Direct Search Method Research Articles

Perimeter-Based Polar Scan Matching (PB-PSM) for 2D Laser Odometry

The paper presents Perimeter-Based Polar Scan Matching (PB-PSM), a new 2D scan matching algorithm. The algorithm favors matches with a larger perimeter overlap between the two input scans, while using a robust cost minimization process (using an adaptive direct search method, made possible due to a linear complexity data association technique). PB-PSM is benchmarked against the previously published PSM and PSM-C algorithms, and numerous realizations of the ICP algorithm. Results for convergence, accuracy, and computational speed are discussed. PB-PSM is employed on several laser scan datasets, both existing and in-house. Quantitative comparison of resulting maps is done using a new metric for evaluating occupancy grid maps accuracy, by calculating the average cell distance from the walls of the true map. The relative importance of each novel contribution is quantified using the new metric. Additional qualitative analysis is provided for previously published and relatively large datasets.

Regarding the rankings of optimization heuristics based on artificially-constructed benchmark functions

Novel Evolutionary Algorithms are usually tested on sets of artificially-constructed benchmark problems. Such problems are often created to make the search of one global extremum (usually minimum) tricky. In this paper it is shown that benchmarking heuristics on either minimization or maximization of the same set of artificially-created functions (with equal bounds and number of allowed function calls) may lead to very different ranking of tested algorithms. As Evolutionary Algorithms and other heuristic optimizers are developed in order to be applicable to real-world problems, such result may raise doubts on the practical meaning of benchmarking them on artificial functions, as there is little reason that searching for the minimum of such functions should be more important than searching for their maximum.Thirty optimization heuristics, including a number of variants of Differential Evolution, as well as other kinds of Evolutionary Algorithms, Particle Swarm Optimization, Direct Search methods and – following the idea borrowed from No Free Lunch – pure random search are tested in the paper. Some discussion regarding the choice of the mean or the median performance for comparison is addressed and a short debate on the overall performance of particular methods is given.

Thermoeconomic optimization of LiBr/H2O-R134a compression-absorption cascade refrigeration cycle

This study presents the thermoeconomic optimization of LiBr/H2O-R134a compression-absorption cascade refrigeration cycle. The detailed exergy-based thermoeconomic analyses, thermoeconomic evaluation with exergoeconomic variables, and thermoeconomic optimization by using non-linear simplex direct search method have been performed for the cascade refrigeration cycle. In the sample application, the thermoeconomic optimization reveals the optimum generator temperature, condenser temperature, absorber temperature, condenser temperature of vapour compression section, effectiveness of solution heat exchanger and compressor isentropic efficiency. This analysis points out that the evaporator equipage and solution heat exchanger should be designed carefully according to the exergoeconomic factor values. The exergetic efficiency and minimum cost of objective function are determined as 7.30% and 4.05 ($/h) for the optimum case of sample application. The minimum cost of objective function is reduced about 3.3%, the coefficient of performance (COPcyclegen) and exergetic efficiency of cascade cycle are improved about 7% and 3.1% respectively, according to the base case.

Validation of a simple kinetic modelling approach for agro-industrial waste anaerobic digesters

Anaerobic co-digestion of agroindustrial wastes constitutes a promising option for the stabilisation of residues producing biogas. A mixture of bovine ruminal content, tannery carving fat and activated sludge purge was considered for this work. Biodegradability tests for individual wastes and for the mixture of wastes were performed in batch and also in continuous conditions in a completely mixed reactor. The continuous reactor was operated at 30-day average residence times with a load volume of 3.0 g VS/L d, reaching a VS removal efficiency of 66%, and yielding 0.38 LCH4/kg VSadded and 0.58 LCH4/kg VSremoved. A first order kinetic model with time delay was used to describe the behaviour of the whole process. The determination of parameters was performed in both systems using direct search methods. Monte Carlo methods were used in order to determine the range of parameters. Ultimate methane yield of 90 ± 6% was obtained from batch tests and 88 ± 9% in the continuous reactor. The kinetic rate constant in the reactor (0.205 ± 0.013 d−1) was twice the value obtained in batch conditions (0.089 ± 0.010 d−1), showing that microbial adaptations occurred in the continuous mode.

Bumper optimum design using the dynamically equivalent beam under various impact conditions

Nowadays it is required for the bumper system to meet the various impact conditions simultaneously; barrier impact, IIHS (Insurance Institute for Highway Safety) bumper impact and pedestrian impact. Firstly, dynamically equivalent bumper beam models were developed for each impact condition and its accuracy was verified by nonlinear finite element analysis result. Dynamically equivalent pedestrian impact beam model was developed by using the equivalent forces of bumper beam and stiffeners. Pedestrian bending angle was obtained by using this equivalent pedestrian beam model. By combining these equivalent beam models, bumper optimum design program was developed. In this optimum design program, direct search method was used for the optimization algorithm. To verify the accuracy of this optimum design program, a nonlinear finite element result was used. By using this optimum design program, it can be secured the bumper impact performances in an early design stage and it will be also contributed to reduce the design time and test costs.

Design optimization of cruciform specimens for biaxial fatigue loading

In order to correctly assess the biaxial fatigue material properties one must experimentally test different load conditions and stress levels. With the rise of new in-plane biaxial fatigue testing machines, using smaller and more efficient electrical motors, instead of the conventional hydraulic machines, it is necessary to reduce the specimen size and to ensure that the specimen geometry is appropriated for the load capacity installed. At the present time there are no standard specimen’s geometries and the indications on literature how to design an efficient test specimen are insufficient. The main goal of this paper is to present the methodology on how to obtain an optimal cruciform specimen geometry, with thickness reduction in the gauge area, appropriated for fatigue crack initiation, as a function of the base material sheet thickness used to build the specimen. The geometry is optimized for maximum stress using several parameters, ensuring that in the gauge area the stress is uniform and maximum with two limit phase shift loading conditions. Therefore the fatigue damage will always initiate on the center of the specimen, avoiding failure outside this region. Using the Renard Series of preferred numbers for the base material sheet thickness as a reference, the reaming geometry parameters are optimized using a derivative-free methodology, called direct multi search (DMS) method. The final optimal geometry as a function of the base material sheet thickness is proposed, as a guide line for cruciform specimens design, and as a possible contribution for a future standard on in-plane biaxial fatigue tests.

A simulation-based fuzzy possibilistic programming model for coal blending management with consideration of human health risk under uncertainty

In this research, a simulation-based fuzzy possibilistic programming (SFPP) model was advanced through integrating California puff (CALPUFF), fuzzy sets theory and inexact optimization within a general framework. It has advantages in uncertainty reflection, pollutant dispersion modeling, and the management of coal blending and the related human health risks. The developed SFPP model was solved through a direct search approach which coupled fuzzy simulation and Genetic Algorithm (GA). This approach can not only handle a coupled simulation–optimization problem considering uncertainties that can be expressed as fuzzy sets, but also provided the additional information (i.e. possibility of constraint satisfaction) indicating that how likely a decision maker can believe the decision results. It also can reduce the chances of being trapped in local optima as GA converges to global optima. Moreover, the employed direct search method can avoid the approximation error originating from surrogate simulators and enhance the confidence level of the generated optimal solutions. The developed model was applied to the planning of coal blending in Gaojing and Shijingshan power plants in the west of Beijing. The results indicated that the developed SFPP model was useful for generating a series of coal blending schemes under different acceptable possibility levels, ensuring that the risk to human health reduce to an acceptable level, identifying desired coal blending strategies for decision makers, and considering a proper balance between system costs and acceptable possibility levels.

Development of Unknown Pollution Source Identification Models Using GMS ANN–Based Simulation Optimization Methodology

AbstractThe detection of groundwater pollution sources is an important but a very difficult task. The location and magnitude of groundwater pollution sources can be identified using inverse optimization technique. The technique is also known as simulation-optimization approach where the aquifer simulation model is incorporated with the optimization model for finding the unknown pollution sources in an aquifer. The efficiency of the simulation-optimization model is highly related to the performance of the simulation model. This study develops three improved methodologies for identification of unknown groundwater pollution sources. In the first approach, the groundwater modeling system (GMS) is linked with the optimization model for solving source identification problem. The optimization model is solved using the direct-search method. The incorporation of GMS with the optimization model allows for the solving of a bigger real-world pollution source identification problem. The challenge of this approach is t...

A Discussion on the Method of Classification of Medical Syndromes in the ICD-10

A medical syndrome is a group of disease symptoms involving multiple systems and organs, and there are various naming categories. Most of the symptoms listed in the ICD-10 (International Classifi cation of Diseases) are named by transliteration of the surnames of the discoverers, while the clinical doctors in our country often use the “ conventional name ” or “ common name ” and other names in the written diagnosis, which may be a problem for the coders. In this paper, by analyzing three situations of the naming structure for syndromes, the author elaborates the direct search method and the code search method, according to the disease classifi cation principles which are commonly used for searching for the disease code of a syndrome, and points out the issues that should be paid attention to in the work of coding disease syndromes. It also analyzes the search methods of several disease syndromes, and provides a reference for medical record administrators to help them in the process of cataloging the diseases.

Minimizing Part Warpage in Injection Molding by Optimizing Wall Thickness Distribution

ABSTRACTThe warpage of injection‐molded parts is an omnipresent problem in new product development. In this study, a method is developed to reduce the warpage by optimizing the wall thickness distribution of a part. This method is based on an iterative optimization procedure consisting of mold flow analysis, a mesh parameterization tool for geometry manipulation, and an optimization algorithm. Starting with the initial design for the mold cavity, the procedure optimizes the wall thickness distribution at user‐defined area sections within prescribed tolerances. A unit‐square parameterization technique is applied that uses mean‐valued coordinates and a second‐order polynomial thickness distribution. Three different optimization algorithms—an evolutionary algorithm, a surrogate‐based response surface method, and a direct search method—are considered, and the optimization performances of these algorithms are evaluated for a warpage demonstrator and real industrial part. The results demonstrate the effectiveness of the developed procedure and plausibility of the optimized thickness distribution.

Preference-based reinforcement learning: evolutionary direct policy search using a preference-based racing algorithm

We introduce a novel approach to preference-based reinforcement learning, namely a preference-based variant of a direct policy search method based on evolutionary optimization. The core of our approach is a preference-based racing algorithm that selects the best among a given set of candidate policies with high probability. To this end, the algorithm operates on a suitable ordinal preference structure and only uses pairwise comparisons between sample rollouts of the policies. Embedding the racing algorithm in a rank-based evolutionary search procedure, we show that approximations of the so-called Smith set of optimal policies can be produced with certain theoretical guarantees. Apart from a formal performance and complexity analysis, we present first experimental studies showing that our approach performs well in practice.

Gradient-Based Adaptive Stochastic Search for Non-Differentiable Optimization

In this paper, we propose a stochastic search algorithm for solving general optimization problems with little structure. The algorithm iteratively finds high quality solutions by randomly sampling candidate solutions from a parameterized distribution model over the solution space. The basic idea is to convert the original (possibly non-differentiable) problem into a differentiable optimization problem on the parameter space of the parameterized sampling distribution, and then use a direct gradient search method to find improved sampling distributions. Thus, the algorithm combines the robustness feature of stochastic search from considering a population of candidate solutions with the relative fast convergence speed of classical gradient methods by exploiting local differentiable structures. We analyze the convergence and converge rate properties of the proposed algorithm, and carry out numerical study to illustrate its performance.

Analysis and optimization of an M/G/1 machine repair problem with multiple imperfect coverage

This paper examines an M/G/1 machine repair problem with multiple imperfect coverage. When an operating machine fails, it is immediately detected and located with coverage probability c. We first use a recursive method and supplementary variable technique to develop steady-state analytic solutions. Various system performance measures are developed based on the steady-state probability distributions. We then construct the expected cost function per machine per unit time and formulate an optimization problem to determine the minimum cost. Direct search and Quasi-Newton methods are implemented to search for the optimal number of operating machines, the optimal repair rate, and the optimal coverage factor. Sensitivity analysis and numerical illustrations are also provided.

Transit route and frequency design: Bi-level modeling and hybrid artificial bee colony algorithm approach

This paper proposes a bi-level transit network design problem where the transit routes and frequency settings are determined simultaneously. The upper-level problem is formulated as a mixed integer non-linear program with the objective of minimizing the number of passenger transfers, and the lower-level problem is the transit assignment problem with capacity constraints. A hybrid artificial bee colony (ABC) algorithm is developed to solve the bi-level problem. This algorithm relies on the ABC algorithm to design route structures and a proposed descent direction search method to determine an optimal frequency setting for a given route structure. The descent direction search method is developed by analyzing the optimality conditions of the lower-level problem and using the relationship between the lower- and upper-level objective functions. The step size for updating the frequency setting is determined by solving a linear integer program. To efficiently repair route structures, a node insertion and deletion strategy is proposed based on the average passenger demand for the direct services concerned. To increase the computation speed, a lower bound of the objective value for each route design solution is derived and used in the fitness evaluation of the proposed algorithm. Various experiments are set up to demonstrate the performance of our proposed algorithm and the properties of the problem.

A class of derivative-free nonmonotone optimization algorithms employing coordinate rotations and gradient approximations

In this paper we study a class of derivative-free unconstrained minimization algorithms employing nonmonotone inexact linesearch techniques along a set of suitable search directions. In particular, we define globally convergent nonmonotone versions of some well-known derivative-free methods and we propose a new linesearch-based nonmonotone algorithm, where search directions are constructed by combining coordinate rotations with simplex gradients. Through extensive numerical experimentation, we show that the proposed algorithm is highly competitive in comparison with some of the most efficient direct search methods and model based methods on a large set of test problems.

Optimal Machine-Tool Settings for the Manufacture of Face-Hobbed Spiral Bevel Gears

In this study, an optimization methodology is proposed to systematically define the optimal head-cutter geometry and machine-tool settings to simultaneously minimize the tooth contact pressure and angular displacement error of the driven gear (the transmission error), and to reduce the sensitivity of face-hobbed spiral bevel gears to the misalignments. The proposed optimization procedure relies heavily on the loaded tooth contact analysis for the prediction of tooth contact pressure distribution and transmission errors influenced by the misalignments inherent in the gear pair. The load distribution and transmission error calculation method employed in this study were developed by the author of this paper. The targeted optimization problem is a nonlinear constrained optimization problem, belonging to the framework of nonlinear programming. In addition, the objective function and the constraints are not available analytically, but they are computable, i.e., they exist numerically through the loaded tooth contact analysis. For these reasons, a nonderivative method is selected to solve this particular optimization problem. That is the reason that the core algorithm of the proposed nonlinear programming procedure is based on a direct search method. The Hooke and Jeeves pattern search method is applied. The effectiveness of this optimization was demonstrated on a face-hobbed spiral bevel gear example. Drastic reductions in the maximum tooth contact pressure (62%) and in the transmission errors (70%) were obtained.

Optimization of thermal insulation to achieve energy savings in low energy house (refurbishment)

Due to the current environmental situation, saving energy and reducing CO2 emission have become the leading drive in modern research. For buildings that require heating, one of the solutions is to optimize a thickness of their thermal insulation and thus improve energy efficiency and reduce energy needs. In this paper, for a small residential house in Serbia, an optimization in the thickness of its thermal insulation layer is investigated by using EnergyPlus software and Hooke–Jeeves direct search method. The embodied energy of thermal insulation is taken into account. The optimization is done for the entire life cycle of thermal insulation. The results show the optimal thickness of thermal insulation that yields the minimum primary energy consumption.

Optimal Tooth Modifications in Face-Hobbed Spiral Bevel Gears to Reduce the Influence of Misalignments on Elastohydrodynamic Lubrication

In this study, an optimization methodology is proposed to systematically define the optimal tooth modifications introduced by head-cutter geometry and machine-tool settings to minimize the influence of misalignments on the elastohydrodynamic (EHD) lubrication characteristics in face-hobbed spiral bevel gears. The goal is to simultaneously maximize the EHD load-carrying capacity of the oil film and to minimize power losses in the oil film when different misalignments are inherent in the gear pair. The proposed optimization procedure relies heavily on the EHD lubrication analysis developed in this paper. The core algorithm of the proposed nonlinear programming procedure is based on a direct search method. Effectiveness of this optimization was demonstrated on a face-hobbed spiral bevel gear example. A drastic increase in the EHD load-carrying capacity of the oil film and a reduction in the power losses in the oil film were obtained.

Multiobjective Memetic Algorithm Applied to the Optimisation of Water Distribution Systems

Finding low-cost designs of water distribution systems (WDSs) which satisfy appropriate levels of network performance within a manageable time is a complex problem of increasing importance. A novel multi-objective memetic algorithm (MA) is introduced as a solution method to this type of problem. The MA hybridises a robust genetic algorithm (GA) with a local improvement operator consisting of the classic Hooke and Jeeves direct search method and a cultural learning component. The performance of the MA and the GA on which it is based are compared in the solution of two benchmark WDS problems of increasing size and difficulty. Solutions that are superior to those reported previously in the literature were achieved. The MA is shown to outperform the GA in each case, indicating that this may be a useful tool in the solution of real-world WDS problems. The potential benefits from search space reduction are also demonstrated.

Inverse modeling of a solar collector involving Fourier and non-Fourier heat conduction

This article applies the golden section search method (GSSM), simplex search method (SSM) and differential evolution (DE) for predicting the unknown Fourier number (Fo), Vernotte number (Ve) and non-dimensional solar heat flux (S∗) in a flat-plate solar collector when subjected to a given temperature requirement. The required temperature field is calculated using an analytical forward method by considering Fourier and non-Fourier heat conduction, and using this, the inverse problem is solved to predict the Fo, Ve and S∗ which are assumed to be the unknown parameters. The study reveals that the temperature field is highly sensitive to the Fo, thus even a small error in the temperature measurement can result in an unrealistic estimation of heating time of the collector. The present study is proposed to be useful in determining the time, the time lag and solar heat flux for controlled heating of an absorber plate within a stipulated time, which will be required to attain a prescribed/desired temperature distribution. Additionally, the study also shows that subjected to different time levels, the same temperature distribution is possible through different absorber plate materials. It has been observed from the present study that apart from SSM and DE, GSSM fails to estimate the unknown parameters at large value of Ve and small value of Fo, due to the associated fluctuation in the measured temperature field. The present study further discusses the computational performance of direct search method (e.g. GSSM and SSM) with that of the evolutionary method (DE) in terms of the maximum number of iteration and CPU time required to achieve the desired objective.