859 resultados para Multi-objective optimization problem


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In this work, we explore simultaneous design and material selection by posing it as an optimization problem. The underlying principles for our approach are Ashby's material selection procedure and structural optimization. For the simplicity and ease of initial implementation of the general procedure, truss structures under static load are considered in this work in view of maximum stiffness, minimum weight/cost and safety against failure. Along the lines of Ashby's material indices, a new design index is derived for trusses. This helps in choosing the most suitable material for any design of a truss. Using this, both the design space and material database are searched simultaneously using optimization algorithms. The important feature of our approach is that the formulated optimization problem is continuous even though the material selection is an inherently discrete problem.

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In this paper, we present a novel formulation for performing topology optimization of electrostatically actuated constrained elastic structures. We propose a new electrostatic-elastic formulation that uses the leaky capacitor model and material interpolation to define the material state at every point of a given design domain continuously between conductor and void states. The new formulation accurately captures the physical behavior when the material in between a conductor and a void is present during the iterative process of topology optimization. The method then uses the optimality criteria method to solve the optimization problem by iteratively pushing the state of the domain towards that of a conductor or a void in the appropriate regions. We present examples to illustrate the ability of the method in creating the stiffest structure under electrostatic force for different boundary conditions.

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Swarm intelligence algorithms are applied for optimal control of flexible smart structures bonded with piezoelectric actuators and sensors. The optimal locations of actuators/sensors and feedback gain are obtained by maximizing the energy dissipated by the feedback control system. We provide a mathematical proof that this system is uncontrollable if the actuators and sensors are placed at the nodal points of the mode shapes. The optimal locations of actuators/sensors and feedback gain represent a constrained non-linear optimization problem. This problem is converted to an unconstrained optimization problem by using penalty functions. Two swarm intelligence algorithms, namely, Artificial bee colony (ABC) and glowworm swarm optimization (GSO) algorithms, are considered to obtain the optimal solution. In earlier published research, a cantilever beam with one and two collocated actuator(s)/sensor(s) was considered and the numerical results were obtained by using genetic algorithm and gradient based optimization methods. We consider the same problem and present the results obtained by using the swarm intelligence algorithms ABC and GSO. An extension of this cantilever beam problem with five collocated actuators/sensors is considered and the numerical results obtained by using the ABC and GSO algorithms are presented. The effect of increasing the number of design variables (locations of actuators and sensors and gain) on the optimization process is investigated. It is shown that the ABC and GSO algorithms are robust and are good choices for the optimization of smart structures.

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Stirred tank bioreactors, employed in the production of a variety of biologically active chemicals, are often operated in batch, fed-batch, and continuous modes of operation. The optimal design of bioreactor is dependent on the kinetics of the biological process, as well as the performance criteria (yield, productivity, etc.) under consideration. In this paper, a general framework is proposed for addressing the two key issues related to the optimal design of a bioreactor, namely, (i) choice of the best operating mode and (ii) the corresponding flow rate trajectories. The optimal bioreactor design problem is formulated with initial conditions and inlet and outlet flow rate trajectories as decision variables to maximize more than one performance criteria (yield, productivity, etc.) as objective functions. A computational methodology based on genetic algorithm approach is developed to solve this challenging multiobjective optimization problem with multiple decision variables. The applicability of the algorithm is illustrated by solving two challenging problems from the bioreactor optimization literature.

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Location area planning problem is to partition the cellular/mobile network into location areas with the objective of minimizing the total cost. This partitioning problem is a difficult combinatorial optimization problem. In this paper, we use the simulated annealing with a new solution representation. In our method, we can automatically generate different number of location areas using Compact Index (CI) to obtain the optimal/best partitions. We compare the results obtained in our method with the earlier results available in literature. We show that our methodology is able to perform better than earlier methods.

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In pay-per-click sponsored search auctions which are currently extensively used by search engines, the auction for a keyword involves a certain number of advertisers (say k) competing for available slots (say m) to display their advertisements (ads for short). A sponsored search auction for a keyword is typically conducted for a number of rounds (say T). There are click probabilities mu(ij) associated with each agent slot pair (agent i and slot j). The search engine would like to maximize the social welfare of the advertisers, that is, the sum of values of the advertisers for the keyword. However, the search engine does not know the true values advertisers have for a click to their respective advertisements and also does not know the click probabilities. A key problem for the search engine therefore is to learn these click probabilities during the initial rounds of the auction and also to ensure that the auction mechanism is truthful. Mechanisms for addressing such learning and incentives issues have recently been introduced. These mechanisms, due to their connection to the multi-armed bandit problem, are aptly referred to as multi-armed bandit (MAB) mechanisms. When m = 1, exact characterizations for truthful MAB mechanisms are available in the literature. Recent work has focused on the more realistic but non-trivial general case when m > 1 and a few promising results have started appearing. In this article, we consider this general case when m > 1 and prove several interesting results. Our contributions include: (1) When, mu(ij)s are unconstrained, we prove that any truthful mechanism must satisfy strong pointwise monotonicity and show that the regret will be Theta T7) for such mechanisms. (2) When the clicks on the ads follow a certain click precedence property, we show that weak pointwise monotonicity is necessary for MAB mechanisms to be truthful. (3) If the search engine has a certain coarse pre-estimate of mu(ij) values and wishes to update them during the course of the T rounds, we show that weak pointwise monotonicity and type-I separatedness are necessary while weak pointwise monotonicity and type-II separatedness are sufficient conditions for the MAB mechanisms to be truthful. (4) If the click probabilities are separable into agent-specific and slot-specific terms, we provide a characterization of MAB mechanisms that are truthful in expectation.

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Ranking problems have become increasingly important in machine learning and data mining in recent years, with applications ranging from information retrieval and recommender systems to computational biology and drug discovery. In this paper, we describe a new ranking algorithm that directly maximizes the number of relevant objects retrieved at the absolute top of the list. The algorithm is a support vector style algorithm, but due to the different objective, it no longer leads to a quadratic programming problem. Instead, the dual optimization problem involves l1, ∞ constraints; we solve this dual problem using the recent l1, ∞ projection method of Quattoni et al (2009). Our algorithm can be viewed as an l∞-norm extreme of the lp-norm based algorithm of Rudin (2009) (albeit in a support vector setting rather than a boosting setting); thus we refer to the algorithm as the ‘Infinite Push’. Experiments on real-world data sets confirm the algorithm’s focus on accuracy at the absolute top of the list.

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The problem of updating the reliability of instrumented structures based on measured response under random dynamic loading is considered. A solution strategy within the framework of Monte Carlo simulation based dynamic state estimation method and Girsanov's transformation for variance reduction is developed. For linear Gaussian state space models, the solution is developed based on continuous version of the Kalman filter, while, for non-linear and (or) non-Gaussian state space models, bootstrap particle filters are adopted. The controls to implement the Girsanov transformation are developed by solving a constrained non-linear optimization problem. Numerical illustrations include studies on a multi degree of freedom linear system and non-linear systems with geometric and (or) hereditary non-linearities and non-stationary random excitations.

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In this paper, we present a methodology for designing a compliant aircraft wing, which can morph from a given airfoil shape to another given shape under the actuation of internal forces and can offer sufficient stiffness in both configurations under the respective aerodynamic loads. The least square error in displacements, Fourier descriptors, geometric moments, and moment invariants are studied to compare candidate shapes and to pose the optimization problem. Their relative merits and demerits are discussed in this paper. The `frame finite element ground structure' approach is used for topology optimization and the resulting solutions are converted to continuum solutions. The introduction of a notch-like feature is the key to the success of the design. It not only gives a good match for the target morphed shape for the leading and trailing edges but also minimizes the extension of the flexible skin that is to be put on the airfoil frame. Even though linear small-displacement elastic analysis is used in optimization, the obtained designs are analysed for large displacement behavior. The methodology developed here is not restricted to aircraft wings; it can be used to solve any shape-morphing requirement in flexible structures and compliant mechanisms.

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The problem of updating the reliability of instrumented structures based on measured response under random dynamic loading is considered. A solution strategy within the framework of Monte Carlo simulation based dynamic state estimation method and Girsanov’s transformation for variance reduction is developed. For linear Gaussian state space models, the solution is developed based on continuous version of the Kalman filter, while, for non-linear and (or) non-Gaussian state space models, bootstrap particle filters are adopted. The controls to implement the Girsanov transformation are developed by solving a constrained non-linear optimization problem. Numerical illustrations include studies on a multi degree of freedom linear system and non-linear systems with geometric and (or) hereditary non-linearities and non-stationary random excitations.

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We consider a scenario where the communication nodes in a sensor network have limited energy, and the objective is to maximize the aggregate bits transported from sources to respective destinations before network partition due to node deaths. This performance metric is novel, and captures the useful information that a network can provide over its lifetime. The optimization problem that results from our approach is nonlinear; however, we show that it can be converted to a Multicommodity Flow (MCF) problem that yields the optimal value of the metric. Subsequently, we compare the performance of a practical routing strategy, based on Node Disjoint Paths (NDPs), with the ideal corresponding to the MCF formulation. Our results indicate that the performance of NDP-based routing is within 7.5% of the optimal.

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Isospectral beams have identical free vibration frequency spectrum for a specific boundary condition. The problem of finding non-uniform beams which are isospectral to a given uniform beam, with fixed-free boundary condition, leads to a multimodal optimization problem. The first Q natural frequencies of the given uniform Euler-Bernoulli beam are determined using analytical solution. The first Q natural frequencies of a non-uniform beam are obtained with the help of finite element modeling. In order to obtain the non-uniform beams isospectral to a given uniform beam, an error function is designed, which calculates the difference between the spectra of the given uniform beam and the non-uniform beam. In our study, this error function is minimized using electromagnetism inspired optimization technique, a population based iterative algorithm inspired by the attraction-repulsion physics of electromagnetism. Numerical results show the existence of the isospectral non-uniform beams for a given uniform beam, which occur as local minima. Non-uniform beams isospectral to a damaged beam, are also explored using the proposed methodology to illustrate the fact that accurate structural damage identification is difficult by just frequency measurements. (C) 2012 Elsevier B.V. All rights reserved.

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Simulated annealing is a popular method for approaching the solution of a global optimization problem. Existing results on its performance apply to discrete combinatorial optimization where the optimization variables can assume only a finite set of possible values. We introduce a new general formulation of simulated annealing which allows one to guarantee finite-time performance in the optimization of functions of continuous variables. The results hold universally for any optimization problem on a bounded domain and establish a connection between simulated annealing and up-to-date theory of convergence of Markov chain Monte Carlo methods on continuous domains. This work is inspired by the concept of finite-time learning with known accuracy and confidence developed in statistical learning theory.

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The work presented in this thesis revolves around erasure correction coding, as applied to distributed data storage and real-time streaming communications.

First, we examine the problem of allocating a given storage budget over a set of nodes for maximum reliability. The objective is to find an allocation of the budget that maximizes the probability of successful recovery by a data collector accessing a random subset of the nodes. This optimization problem is challenging in general because of its combinatorial nature, despite its simple formulation. We study several variations of the problem, assuming different allocation models and access models, and determine the optimal allocation and the optimal symmetric allocation (in which all nonempty nodes store the same amount of data) for a variety of cases. Although the optimal allocation can have nonintuitive structure and can be difficult to find in general, our results suggest that, as a simple heuristic, reliable storage can be achieved by spreading the budget maximally over all nodes when the budget is large, and spreading it minimally over a few nodes when it is small. Coding would therefore be beneficial in the former case, while uncoded replication would suffice in the latter case.

Second, we study how distributed storage allocations affect the recovery delay in a mobile setting. Specifically, two recovery delay optimization problems are considered for a network of mobile storage nodes: the maximization of the probability of successful recovery by a given deadline, and the minimization of the expected recovery delay. We show that the first problem is closely related to the earlier allocation problem, and solve the second problem completely for the case of symmetric allocations. It turns out that the optimal allocations for the two problems can be quite different. In a simulation study, we evaluated the performance of a simple data dissemination and storage protocol for mobile delay-tolerant networks, and observed that the choice of allocation can have a significant impact on the recovery delay under a variety of scenarios.

Third, we consider a real-time streaming system where messages created at regular time intervals at a source are encoded for transmission to a receiver over a packet erasure link; the receiver must subsequently decode each message within a given delay from its creation time. For erasure models containing a limited number of erasures per coding window, per sliding window, and containing erasure bursts whose maximum length is sufficiently short or long, we show that a time-invariant intrasession code asymptotically achieves the maximum message size among all codes that allow decoding under all admissible erasure patterns. For the bursty erasure model, we also show that diagonally interleaved codes derived from specific systematic block codes are asymptotically optimal over all codes in certain cases. We also study an i.i.d. erasure model in which each transmitted packet is erased independently with the same probability; the objective is to maximize the decoding probability for a given message size. We derive an upper bound on the decoding probability for any time-invariant code, and show that the gap between this bound and the performance of a family of time-invariant intrasession codes is small when the message size and packet erasure probability are small. In a simulation study, these codes performed well against a family of random time-invariant convolutional codes under a number of scenarios.

Finally, we consider the joint problems of routing and caching for named data networking. We propose a backpressure-based policy that employs virtual interest packets to make routing and caching decisions. In a packet-level simulation, the proposed policy outperformed a basic protocol that combines shortest-path routing with least-recently-used (LRU) cache replacement.

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A general framework for multi-criteria optimal design is presented which is well-suited for automated design of structural systems. A systematic computer-aided optimal design decision process is developed which allows the designer to rapidly evaluate and improve a proposed design by taking into account the major factors of interest related to different aspects such as design, construction, and operation.

The proposed optimal design process requires the selection of the most promising choice of design parameters taken from a large design space, based on an evaluation using specified criteria. The design parameters specify a particular design, and so they relate to member sizes, structural configuration, etc. The evaluation of the design uses performance parameters which may include structural response parameters, risks due to uncertain loads and modeling errors, construction and operating costs, etc. Preference functions are used to implement the design criteria in a "soft" form. These preference functions give a measure of the degree of satisfaction of each design criterion. The overall evaluation measure for a design is built up from the individual measures for each criterion through a preference combination rule. The goal of the optimal design process is to obtain a design that has the highest overall evaluation measure - an optimization problem.

Genetic algorithms are stochastic optimization methods that are based on evolutionary theory. They provide the exploration power necessary to explore high-dimensional search spaces to seek these optimal solutions. Two special genetic algorithms, hGA and vGA, are presented here for continuous and discrete optimization problems, respectively.

The methodology is demonstrated with several examples involving the design of truss and frame systems. These examples are solved by using the proposed hGA and vGA.