a very large network and solved by Dijkstra's algorithm. Computational experience is also presented. [ABSTRACT FROM AUTHOR]

This paper is concerned with an optimization method for manufacturing systems. This method can be applied to optimize problems with any type of variables (variables from a real set, e.g., conveyor speed; an integer set, e.g., size of buffer; or any general set, e.g., dispatching rules). It is based on the association of an evolutionary algorithm and a simulation model. Extensions of Michalewicz's evolutionary operators and algorithm are proposed to tackle manufacturing system problems. The particular case of stochastic models is discussed. This method is applied to an example: the configuration of a workshop producing plastic yoghurt pots. The criterion to optimize is the cost of the workshop and the three variables are the size of a silo, the size of a warehouse and a choice between two manufacturing methods. The application has been realized by connecting an evolutionary algorithm programmed in C and a simulation language. [ABSTRACT FROM AUTHOR]

Various methods have been proposed to conduct optimization via discrete-event simulation. Prevalent among these are gradient-based algorithms, and more recently, so-called retrospective approaches that deterministically optimize over simulated outcomes. In this paper we compare and contrast the performance of these two approaches for the optimization of a periodic review (s, S) inventory system. In practice, gradient-based methods often exhibit undesirably slow convergence, whereas the retrospective approach can be computationally burdensome. We propose a hybrid algorithm that combines aspects of both approaches to mitigate these shortcomings. [ABSTRACT FROM AUTHOR]

This paper considers the problem of finding minimal length tree networks on the unit sphere Φ of a given point set (V) where distance is measured along great circular arcs. The related problems of finding a Steiner Minimal Tree SMT (V) and of finding a Minimum Spanning Tree MST(V) are treated through a simplicial decomposition technique based on computing the Delaunay Triangulation DT (V) and the Voronoi Diagram VD(V) of the given point set. O (N log N) algorithms for computing DT(V), VD(V), and WST(V) as well as an O(N log N) heuristic for finding a sub-optimal SMT(V) solution are presented, together with experimental results for randomly distributed points on Φ. [ABSTRACT FROM AUTHOR]

The DFP algorithm of unconstrained optimization possesses excellent properties of convergence for convex functions. However, a convergence theory of the DFP algorithm without the convexity assumption has not yet been established. This paper gives the following result: If the objective function is suitably smooth, and if the DFP algorithm produces a convergent point sequence, then the limit point of the sequence is a critical point of the objective function. Also, some open questions are mentioned. [ABSTRACT FROM AUTHOR]

Optimization algorithms or heuristics in which the user interacts significantly either during the solution process or as part of post-optimality analysis are becoming increasingly popular. An important underlying premise of such man/machine systems is that there are some steps in solving a problem in which the computer has an advantage and other steps in which a human has an advantage. This paper first discusses how man/machine systems can be useful in facilitating model specification and revision, coping with aspects of a problem that are difficult to quantify and assisting in the solution process. We then survey successful systems that have been developed in the areas of vehicle scheduling, location problems, job shop scheduling, course scheduling, and planning language-based optimization. [ABSTRACT FROM AUTHOR]

This paper presents a solution method for the reliability optimization problem of systems which is formulated as a mixed-integer nonlinear programming problem with multiple constraints. The system structure is series, series-parallel, or complex. In the solution method, the optimal solution is obtained by solving the surrogate dual problem. Surrogate problems with only one constraint which appear in the optimization process are solved by a technique using dynamic programming. Some computational experiences are shown along with comparison with other approaches. [ABSTRACT FROM AUTHOR]

Studies of the convergence of algorithms often revolve around the existence of a function with respect to which monotonic descent is required. In this paper, we show that under relatively lenient conditions, "stage-dependent descent" (not necessarily monotonic) is sufficient to guarantee convergence. This development also provides the impetus to examine optimization algorithms. We show that one of the important avenues in the study of convergence, namely, the theory of epi-convergence imposes stronger conditions than are necessary to establish the convergence of an optimization algorithm. Working from a relaxation of epi-convergence, we introduce the notion of ∂-compatibility, and prove several results that permit relaxations of conditions imposed by previous approaches to algorithmic convergence. Finally, to illustrate the usefulness of the concepts, we combine stage-dependent descent with results derivable from ∂-compatibility to provide a basis for the convergence of a general algorithmic statement that might be used for stochastic and nondifferentiable optimization. [ABSTRACT FROM AUTHOR]

This paper deals with undiscounted infinite stage two-person zero-sum stochastic games with finite state and action spaces. It was recently shown that such games possess a value. But in general there are no optimal strategies. We prove that for each player there exists a nonempty set of easy initial states, i.e. starting states for which the player possesses an optimal stationary strategy. This result is proved with the aid of facts derived by Bewley and Kohlberg for the limit discount equation for stochastic games. [ABSTRACT FROM AUTHOR]

This is the second in a series of three papers that empirically examine the competitiveness of simulated annealing in certain well-studied domains of combinatorial optimization. Simulated annealing is a randomized technique proposed by S. Kirkpatrick, C D. Gelatt and M P. Vecchi for improving local optimization algorithms. Here we report on experiments at adapting simulated annealing to graph colortag and number partitioning, two problems for which local optimization had not previously been thought suitable. For graph coloring, we report on three simulated annealing schemes, all of which can dominate traditional techniques for certain types of graphs, at least when large amounts of computing rune are available. For number partitioning, simulated annealing is not competitive with the differencing algorithm of N. Karmarkar and R. M Karp, except on relatively small instances. Moreover, if running time is taken into account, natural annealing schemes cannot even outperform multiple random runs of the local optimization algorithms on which they are based, in sharp contrast to the observed performance of annealing on other problems. [ABSTRACT FROM AUTHOR]

This paper deals with the solution to a discrete optimization problem by decomposition. It develops a criterion for ranking the decomposition procedures, discusses the properties of the optimal decompositions, and gives an algorithm for finding the best decomposition in the case of no storage limitation. [ABSTRACT FROM AUTHOR]

Source localization based on time of arrival (TOA) measurements in the presence of clock asynchronization and sensor position uncertainties is investigated in this paper. Different from the traditional numerical algorithms, a neural circuit named Lagrange programming neural network (LPNN) is employed to tackle the nonlinear and nonconvex constrained optimization problem of source localization. With the augmented term, two types of neural networks are developed from the original maximum likelihood functions based on the general framework provided by LPNN. The convergence and local stability of the proposed neural networks are analyzed in this paper. In addition, the Cramér-Rao lower bound is also derived as a benchmark in the presence of clock asynchronization and sensor position uncertainties. Simulation results verify the superior performance of the proposed LPNN over the traditional numerical algorithms and its robustness to resist the impact of a high level of measurement noise, clock asynchronization, as well as sensor position uncertainties. [ABSTRACT FROM AUTHOR]

Detecting community structures helps to reveal the functional units of complex networks. In this paper, the community detection problem is regarded as a modularity-based multi-objective optimization problem (MOP), and a parallel conical area community detection algorithm (PCACD) is designed to solve this MOP effectively and efficiently. In consideration of the global properties of the selection and update mechanisms, PCACD employs a global island model and targeted elitist migration policy in a conical area evolutionary algorithm (CAEA) to discover community structures at different resolutions in parallel. Although each island is assigned only a portion of all sub-problems in the island model, it preserves a complete population to accomplish the global selection and update. Meanwhile the migration policy directly migrates each elitist individual to an appropriate island in charge of the sub-problem associated with this individual to share essential evolutionary achievements. In addition, a modularity-based greedy local search strategy is also applied to accelerate the convergence rate. Comparative experimental results on six real-world networks reveal that PCACD is capable of discovering potential high-quality community structures at diverse resolutions with satisfactory running efficiencies. [ABSTRACT FROM AUTHOR]

Sparse arrays can fix array aperture with a reduced number of elements to maintain resolution while reducing cost. However, grating lobe suppression, high peak side-lobe level reduction (PSLL), and constraints on the location of the array elements in the practical deployment of arrays are challenging problems. Based on simulated annealing, the element locations of a sparse planar array in smart ocean applications with minimum spacing and geographic constraints are optimized in this paper by minimizing the sum of PSLL. The robustness of the deployment-optimized spare planar array with mis-calibration is further considered. Numerical simulations show the effectiveness of the proposed solution. [ABSTRACT FROM AUTHOR]

In this paper an inverse and iterative method for the identification of material behavior is presented, based on the Finite Element Model Updating (FEMU) strategy. The FE simulations are performed with a commercial FE software code, using a self-implemented elastic material model at finite strain. The iterative identification procedure is based on an experimental test (numerical) whose measured kinematic values are compared to the corresponding simulated ones. Through an optimization algorithm the material parameters are varied in a way that the least-squares sum of the kinematic values is minimized and the optimal material parameters yielding the material behavior are identified. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

This paper presents a combined simulation-optimization model for simulating reservoir operations without any detailed operation rules; it features the integration of a nonlinear, multiple-objective function and a heuristic search method, the Shuffled Complex Evolution method, developed at the University of Arizona. The model is applied to optimal water allocations from both Balan Reservoir and Seomjingang Dam in South Korea, an irrigation reservoir and a multipurpose, multioutlet reservoir, respectively, that primarily supply irrigation water. In the case of the optimal operation of Balan Reservoir, the simulation results show that the optimal release patterns are similar to those of historical operations because the demands for irrigation water are accurately predicted and guide optimal reservoir operations. In addition, the model is successfully applied to establishing a long-term reservoir operation plan. As for the optimal operation of Seomjingang Dam, the reservoir operations are affected by the target water stages, and the model provides reasonable results, irrespective of inflow conditions. Moreover, the model is employed to create a new operation rule that is necessary to adapt to changes in the circumstances related to water management. Consequently, it is concluded that the model is useful for assessing reservoirs' irrigation water supply capacities when establishing operation plans and providing feasible alternatives for new operation rules, and it could be applied to real-time reservoir operations. [ABSTRACT FROM AUTHOR]

In this paper, we consider beamforming (BF) for cooperative networks with one multi—antenna source, multiple multi—antenna amplify—and—forward (AF) relays, and one single—antenna destination. The source BF vector and the AF—BF matrices at the relays are optimized for maximization of the signal—to—noise ratio (SNR) at the destination under three different power constraints. In particular, we consider individual relay power constraints, a joint relay power constraint, and a joint power constraint for the source and the relays. We solve the associated optimization problems in two stages. In the first stage, we find the optimal AF—BF matrices for a given BF vector at the source. For the cases of individual and joint relay power constraints, closed—form solutions for the AF—BF matrices are provided, respectively. Furthermore, for the case of a joint source—relay power constraint, the AF—BF matrices are obtained in closed form up to a scalar power allocation factor and an efficient numerical algorithm for the power allocation between the source and the relays is given. In the second stage, the optimal source BF vectors are computed. Thereby, we show that for the joint relay and the joint source—relay power constraints, the resulting problem can be transformed into a non—convex polynomial programming problem which allows for an exact solution for small—scale networks. For large—scale networks and networks with individual relay power constraints, we propose efficient suboptimal optimization methods for the source BF vector. Simulation results show the benefits of having multiple antennas at the source and/or multiple multi—antenna relays and illustrate the performance differences introduced by the three different power constraints. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of resource allocation in the DFT-Spread-OFDMA (DFT-S-OFDMA) uplink. We show that the resource allocation problem can be formulated as a set packing problem, which in general is NP-hard. We propose polynomial-time message-passing based algorithms, one of which is guaranteed to yield a solution that is within a constant fraction of the optimal solution and is also asymptotically optimal in the limit as the number of subcarriers in the system goes to infinity. The message-passing based algorithm is also extended to solve the resource allocation problem over a multi-cell uplink in a distributed fashion. Our algorithms account for finite input alphabets and non-ideal practical outer codes. Extensive simulations are performed to assess the performance of the proposed algorithms and it is shown that they yield near-optimal solutions at a low complexity and with a low memory requirement. [ABSTRACT FROM PUBLISHER]

The aggregate capacity of wireless ad hoc networks can be increased substantially if each node is equipped with multiple network interface cards (NICs) and each NIC operates on a distinct frequency channel. Most of the recently proposed channel assignment algorithms are based on combinatorial techniques. Combinatorial channel assignment schemes may sometimes result in computationally complicated algorithms as well as inefficient utilization of the available frequency spectrum. In this paper, we analytically model channel and interface assignment problems as tractable continuous optimization problems within the framework of network utility maximization (NUM). In particular, the link data rate models for both single-channel reception and multichannel reception scenarios are derived. The assignment of both nonoverlapped and partially overlapped channels is also considered. We then propose two distributed multi-interface multichannel random access (DMMRA) algorithms for single-channel reception and multichannel reception scenarios. The DMMRA algorithms are fast, distributed, and easy to implement. Each algorithm solves the formulated NUM problem for each scenario. DMMRA requires each node to only iteratively solve a local, myopic, and convex optimization problem. Convergence and optimality properties of our algorithms are studied analytically. Simulation results show that our proposed algorithms significantly outperform utility-optimal combinatorial channel assignment algorithms in terms of both achieved network utility and throughput. [ABSTRACT FROM AUTHOR]

Among many algorithms, gradient descent algorithm (GDA) is a simple tool to derive an optimal quantity in dealing with an optimization problem in the linear space. Apart from the initial value, the step size has a great impact on the convergence rate of this algorithm. Its affect on the geometric structure of the consecutive configurations is more crucial if one works with an optimization problem in the statistical shape analysis. In other words, if the step size of the GDA is not properly tuned, the geometry might not be preserved while the algorithm is moving forward to reach an optimal mean shape. In order to improve the performance of the GDA, we introduce a dynamic step size and a new criterion both to check the geometry in each step of the algorithm and to accelerate the convergence rate. These lead to a new robust algorithm on deriving the intrinsic mean on the shape space. We compare the performance of our proposed procedure to the usual GDA using a real shape data accompanied with simulation studies. [ABSTRACT FROM AUTHOR]