Direct Search Method Research Articles

3D Seismic survey design using mixed‐radix based algorithm inversion

ABSTRACTThe determination of three‐dimensional geometry and acquisition parameters, the seismic acquisition survey design, is constantly subject of studies in obtaining data with the highest seismic quality, operational efficiency and cost minimization. In this paper, we propose a methodology for inverting geometry parameters of three‐dimensional orthogonal land seismic surveys based on a direct search method using a mixed‐radix based algorithm. In this algorithm, the search space is discretized on a mixed‐radix base, which depends on the extreme values and the search resolution of each parameter. We will show how to reparametrize the orthogonal acquisition geometry elements in order to obtain the independents and integers parameters that are necessary to construct the mixed‐radix base. For the optimization purpose, we define an objective function to contemplate target parameters associated with the elements of the acquisition geometry directly related to the geophysical and operational constraints. Taking in account that the mathematical functions and the objective function we define for the problem have no significant computational cost, all model space parameters are fast and efficiently tested. We applied the algorithm, using as input data, provided by a one‐line roll orthogonal reference geometry, assuming a pair of geological objectives as shallow and deep targets. All selected models that meet both the proposed objectives and the constraints are organized by decreasing order of fitness so that with the mixed‐radix inversion algorithm we found not only the best model, but also a set of suitable models. Likewise, with the best set of geometries, it is possible to establish a direct comparison between them, analysing their adherence to the technical and operational requirements according to the availability and degree of detail of each one. We show the top 10 best results as a table, allowing a direct comparison between all aspects of these geometries, and we summarize the results showing graphically the fitness of all selected geometries and the inverted geometry elements for the 1000 best geometries. These graphical displays provide a direct way to understand how each model behaves as the fitness decreases. The algorithm is very flexible and its application can be extended to any environment and type of acquisition geometry, and in any phase study of an area be it regional, exploratory or development.

Optimization analysis of management operation for a server farm

ABSTRACTThis paper analyses a server farm with a simple management operation, which is desirable to reduce power consumption. A block of servers is named as ‘reserves’. Depending on the number of jobs staying in the system, power-up and power-down thresholds are employed to control the state of the reserves. In addition, the process of power-up is not immediately. During the period, the servers cannot serve jobs but still consuming power. The server may be subject to be breakdown. This system was modelled by an infinite capacity queueing system and analysed by matrix-geometric technique. The matrix-geometric method is applied to compute the rate matrix and the stationary probabilities. A cost model is formulated to search the optimum number of permanent server and the optimum power-down threshold. The optimization tasks are carried out by the direct search method. Both analytic processes and numerical results provide very useful and helpful information for decision-makers.

Accelerated Directional Search with Non-Euclidean Prox-Structure

In the paper we propose an accelerated directional search method with non-euclidian prox-structure. We consider convex unconstraint optimization problem in $\mathbb{R}^n$. For simplicity we start from the zero point. We expect in advance that 1-norm of the solution is close enough to its 2-norm. In this case the standard accelerated Nesterov's directional search method can be improved. In the paper we show how to make Nesterov's method $n$-times faster (up to a $\log n$-factor) in this case. The basic idea is to use linear coupling, proposed by Allen-Zhu & Orecchia in 2014, and to make Grad-step in 2-norm, but Mirr-step in 1-norm. We show that for constrained optimization problems this approach stable upon an obstacle.

Multi-objective airfoil shape optimization using an adaptive hybrid evolutionary algorithm

In this study, multi-objective aerodynamic optimization problems were conducted with a hybrid evolutionary-adaptive directional local search method for convergence enhancement. The directional search operator includes selection of search direction and one-dimensional search. Probability for the directional operator is adaptively changed based on relative effectiveness of the directional search operator and evolutionary operators such as crossover and mutation. The adaptive directional operator is combined with a baseline evolutionary multi-objective algorithm (EMOA) such as NSGA-II or MOGA. Multi-objective airfoil shape optimization examples are defined as drag minimization/lift maximization and L/D maximization at high lift and cruise conditions in subsonic and transonic regimes. The CST method and the B-spline method were used for airfoil shape parameterization. Design examples with drag minimization and L/D maximization at cruise conditions are all found to have uni-modal design spaces, and the local search operator is effective for those examples. However, lift maximization and high angle of attack cases show multi-modality in the design spaces due to flow separations and thus the local search is not effective for those cases. Design results show that the adaptive directional search method significantly enhances convergence of problems in which the directional search is effective, and also minimizes unnecessary spending of computational budget for cases in which the directional search does not produce competitive solutions. The present method improves search performance for different airfoil parameterization methods and different baseline EMOAs. Statistical tests confirm that the adaptive hybrid method is superior to the baseline EMOA.

Improved optimal design of concrete gravity dams founded on anisotropic soils utilizing simulation-optimization model and hybrid genetic algorithm

ABSTRACT Incorporating numerically predicted responses of seepage characteristics based on large numbers of surrogate models to identify the optimum design of Concrete Gravity Dams (CGD) can lead to sub-optimal or local solution, even when the evolutionary Genetic Algorithm (GA) optimization solver is utilized. The optimization task aims to find the safe and minimum cost design for the CGD built on anisotropic permeable soils, considering the effect of seepage under the CGD. In each iteration of the optimization model solution, the GA-based linked Simulation-Optimization (S-O) approach evaluates the objective function and the constraints based on the responses of the Support Vector Machine (SVM) surrogate models. This paper focused on improving the GA performance to find the global or a near global optimum design of a complex optimization model, minimizing the construction cost, and providing a design safety of the CGD. This could be achieved by using the Hybrid Genetic Algorithm (HGA) optimization solver. The HGA merges two optimization search techniques: the direct search methods utilizing GA, and the gradient search method using the Interior Point Algorithm (IPA). The solution results showed that the HGA was more efficient in finding improved or, global optimum design of the CGD. Physically, the low anisotropic ratio of hydraulic conductivity (0.1, 0.3, 0.5) resulted in critical seepage characteristics, which substantially affects the optimum hydraulic design of CGD, and increases the corresponding construction cost.

Direct search based on probabilistic feasible descent for bound and linearly constrained problems

Direct search is a methodology for derivative-free optimization whose iterations are characterized by evaluating the objective function using a set of polling directions. In deterministic direct search applied to smooth objectives, these directions must somehow conform to the geometry of the feasible region, and typically consist of positive generators of approximate tangent cones (which then renders the corresponding methods globally convergent in the linearly constrained case). One knows however from the unconstrained case that randomly generating the polling directions leads to better complexity bounds as well as to gains in numerical efficiency, and it becomes then natural to consider random generation also in the presence of constraints. In this paper, we study a class of direct-search methods based on sufficient decrease for solving smooth linearly constrained problems where the polling directions are randomly generated (in approximate tangent cones). The random polling directions must satisfy probabilistic feasible descent, a concept which reduces to probabilistic descent in the absence of constraints. Such a property is instrumental in establishing almost-sure global convergence and worst-case complexity bounds with overwhelming probability. Numerical results show that the randomization of the polling directions can be beneficial over standard approaches with deterministic guarantees, as it is suggested by the respective worst-case complexity bounds.

Smoothing Photovoltaic Power Fluctuations for Cascade Hydro-PV-Pumped Storage Generation System Based on a Fuzzy CEEMDAN

Due to strong volatility and intermittent characteristics, the fluctuations of the photovoltaic (PV) output is inevitable which cause negative impacts on power system operation. However, such an issue can be resolved in a combined cascade hydro-PV-pumped storage (CH-PV-PS) generation system through an appropriate control. Based on the optimal base power of variable-speed pumped storage station (VSPSS), a smoothing method of fuzzy complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) is proposed in this paper. To prevent smoothing insufficient and excessive, the fuzzy CEEMDAN algorithm is used to obtain the target power of the photovoltaic-pumped storage (PV-PS) generation system and the control signal of cascade hydro stations (CHSs) for eliminating large amplitude fluctuations of the PV output. Furthermore, in order to overcome the drawback that too frequent conversion of unit operating mode would reduce the service life and smoothing effect of the VSPSS unit, the optimization model of the base power of the VSPSS is established and solved by the grid adaptive direct search method (MADS) to obtain the control signal of the VSPSS for suppressing the short-term fluctuations of the PV output. Finally, the performance of the method is evaluated through using the PV station data in Xiaojin County, Sichuan province, China. The simulation results reveal that compared with the fixed base power smoothing method, this method can effectively suppress the PV power fluctuations and improve the smoothing effect and energy efficiency.

IMPROVEMENT THE DETERMINING METHOD OF BRAKING MODE OF CONTROLLED CUT OF DESIGN GROUP

Purpose. The application of automation systems of breaking up process on the gravity hump is the efficiency improvement of their operation, absolute provision of trains breaking up safety demands, as well as improvement of hump staff working conditions. One of the main tasks of the indicated systems is the assurance of cuts reliable separation at all elements of their rolling route to the classification track. This task is a sophisticated optimization problem and has not received a final decision. Therefore, the task of determining the cuts braking mode is quite relevant. The purpose of this research is to find the optimal braking mode of control cut of design group. Methodology. In order to achieve the purpose is offered to use the direct search methods in the work, namely the Box complex method. This method does not require smoothness of the objective function, takes into account its limitations and does not require calculation of the function derivatives, and uses only its value. Findings. Using the Box method was developed iterative procedure for determining the control cut optimal braking mode of design group. The procedure maximizes the smallest controlled time interval in the group. To evaluate the effectiveness of designed procedure the series of simulation experiments of determining the control cut braking mode of design group was performed. The results confirmed the efficiency of the developed optimization procedure. Originality. Authors formalized the task of optimizing control cut braking mode of design group, taking into account the cuts separation of design group at all elements (switches, retarders) during cuts rolling to the classification track. The problem of determining the optimal control cut braking mode of design group was solved. The developed braking mode ensures cuts reliable separation of the group not only at the switches but at the retarders of brake position. Practical value. The developed procedure can be successfully used to determine the optimal braking modes of cuts in automation systems of trains breaking up on the gravity humps.

Calibration of parameters in Dynamic Energy Budget models using Direct-Search methods.

Dynamic Energy Budget (DEB) theory aims to capture the quantitative aspects of metabolism at the individual level, for all species. The parametrization of a DEB model is based on information obtained through the observation of natural populations and experimental research. Currently the DEB toolbox estimates these parameters using the Nelder-Mead Simplex method, a derivative-free direct-search method. However, this procedure presents some limitations regarding convergence and how to address constraints. Framed in the calibration of parameters in DEB theory, this work presents a numerical comparison between the Nelder-Mead Simplex method and the SID-PSM algorithm, a Directional Direct-Search method for which convergence can be established both for unconstrained and constrained problems. A hybrid version of the two methods, named as Simplex Directional Direct-Search, provides a robust and efficient algorithm, able to solve the constrained optimization problems resulting from the parametrization of the biological models.

PENGARUH INISIALISASI POPULASI RANDOM SEARCH PADA ALGORITMA BEREVOLUSI DALAM OPTIMASI TRAVELLING SALESMAN PROBLEM (TSP)

<p>Traveling Salesman Problem (TSP) is a problem where each initial route of departure and return path between regions remains the same. The problem with TSP is how to get the optimum results to get the shortest path that will be passed, to solve TSP problems, one way can be by using evolved algorithms. Evolution Algorithm (AE) is a method that uses natural selection as the main idea in solving a particular problem. This algorithm is implemented through computer simulations starting from the individual population that will be randomly generated and then evaluated to achieve the best solution. Random search is included in part of stochastic optimization and global optimization. Random search is a direct search method that does not require derivatives to search for continue domains. The purpose of this study was to see the effect of population initialization with random search on algorithms evolving in TSP optimization. Results of initialization strategy implementation Random search has shown more optimal results compared to pure initialization without using random search. This is due to the initialization searching for space for random initialization.</p>

Optimization of a thermoelectric generator for heavy-duty vehicles

A thermoelectric generator used to recover energy from the exhaust gases of a heavy-duty freight vehicle is numerically simulated and optimized using two different algorithms: a gradient-based search method, and a global and local direct search method. The model uses a one-dimensional finite volume method to calculate the temperature and the convective heat transfer of the hot and cold fluids along the streamwise direction, as well as the pressure drop, and employs a thermal resistance network and a global energy balance to account for the heat transfer and the thermoelectric effect. Three different heat exchanger configurations are studied with plain, offset strip or triangular fins. The objective function is the net output power, and the geometrical dimensions of the heat exchanger and thermoelectric units are taken as design variables. The results show that the height of the fins, the spacing between them, the height and side length of the cross section of the thermoelectric units, and the distance between the legs are critical parameters in the optimization process. The thickness of the fins, wall ducts, electrical conductor and ceramic strips should be as small as possible, as well as the height of the cooling wall duct. The two optimization methods yield similar optimal solutions.

Thermal design improvement of a double-layered microchannel heat sink by using multi-walled carbon nanotube (MWCNT) nanofluids with non-Newtonian viscosity

In the present study, numerical optimization of a double layer micro channel heat sink is addressed. Carbon based nanofluids with a non-Newtonian viscosity is assumed as the coolant. A conjugate numerical model based on finite volume method and two-phase mixture model is used to simulate the heat and fluid flow through the two three-dimensional domains; the solid walls and the coolant. A direct search method is applied to find the optimal design of the micro channel heat sinks such that the thermal resistance of the heat sink is minimized under the constraint of fixed pumping powers. The numerical model is validated against experimental data. A comprehensive sensitivity analysis is undertaken to properly bracket the optimum design point of the heat sink and the optimum point is directly searched for several pumping powers. It is shown that using carbon based nanofluid results in the reduction of overall thermal resistance of the double layer microchannel heat sink in comparison with oxide-metallic nanofluid (with Newtonian rheological behavior). The superior thermal performance of MWCNT/water nanofluids is attributed to the high conductivity of the carbon nano particles and the shear thinning behavior of the nanofluid. Up to 14% enhancement in the thermal performance of the micro channel heat sink is reached by the use of non-Newtonian carbon base nanofluids.

Genetic evolution vs. function approximation: Benchmarking algorithms for architectural design optimization

Abstract This article presents benchmark results from seven simulation-based problems from structural, building energy, and daylight optimization. Growing applications of parametric design and performance simulations in architecture, engineering, and construction allow the harnessing of simulation-based, or black-box, optimization in the search for less resource- and/or energy consuming designs. In architectural design optimization (ADO) practice and research, the most commonly applied black-box algorithms are genetic algorithms or other metaheuristics, to the neglect of more current, global direct search or model-based, methods. Model-based methods construct a surrogate model (i.e., an approximation of a fitness landscape) that they refine during the optimization process. This benchmark compares metaheuristic, direct search, and model-based methods, and concludes that, for the given evaluation budget and problems, the model-based method (RBFOpt) is the most efficient and robust, while the tested genetic algorithms perform poorly. As such, this article challenges the popularity of genetic algorithms in ADO, as well as the practice of using them for one-to-one comparisons to justify algorithmic innovations. Highlights Benchmarks optimization algorithms on structural, energy, and daylighting problems. Benchmarks metaheuristic, direct search, and model-based optimization methods. Challenges the popularity of genetic algorithms in architectural design optimization. Presents model-based methods as a more efficient and reliable alternative.

Determining an appropriate unstructured kinetic model for batch ethanol fermentation data using a direct search method

In this paper, we study an extracellular process of a biochemical system such as batch ethanol fermentation system by considering an unstructured kinetic model with four different well-known models for the specific growth rate of the yeast cells. Then, we fit the unstructured models to the experimental data for determining the appropriate model that can capture the dynamic behaviour of the batch ethanol fermentation experimental data. The fitting procedure is proceeded by minimising a least-squared error between the model solutions and the experimental data using a direct search method. Our simulations show that the unstructured model with Aiba-type structured model for the specific growth rate of the yeast cell has the best approximating ability to describe the dynamic of the batch ethanol fermentation data.

Hybrid bat algorithm and direct search methods for solving minimax problems

Hybrid bat algorithm and direct search methods for solving minimax problems

Solving Integer Programming Problems by Hybrid Bat Algorithm and Direct Search Method

The goal of this work is to suggest a new hybrid algorithm to solve integer programming by incorporating the bat algorithm with direct search methods. The suggested algorithm is named hybrid bat direct search algorithm (HBDS). In HBDS, the global diversification and the local intensification process are balanced.

Scalable Multiobjective Control for Large-Scale Water Resources Systems Under Uncertainty

Advances in modeling and control have always played an important role in supporting water resources systems planning and management. Changes in climate and society are now introducing additional challenges for controlling these systems, motivating the emergence of complex, integrated simulation models to explore key causal relationships and dependences related to uncontrolled sources of variability. In this brief, we contribute a massively parallel implementation of the evolutionary multiobjective direct policy search method for controlling large-scale water resources systems under uncertainty. The method combines direct policy search with nonlinear approximating networks and a hierarchical parallelization of the Borg multiobjective evolutionary algorithm. This computational framework successfully identifies control policies that address both the presence of multidimensional tradeoffs and severe uncertainties in the system dynamics and policy performance. We demonstrate the approach on a challenging real-world application, represented by the optimal control of a network of four multipurpose water reservoirs in the Red River basin in Northern Vietnam, under observed and synthetically generated hydrologic conditions. Results show that the reliability of the computational framework in finding near-optimal solutions increases with the number of islands in the adopted hierarchical parallelization scheme. This setting reduces the vulnerabilities of the designed solutions to the system’s uncertainty and improves the discovery of robust control policies addressing key system performance tradeoffs.

Proper initialization is crucial for the Nelder–Mead simplex search

The Nelder–Mead simplex search as one of the oldest direct search methods is still in use today. Despite its flaws, such as possible convergence to non-stationary points, in practice the algorithm offers a competitive performance compared to other direct search algorithms. However, we show that some of the most common initialization procedures can increase the runtime of the algorithm by orders of magnitude, even on a trivial spherical test function. These results also hold for the Nelder–Mead variant with sufficient decrease condition and oriented restarts by Kelley and the variant with adaptive parameters by Gao and Han. As a remedy, we recommend to normalize the search space and to choose the initial simplex independent of the starting point.

Efficiency Optimisation of Blade Shape in Steam and ORC Turbines

Abstract This paper is devoted to direct constrained optimisation of blading systems of large power and small power turbines so as to increase their internal efficiency. The optimisation is carried out using hybrid stochastic-deterministic methods such as a combination of a direct search method of Hooke-Jeeves and simulated annealing or a combination of a bat algorithm and simplex method of Nelder-Mead. Among free shape parameters are blade number and stagger angle, stacking blade line parameters and blade section (profile) parameters. One practical example of efficiency optimisation of turbine blading systems is modification of low load profiles PLK-R2 for high pressure (HP) stages of large power steam turbines. Another optimised geometry is that of an ORC radial-axial cogeneration turbine of 50 kWe. Up to 1% efficiency increase can easily be obtained from optimisation of HP blade profiles, especially by making the rotor blade more aft-loaded and reducing the intensity of endwall flows. Almost 2% efficiency rise was obtained for the optimised 50 kWe ORC turbine due to flow improvement at the suction side of the blade.

Meta optimization of stand management with population-based methods

The amount of different products and services obtained from forests depends on several management decisions such as thinning years, thinning intensity, thinning type, and rotation length. The relationships between management actions and the various outputs obtained from forests are complicated. This makes stand management optimization challenging, especially if the number of simultaneously maximized outputs and the number of optimized variables are high. The direct search method of Hooke and Jeeves (HJ) has been used much in stand management optimization. In recent years, population-based methods have been proposed as an alternative to the HJ method. The performance of a population-based method depends on its parameters such as number iterations and population size (number of solution vectors used in the population-based method). This study used two-level meta optimization to simultaneously optimize the parameters of a population-based method and the management schedule of a stand. Four population-based methods were analysed: differential evolution (DE), particle swarm optimization (PS), evolution strategy optimization (ES), and the method of Nelder and Mead (NM). With optimal parameter values, DE and PS found the best stand management schedules, followed by ES and NM. DE and PS performed better than HJ. Therefore, DE and PS should be used more in forest management and their search algorithms should be further developed.