U-curve: A branch-and-bound optimization algorithm for U-shaped cost functions on Boolean lattices applied to the feature selection problem

This paper presents the formulation of a combinatorial optimization problem with the following characteristics: (i) the search space is the power set of a finite set structured as a Boolean lattice; (ii) the cost function forms a U-shaped curve when applied to any lattice chain. This formulation applies for feature selection in the context of pattern recognition. The known approaches for this problem are branch-and-bound algorithms and heuristics that explore partially the search space. Branch-and-bound algorithms are equivalent to the full search, while heuristics are not. This paper presents a branch-and-bound algorithm that differs from the others known by exploring the lattice structure and the U-shaped chain curves of the search space. The main contribution of this paper is the architecture of this algorithm that is based on the representation and exploration of the search space by new lattice properties proven here. Several experiments, with well known public data, indicate the superiority of the proposed method to the sequential floating forward selection (SFFS), which is a popular heuristic that gives good results in very short computational time. In all experiments, the proposed method got better or equal results in similar or even smaller computational time. (C) 2009 Elsevier Ltd. All rights reserved.

Social interaction as a heuristic for combinatorial optimization problems

We investigate the performance of a variant of Axelrod's model for dissemination of culture-the Adaptive Culture Heuristic (ACH)-on solving an NP-Complete optimization problem, namely, the classification of binary input patterns of size F by a Boolean Binary Perceptron. In this heuristic, N agents, characterized by binary strings of length F which represent possible solutions to the optimization problem, are fixed at the sites of a square lattice and interact with their nearest neighbors only. The interactions are such that the agents' strings (or cultures) become more similar to the low-cost strings of their neighbors resulting in the dissemination of these strings across the lattice. Eventually the dynamics freezes into a homogeneous absorbing configuration in which all agents exhibit identical solutions to the optimization problem. We find through extensive simulations that the probability of finding the optimal solution is a function of the reduced variable F/N(1/4) so that the number of agents must increase with the fourth power of the problem size, N proportional to F(4), to guarantee a fixed probability of success. In this case, we find that the relaxation time to reach an absorbing configuration scales with F(6) which can be interpreted as the overall computational cost of the ACH to find an optimal set of weights for a Boolean binary perceptron, given a fixed probability of success.

Design of compliant mechanisms considering thermal effect compensation and topology optimization

Compliant mechanisms can achieve a specified motion as a mechanism without relying on the use of joints and pins. They have broad application in precision mechanical devices and Micro-Electro Mechanical Systems (MEMS) but may lose accuracy and produce undesirable displacements when subjected to temperature changes. These undesirable effects can be reduced by using sensors in combination with control techniques and/or by applying special design techniques to reduce such undesirable effects at the design stage, a process generally termed ""design for precision"". This paper describes a design for precision method based on a topology optimization method (TOM) for compliant mechanisms that includes thermal compensation features. The optimization problem emphasizes actuator accuracy and it is formulated to yield optimal compliant mechanism configurations that maximize the desired output displacement when a force is applied, while minimizing undesirable thermal effects. To demonstrate the effectiveness of the method, two-dimensional compliant mechanisms are designed considering thermal compensation, and their performance is compared with compliant mechanisms designs that do not consider thermal compensation. (C) 2010 Elsevier B.V. All rights reserved.

Dynamic Design of Piezoelectric Laminated Sensors and Actuators using Topology Optimization

Sensors and actuators based on piezoelectric plates have shown increasing demand in the field of smart structures, including the development of actuators for cooling and fluid-pumping applications and transducers for novel energy-harvesting devices. This project involves the development of a topology optimization formulation for dynamic design of piezoelectric laminated plates aiming at piezoelectric sensors, actuators and energy-harvesting applications. It distributes piezoelectric material over a metallic plate in order to achieve a desired dynamic behavior with specified resonance frequencies, modes, and enhanced electromechanical coupling factor (EMCC). The finite element employs a piezoelectric plate based on the MITC formulation, which is reliable, efficient and avoids the shear locking problem. The topology optimization formulation is based on the PEMAP-P model combined with the RAMP model, where the design variables are the pseudo-densities that describe the amount of piezoelectric material at each finite element and its polarization sign. The design problem formulated aims at designing simultaneously an eigenshape, i.e., maximizing and minimizing vibration amplitudes at certain points of the structure in a given eigenmode, while tuning the eigenvalue to a desired value and also maximizing its EMCC, so that the energy conversion is maximized for that mode. The optimization problem is solved by using sequential linear programming. Through this formulation, a design with enhancing energy conversion in the low-frequency spectrum is obtained, by minimizing a set of first eigenvalues, enhancing their corresponding eigenshapes while maximizing their EMCCs, which can be considered an approach to the design of energy-harvesting devices. The implementation of the topology optimization algorithm and some results are presented to illustrate the method.

Piezoresistive sensor design using topology optimization

Piezoresistive materials, materials whose resistivity properties change when subjected to mechanical stresses, are widely utilized in many industries as sensors, including pressure sensors, accelerometers, inclinometers, and load cells. Basic piezoresistive sensors consist of piezoresistive devices bonded to a flexible structure, such as a cantilever or a membrane, where the flexible structure transmits pressure, force, or inertial force due to acceleration, thereby causing a stress that changes the resistivity of the piezoresistive devices. By applying a voltage to a piezoresistive device, its resistivity can be measured and correlated with the amplitude of an applied pressure or force. The performance of a piezoresistive sensor is closely related to the design of its flexible structure. In this research, we propose a generic topology optimization formulation for the design of piezoresistive sensors where the primary aim is high response. First, the concept of topology optimization is briefly discussed. Next, design requirements are clarified, and corresponding objective functions and the optimization problem are formulated. An optimization algorithm is constructed based on these formulations. Finally, several design examples of piezoresistive sensors are presented to confirm the usefulness of the proposed method.

Tailoring vibration mode shapes using topology optimization and functionally graded material concepts

Tailoring specified vibration modes is a requirement for designing piezoelectric devices aimed at dynamic-type applications. A technique for designing the shape of specified vibration modes is the topology optimization method (TOM) which finds an optimum material distribution inside a design domain to obtain a structure that vibrates according to specified eigenfrequencies and eigenmodes. Nevertheless, when the TOM is applied to dynamic problems, the well-known grayscale or intermediate material problem arises which can invalidate the post-processing of the optimal result. Thus, a more natural way for solving dynamic problems using TOM is to allow intermediate material values. This idea leads to the functionally graded material (FGM) concept. In fact, FGMs are materials whose properties and microstructure continuously change along a specific direction. Therefore, in this paper, an approach is presented for tailoring user-defined vibration modes, by applying the TOM and FGM concepts to design functionally graded piezoelectric transducers (FGPT) and non-piezoelectric structures (functionally graded structures-FGS) in order to achieve maximum and/or minimum vibration amplitudes at certain points of the structure, by simultaneously finding the topology and material gradation function. The optimization problem is solved by using sequential linear programming. Two-dimensional results are presented to illustrate the method.

Multi-Objective Optimization Design of Tanker Ships via a Genetic Algorithm

The cost of a new ship design heavily depends on the principal dimensions of the ship; however, dimensions minimization often conflicts with the minimum oil outflow (in the event of an accidental spill). This study demonstrates one rational methodology for selecting the optimal dimensions and coefficients of form of tankers via the use of a genetic algorithm. Therein, a multi-objective optimization problem was formulated by using two objective attributes in the evaluation of each design, specifically, total cost and mean oil outflow. In addition, a procedure that can be used to balance the designs in terms of weight and useful space is proposed. A genetic algorithm was implemented to search for optimal design parameters and to identify the nondominated Pareto frontier. At the end of this study, three real ships are used as case studies. [DOI:10.1115/1.4002740]

Real time optimization (RTO) with model predictive control (MPC)

This paper studies a simplified methodology to integrate the real time optimization (RTO) of a continuous system into the model predictive controller in the one layer strategy. The gradient of the economic objective function is included in the cost function of the controller. Optimal conditions of the process at steady state are searched through the use of a rigorous non-linear process model, while the trajectory to be followed is predicted with the use of a linear dynamic model, obtained through a plant step test. The main advantage of the proposed strategy is that the resulting control/optimization problem can still be solved with a quadratic programming routine at each sampling step. Simulation results show that the approach proposed may be comparable to the strategy that solves the full economic optimization problem inside the MPC controller where the resulting control problem becomes a non-linear programming problem with a much higher computer load. (C) 2010 Elsevier Ltd. All rights reserved.

On the cutting stock problem under stochastic demand

This paper addresses the one-dimensional cutting stock problem when demand is a random variable. The problem is formulated as a two-stage stochastic nonlinear program with recourse. The first stage decision variables are the number of objects to be cut according to a cutting pattern. The second stage decision variables are the number of holding or backordering items due to the decisions made in the first stage. The problem`s objective is to minimize the total expected cost incurred in both stages, due to waste and holding or backordering penalties. A Simplex-based method with column generation is proposed for solving a linear relaxation of the resulting optimization problem. The proposed method is evaluated by using two well-known measures of uncertainty effects in stochastic programming: the value of stochastic solution-VSS-and the expected value of perfect information-EVPI. The optimal two-stage solution is shown to be more effective than the alternative wait-and-see and expected value approaches, even under small variations in the parameters of the problem.

GRASP heuristic with path-relinking for the multi-plant capacitated lot sizing problem

This paper addresses the independent multi-plant, multi-period, and multi-item capacitated lot sizing problem where transfers between the plants are allowed. This is an NP-hard combinatorial optimization problem and few solution methods have been proposed to solve it. We develop a GRASP (Greedy Randomized Adaptive Search Procedure) heuristic as well as a path-relinking intensification procedure to find cost-effective solutions for this problem. In addition, the proposed heuristics is used to solve some instances of the capacitated lot sizing problem with parallel machines. The results of the computational tests show that the proposed heuristics outperform other heuristics previously described in the literature. The results are confirmed by statistical tests. (C) 2009 Elsevier B.V. All rights reserved.

A contribution for thermoeconomic modelling: A methodology proposal

This work presents a thermoeconomic optimization methodology for the analysis and design of energy systems. This methodology involves economic aspects related to the exergy conception, in order to develop a tool to assist the equipment selection, operation mode choice as well as to optimize the thermal plants design. It also presents the concepts related to exergy in a general scope and in thermoeconomics which combines the thermal sciences principles (thermodynamics, heat transfer, and fluid mechanics) and the economic engineering in order to rationalize energy systems investment decisions, development and operation. Even in this paper, it develops a thermoeconomic methodology through the use of a simple mathematical model, involving thermodynamics parameters and costs evaluation, also defining the objective function as the exergetic production cost. The optimization problem evaluation is developed for two energy systems. First is applied to a steam compression refrigeration system and then to a cogeneration system using backpressure steam turbine. (C) 2010 Elsevier Ltd. All rights reserved.

An electromechanical finite element model for piezoelectric energy harvester plates

Vibration-based energy harvesting has been investigated by several researchers over the last decade. The goal in this research field is to power small electronic components by converting the waste vibration energy available in their environment into electrical energy. Recent literature shows that piezoelectric transduction has received the most attention for vibration-to-electricity conversion. In practice, cantilevered beams and plates with piezoceramic layers are employed as piezoelectric energy harvesters. The existing piezoelectric energy harvester models are beam-type lumped parameter, approximate distributed parameter and analytical distributed parameter solutions. However, aspect ratios of piezoelectric energy harvesters in several cases are plate-like and predicting the power output to general (symmetric and asymmetric) excitations requires a plate-type formulation which has not been covered in the energy harvesting literature. In this paper. an electromechanically coupled finite element (FE) plate model is presented for predicting the electrical power output of piezoelectric energy harvester plates. Generalized Hamilton`s principle for electroelastic bodies is reviewed and the FE model is derived based on the Kirchhoff plate assumptions as typical piezoelectric energy harvesters are thin structures. Presence of conductive electrodes is taken into account in the FE model. The predictions of the FE model are verified against the analytical solution for a unimorph cantilever and then against the experimental and analytical results of a bimorph cantilever with a tip mass reported in the literature. Finally, an optimization problem is solved where the aluminum wing spar of an unmanned air vehicle (UAV) is modified to obtain a generator spar by embedding piezoceramics for the maximum electrical power without exceeding a prescribed mass addition limit. (C) 2009 Elsevier Ltd. All rights reserved.

Enlarging the domain of attraction of stable MPC controllers, maintaining the output performance

This work presents an alternative way to formulate the stable Model Predictive Control (MPC) optimization problem that allows the enlargement of the domain of attraction, while preserving the controller performance. Based on the dual MPC that uses the null local controller, it proposed the inclusion of an appropriate set of slacked terminal constraints into the control problem. As a result, the domain of attraction is unlimited for the stable modes of the system, and the largest possible for the non-stable modes. Although this controller does not achieve local optimality, simulations show that the input and output performances may be comparable to the ones obtained with the dual MPC that uses the LQR as a local controller. (C) 2009 Elsevier Ltd. All rights reserved.

Forward-looking versus recursive-dynamic modeling in climate policy analysis: A comparison

This paper develops a multi-regional general equilibrium model for climate policy analysis based on the latest version of the MIT Emissions Prediction and Policy Analysis (EPPA) model. We develop two versions so that we can solve the model either as a fully inter-temporal optimization problem (forward-looking, perfect foresight) or recursively. The standard EPPA model on which these models are based is solved recursively, and it is necessary to simplify some aspects of it to make inter-temporal solution possible. The forward-looking capability allows one to better address economic and policy issues such as borrowing and banking of GHG allowances, efficiency implications of environmental tax recycling, endogenous depletion of fossil resources, international capital flows, and optimal emissions abatement paths among others. To evaluate the solution approaches, we benchmark each version to the same macroeconomic path, and then compare the behavior of the two versions under a climate policy that restricts greenhouse gas emissions. We find that the energy sector and CO(2) price behavior are similar in both versions (in the recursive version of the model we force the inter-temporal theoretical efficiency result that abatement through time should be allocated such that the CO(2) price rises at the interest rate.) The main difference that arises is that the macroeconomic costs are substantially lower in the forward-looking version of the model, since it allows consumption shifting as an additional avenue of adjustment to the policy. On the other hand, the simplifications required for solving the model as an optimization problem, such as dropping the full vintaging of the capital stock and fewer explicit technological options, likely have effects on the results. Moreover, inter-temporal optimization with perfect foresight poorly represents the real economy where agents face high levels of uncertainty that likely lead to higher costs than if they knew the future with certainty. We conclude that while the forward-looking model has value for some problems, the recursive model produces similar behavior in the energy sector and provides greater flexibility in the details of the system that can be represented. (C) 2009 Elsevier B.V. All rights reserved.

Orthogonal packing of identical rectangles within isotropic convex regions

A mixed integer continuous nonlinear model and a solution method for the problem of orthogonally packing identical rectangles within an arbitrary convex region are introduced in the present work. The convex region is assumed to be made of an isotropic material in such a way that arbitrary rotations of the items, preserving the orthogonality constraint, are allowed. The solution method is based on a combination of branch and bound and active-set strategies for bound-constrained minimization of smooth functions. Numerical results show the reliability of the presented approach. (C) 2010 Elsevier Ltd. All rights reserved.