SU‐E‐T‐640: Using An Open Source Interior Point Optimization Solver for Intensity Modulated Radiotherapy Treatment Planning

We consider bilevel problem in the following formulation. The follower problem is a convex quadratic problem which linearly depends on the leader variable. The leader problem is a quadratic problem. We are looking for an optimistic solution. Optimal value function of the follower problem is used to reformulate bilevel problem as a standard (one-level) optimization problem. By this way we obtain a nonconvex multiextremal problem with implicit nonconvex constraint generated by the optimal value function. We show how to construct an explicit piecewise quadratic function which is support to the optimal value function at a given point. Usage of the support functions allows us to approximate the implicit one-level problem by a number of explicit nonconvex quadratic problems. In our talk we describe an iterative procedure based on such approximation.

It is our great pleasure to welcome you to BADS 2011, the third Workshop on Bio-Inspired and Self-* Algorithms for Distributed Systems, co-located with ICAC 2011, the 8th IEEE/ACM International Conferenceon Autonomic Computing, Karlsruhe, Germany, June 14-18, 2011. BADS 2011 aims to provide a forum for exploring bio-inspired and self-* algorithms to build autonomic distributed systems; i.e., self-managing distributed systems that can organize, configure, optimize, scale, protect and/or heal themselves with minimal human intervention. Computing inspired by biology has a long history since 1950s. Its common objectives are to formulate theoretical models that are faithfully designed after biological principles, phenomena and processes and to exploit the models for developing computational tools (e.g., algorithms) and systems. Well-known bio-inspired algorithms include artificial neural networks, evolutionary algorithms, swarm intelligence, artificial immune systems, reaction-diffusion algorithms, epidemic algorithms, cellular automata algorithms, gene expression/regulatory algorithms and Lindenmayer system. They have been successfully used as alternative and/or superior solutions to the problems that traditional algorithms cannot solve satisfactorily. In recognition of their achievements and potential, bio-inspired algorithms were named one of Scientific American magazine's 10 "World Changing Ideas 2010." The BADS workshop series focuses on distributed computing and examines the opportunities, current state-of-the-art, challenges and future outlook to create autonomic distributed systems with bio-inspired algorithms. We cover a broad range of aspects in distributed computing, including communication protocols, resource clustering, allocation and management, topology management, parallelism and concurrency, overlay construction and maintenance, decentralized information search and delivery, load distribution, synchronization, service selection, composition and deployment, labor division and task allocation, anomaly and misbehavior detection, malware propagation and detection. Following the success of its former editions in 2009 and 2010, BADS 2011 continues to focus on bio-inspired, autonomic distributed systems. In addition, it expands its themes to cover a general class of algorithms that exhibit self-* properties (e.g., self-configuring, self-organizing, self-managing, self-healing, self-scaling and selfadaptive properties) in the context of distributed computing. BADS 2011 has seven research papers selected through a rigorous review process. Each paper was reviewed and judged by at least three PC members on merits including correctness, originality, technical strength, quality of presentation and relevance to the workshop themes. We would like to sincerely thank the Program Committee members who have greatly contributed to the success of BADS 2011. BADS 2011 is organized in two sessions and one keynote presentation. The first session includes papers that present bio-inspired approaches for distributed computing. The second session focuses on solving optimization problems with distributed bio-inspired and self-* algorithms. The keynote presentation, entitled "Methods for Self-organizing Distributed Software", is given by Elisabetta Di Nitto, and focuses on the applications of self-organization in distributed systems. In nature, self-organization occurs such that a global behavior emerges from simple and local decisions made autonomously by each element of the system. This keynote overviews the benefits and challenges to apply the notion of self-organization for the development of distributed systems. It also presents several example applications such as energy efficiency and configuration optimization in cloud computing. The first session, "Bio-inspired Approaches for Distributed Computing", comprises four papers. The first paper, "Memetic Algorithm for Web Service Selection" by Ludwig, studies the service selection process, whose aim is to locate services of interest in service-oriented environments. The author proposes two approaches based on a genetic algorithm and a memetic algorithm to match consumers with services based on Quality of Service attributes. Both approaches are compared with an optimal assignment algorithm, called the Munkres algorithm, as well as with random approaches. The next paper, "OZMOS: Bio-Inspired Load Balancing in a Chord-based P2P Grid" by Brocco, proposes a load balancing mechanism, called Ozmos, that follows the principle of osmosis to relocate tasks between nodes in a P2P-based Grid. Bio-inspired agents are deployed to share information about the status of the Grid as well as to reschedule tasks between nodes. The efficacy of the proposed algorithm is illustrated in achieving system-wide load balance in Grids of different scales, with both homogenous and heterogeneous resources. The third paper, "Model-Driven Performance Engineering for Wireless Sensor Networks with Feature Modeling and Event Calculus" by Boonma and Suzuki, proposes an application development framework for wireless sensor networks. The proposed framework allows developers to graphically configure their applications and generate application code. With event calculus, the framework also estimates each application's performance such as per-node power consumption and network lifetime without running it on simulators and real networks. The proposed framework currently targets a shortest-path routing; however, it is a promising next step to estimate the performance of bio-inspired routing protocols such as pheromone-based chemotaxis routing. The last paper of the first session, "Description and Composition of Bio-Inspired Design Patterns: the Gradient Case" by Fernandez-Marquez, Arcos, Di Marzo Serugendo, Viroli and Montagna, investigates a group of bioinspired mechanisms in terms of design patterns. The authors show the relations between the different patterns and identify the boundaries of each mechanism. The mechanisms are organized into different levels. In basic level, Spreading, Aggregation and Evaporation are studied. Gradient is investigated in mid-level, and top-level mechanisms are Chemotaxis, Morphogenesis, and Quorum sensing. The second session, "Solving Optimization Problems with Distributed Evolutionary Algorithms", opens with a paper entitled "Protein Structure Prediction Using Particle Swarm Optimization and a Distributed Parallel Approach" by Kondov and Berlich. It demonstrates the efficiency of the standard Particle Swarm Optimization (PSO) algorithm to find the folded state of two proteins of different sizes starting from completely extended conformations. They illustrate that the predicted structure of the larger protein is in good agreement with the structure from the Protein Data Bank within the experimental resolution. The parallelization of PSO is shown to speed up the simulation linearly with the number of workers and it reduces the prediction time dramatically without loss of accuracy. The next paper, "Discrete Optimization Problem Solving with three Variants of Hybrid Binary Particle Swarm Optimization" by Singh V., Singh D., Tiwari and Shukla, presents three variants of the binary PSO algorithm in order to solve discrete optimization problems. This is achieved by introducing an additional step of crossover that varies in all the three variants. These hybrid algorithms show competitive results compared to other state-of-theart metaheuristics. The third paper, "Self-organized Invasive Parallel Optimization" by Mostaghim, Pfeiffer and Schmeck, proposes a new parallelization framework for optimization algorithms. In this approach, the self-organized resources are represented as a unified resource to the user who only specifies the optimization problem and his/her preferences to the system. The invasive approach starts with one resource and automatically divides the optimization task stepwise into smaller tasks, which are assigned to more resources. The job assignment pattern is decided on demand, i.e., the number of required resources is estimated during the optimization process. The authors examine their generic framework on multi-objective problems.

In this paper we present a new algorithmic realization of a projection-based scheme for general convex constrained optimization problem. The general idea is to transform the original optimization problem to a sequence of feasibility problems by iteratively constraining the objective function from above until the feasibility problem is inconsistent. For each of the feasibility problems one may apply any of the existing projection methods for solving it. In particular, the scheme allows the use of subgradient projections and does not require exact projections onto the constraints sets as in existing similar methods. We also apply the newly introduced concept of superiorization to optimization formulation and compare its performance to our scheme. We provide some numerical results for convex quadratic test problems as well as for real-life optimization problems coming from medical treatment planning.

In the previous chapter we showed that every polynomial map whose Jacobian matrix is invertible is stably equivalent to a polynomial map of the form X + H, where J H is nilpotent. For polynomial maps over a field of characteristic zero, such maps with the additional assumption that H is cubic homogeneous were first studied by Wright in dimension 3, [294] and Hubbers in dimension 4, [156]. In both cases it turned out that the rows of the Jacobian matrix are linearly dependent over the coefficient field. This gave rise to the formulation of a (still open) dependence problem, 7.1.5. This problem led Hubbers and the author to the discovery of a large class of polynomial maps (over an arbitrary commutative ring A) having nilpotent Jacobian matrix. This class will be defined and studied in §2 and is denoted by H(n, A). So H(n, A) is a subset of N(n, A), the set of all polynomial maps H ∈ A [X]n with J H nilpotent. If A is a UFD of characteristic zero we will show that H(2, A) = N(2, A). However if n ≥ 3 the class N(n, A) is essentially larger than H(n, A). Furthermore we will show that all maps of the form X + H with H ∈ H(n, A) are polynomial automorphisms. In fact we show that every such map is a finite product of exponentials of a special kind of locally nilpotent derivations, the so-called nice derivations, 7.3.18, and we deduce that all these maps are stably tame. At the end of §3 we give a shorter proof of this stable tameness result due to Hubbers and Wright in [158].KeywordsInduction HypothesisJacobian MatrixCharacteristic ZeroMain DiagonalRing HomomorphismThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The problem of finding the best rank-one approximation to higher-order tensors has extensive engineering and statistical applications. It is well-known that this problem is equivalent to a homogeneous polynomial optimization problem. In this paper, we study theoretical results and numerical methods of this problem, particularly focusing on the 4-th order symmetric tensor case. First, we reformulate the polynomial optimization problem to a matrix programming, and show the equivalence between these two problems. Then, we prove that there is no duality gap between the reformulation and its Lagrangian dual problem. Concerning the approaches to deal with the problem, we propose two relaxed models. The first one is a convex quadratic matrix optimization problem regularized by the nuclear norm, while the second one is a quadratic matrix programming regularized by a truncated nuclear norm, which is a D.C. function and therefore is nonconvex. To overcome the difficulty of solving this nonconvex problem, we approximate the nonconvex penalty by a convex term. We propose to use the proximal augmented Lagrangian method to solve these two relaxed models. In order to obtain a global solution, we propose an alternating least eigenvalue method after solving the relaxed models and prove its convergence. Numerical results presented in the last demonstrate, especially for nonpositive tensors, the effectiveness and efficiency of our proposed methods.

In the present work, two main goals are followed. First, free vibrations of multiscale nanocomposite plates consist of agglomerated carbon nanotubes (CNTs), E‐glass fibers, and polymer are presented based on first‐order shear deformation theory. Mori‐Tanaka (MT) approach and fiber micromechanics are used to estimate the mechanical properties of CNT/fiber/polymer composite (CNTFPC) plate. For natural frequency analysis of the CNTFPC plate, 2‐D generalized differential quadrature (GDQ) method as an efficient and accurate numerical tool is implemented to solve the governing equations. The accuracy of the MT method and GDQ technique are examined by comparing the present results with the experimental or numerical data available in the literature. A parametric study is carried out to investigate the influences of CNTs volume fraction, CNTs agglomeration, fiber volume fraction, different geometrical parameters such as the thickness‐to‐length ratio, different laminate lay‐up (cross‐ply and angle‐ply) and various boundary conditions on the natural frequencies of CNTFPC plates. As for the second goal of the paper, stacking sequence optimization of CNTFPC plates is presented to maximize the fundamental natural frequency of the structure. The search space of optimization problem is large and consequently the optimization processes becomes too much time consuming. Therefore, a biologically‐inspired meta‐heuristic algorithm called firefly algorithm that solves optimization problems without using gradient‐based information on the objective functions and the constraints is applied to obtain the best stacking sequence of CNTFPC plate. POLYM. COMPOS., 39:1433–1446, 2018. © 2016 Society of Plastics Engineers

ABSTRACTThis article presents an enhanced particle swarm optimization (EPSO) algorithm for size and shape optimization of truss structures. The proposed EPSO introduces a particle categorization mechanism into the particle swarm optimization (PSO) to eliminate unnecessary structural analyses during the optimization process and improve the computational efficiency of the PSO-based structural optimization. The numerical investigation, including three benchmark truss optimization problems, examines the efficiency of the EPSO. The results demonstrate that the particle categorization mechanism greatly reduces the computational requirements of the PSO-based approaches while maintaining the original search capability of the algorithms in solving optimization problems with computationally cheap objective function and expensive constraints.

Multi-disciplinary and multi-objective optimization problem re-formulation in computational design exploration: A case of conceptual sports building design

III.4 - Hopfield Model and Optimization Problems

In many scientific computing applications involving nonlinear systems or methods of optimization, a sequence of Jacobian or Hessian matrices is required. Automatic differentiation (AD) technology can be used to accurately determine these matrices, and it is well known that if these matrices exhibit a sparsity pattern (for all iterates), then not only can AD take advantage of this sparsity for significant efficiency gains, AD can also determine the sparsity pattern itself, with some additional work in the first iteration. Practical nonlinear systems and optimization problems often exhibit patterns beyond just “zero-nonzero.” For example, some elements may be duplicates of other elements at all iterates; some elements may be constant (not necessarily zero) for all iterates. Here we show how the popular graph-coloring approach to AD can be adapted to account for these cases as well, with resulting gains in efficiency. In addition, we address the problem of determining, by AD technology, a prescribed set of the entries of the Jacobian (or Hessian, in the optimization context) matrix.

Application of a Derivative-Free Method with Projection Skill to Solve an Optimization Problem

In this article, we introduce a frequency-based waveform design to maximize binary target classification. The optimization problems can be solved via optimal solvers available in the literature. The presented formulation is applicable to the classification scenarios where the extended target frequency responses (TFRs) are complex, random, and normally distributed with unequal mean vectors. However, their covariance matrices are either identical or different. For the former, i.e., identical covariance matrices, the optimization problem consists of a cost function that has been obtained by deriving a closed-form expression of the probability of misclassification. For the latter, i.e., different covariance matrices, we present an optimization problem where the cost function has been obtained via the Fisher separation function. For this, we also present a closed-form expression for an approximate solution to the optimization problem. We show that the proposed solution achieves performance levels comparable to the exact solution of the optimization problem obtained via state-of-the-art optimization solvers while incurring low computational complexity. We expand on the two main scenarios by introducing clutter (i.e., signal-dependent interference) in the signal model and studying possible closed-form designs in extreme waveform energy levels. Simulations are conducted using synthetically generated data in addition to the civilian vehicle data from the Moving and Stationary Target Acquisition and Recognition (MSTAR) dataset, in order to validate the proposed method.

Application of the least-squares inversion method: Fourier series versus waveform inversion

In this paper, optimal cyclic reference trajectories are designed for three walking gaits of a quadruped robot, the curvet, the amble, the trot, taking into account the actuators characteristics and for a given motion robot velocity. The objectives of this study are multiple: • Automatic design of admissible reference trajectories, • Definition of the maximal speed of the robot for given actuators, • Study of the evolution of the torque cost for various motion velocities, • Comparison of three different gaits with respect to a sthenic criterion. For the gaits studied, during some phases the system is underactuated. The design of the cyclic gaits takes this fact into account. The optimization problem is solved with an algebraic optimization technique. The actuated joint evolution is chosen as a polynomial function of time. The coefficients of the polynomial functions are optimization parameters. The evolution of the passive joint is defined using the dynamic model to have admissible trajectory. During the optimization process, the constraints on the ground reactions, the validity of impact, the torques, the joints velocities of the robot are taken into account. Simulation results are presented for the three gaits. All motions are realistics. Curvet is the less efficient gait with respect to the criterion studied. For slow motion, trot is the more efficient gait. But amble permits the fastest motion with the same actuators.

In this paper, we propose a new algorithm for solving convex quadratic programming problems with bounded variables. Instead of using the standard direction of the adaptive method, which is constructed by minimising only the linear part of the objective function increment, we will suggest a new descent direction, called 'hybrid direction'. This latter is constructed by minimising a quadratic part of the increment. Furthermore, we define a quantity called 'optimality estimate' from which we derive sufficient and necessary conditions of optimality. On the basis of this new concept, we construct an algorithm for solving convex quadratic programs. In order to compare our method with the active-set method implemented in MATLAB, numerical experiments on randomly generated test problems are presented.