Multilevel Coordinate Search Research Articles

Ability of Black-Box Optimisation to Efficiently Perform Simulation Studies in Power Engineering

Abstract In this study, the potential of the so-called black-box optimisation (BBO) to increase the efficiency of simulation studies in power engineering is evaluated. Three algorithms (“Multilevel Coordinate Search” (MCS) and “Stable Noisy Optimization by Branch and Fit” (SNOBFIT) by Huyer and Neumaier and “blackbox: A Procedure for Parallel Optimization of Expensive Black-box Functions” (blackbox) by Knysh and Korkolis) are implemented in MATLAB and compared for solving two use cases: the analysis of the maximum rotational speed of a gas turbine after a load rejection and the identification of transfer function parameters by measurements. The first use case has a high computational cost, whereas the second use case is computationally cheap. For each run of the algorithms, the accuracy of the found solution and the number of simulations or function evaluations needed to determine the optimum and the overall runtime are used to identify the potential of the algorithms in comparison to currently used methods. All methods provide solutions for potential optima that are at least 99.8% accurate compared to the reference methods. The number of evaluations of the objective functions differs significantly but cannot be directly compared as only the SNOBFIT algorithm does stop when the found solution does not improve further, whereas the other algorithms use a predefined number of function evaluations. Therefore, SNOBFIT has the shortest runtime for both examples. For computationally expensive simulations, it is shown that parallelisation of the function evaluations (SNOBFIT and blackbox) and quantisation of the input variables (SNOBFIT) are essential for the algorithmic performance. For the gas turbine overspeed analysis, only SNOBFIT can compete with the reference procedure concerning the runtime. Further studies will have to investigate whether the quantisation of input variables can be applied to other algorithms and whether the BBO algorithms can outperform the reference methods for problems with a higher dimensionality.

A splitting algorithm for simulation-based optimization problems with categorical variables

ABSTRACTIn the design of complex products, some product components can only be chosen from a finite set of options. Each option then corresponds to a multidimensional point representing the specifications of the chosen components. A splitting algorithm that explores the resulting discrete search space and is suitable for optimization problems with simulation-based objective functions is presented. The splitting rule is based on the representation of a convex relaxation of the search space in terms of a minimum spanning tree and adopts ideas from multilevel coordinate search. The objective function is underestimated on its domain by a convex quadratic function. The main motivation is the aim to find—for a vehicle and environment specification—a configuration of the tyres such that the energy losses caused by them are minimized. Numerical tests on a set of optimization problems are presented to compare the performance of the algorithm developed with that of other existing algorithms.

Optimization of multistage fractured horizontal well in tight oil based on embedded discrete fracture model

Optimizing multistage fractured horizontal wells (MFHW) can tap the full potential of tight oil reservoirs. Although recent studies have introduced various frameworks, most of the significant parameters for MFHW are not optimized simultaneously, which may lead to actual performance that is far below expected performance, especially in heterogeneous reservoirs. Here, we present an efficient optimization framework that couples embedded discrete fracture model (EDFM) and intelligent algorithms to maximize net present value. We also examined the performance of four optimization algorithms in our model: genetic algorithm (GA), multilevel coordinate search (MCS), covariance matrix adaptation evolution strategy (CMA-ES), and generalized pattern search (GPS). Our results suggest that because CMA-ES handles MFHW optimization robustly and effectively, it may be utilized in future applications. Our framework serves as an efficient tool to optimize MFHW design, which plays an increasingly significant role in the enhancement of tight oil recovery.

MO-MCS, a Derivative-Free Algorithm for the Multiobjective Optimization of Adsorption Processes

Cyclic adsorption processes for gas separation, such as pressure and temperature swing adsorption (PSA and TSA), are nonstationary multicolumn processes. Their design involves many degrees of freedom, which offers a very high flexibility while calling for a systematic and rigorous optimization approach. As an additional challenge, optimization of these separation processes involves multiple objectives, e.g., minimal energy demand and maximal productivity, which have to be pursued while fulfilling given process specifications, e.g., purity and recovery of the target components. This work extends the multilevel coordinate search (MCS), a well-known model-based derivative-free algorithm, to constrained multiobjective problems. The algorithm, called MO-MCS, combines a built-in parallel computing strategy with the use of look-up tables with the goal of minimizing the computational time needed to determine the Pareto curve. The comparison with state-of-the-art optimizers indicates that MO-MCS shows better perfo...

Multiple cracks identification for piezoelectric structures

We propose a novel iterative procedure to solve the inverse problem of detecting multiple cracks in two-dimensional piezoelectric structures under dynamic electric loads. The effect of dynamic electric loads and a time-harmonic excitation with a single frequency is investigated. The crack is detected through the solution of an inverse time-dependent problem. The extended finite element method (XFEM) is employed for solving the forward problem as it allows the use of a single regular mesh for a large number of iterations with different crack geometries. The Newmark-beta method is employed for the time integration. In each iteration the forward problem is solved for various crack geometries, and at each iteration, the mechanical and electrical response of the piezoelectric structure is minimized at known specific points along the boundary to match the measured data. The minimization of the objective function is performed by multilevel coordinate search (MCS) method. The algorithm is an intermediate between purely heuristic methods and methods that allow an assessment of the quality of the minimum obtained and is in spirit similar to the direct method for global optimization. In this paper, the XFEM-MCS methodology under the dynamic electric load is applied to two-dimensional electromechanical problems where different number of straight cracks are considered. The results show that this methodology can be effectively employed for detecting multiple cracks in piezoelectric materials.

A multilevel coordinate search algorithm for well placement, control and joint optimization

Determining optimal well placements and controls are two important tasks in oil field development. These problems are computationally expensive, nonconvex, and contain multiple optima. The practical solution of these problems require efficient and robust algorithms. In this paper, the multilevel coordinate search (MCS) algorithm is applied for well placement and control optimization problems. MCS is a derivative-free algorithm that combines global and local search. Both synthetic and real oil fields are considered. The performance of MCS is compared to generalized pattern search (GPS), particle swarm optimization (PSO), and covariance matrix adaptive evolution strategy (CMA-ES) algorithms. Results show that the MCS algorithm is strongly competitive, and outperforms for the joint optimization problem and with a limited computational budget. The effect of parameter settings for MCS are compared for the test examples. For the joint optimization problem we compare the performance of the simultaneous and sequential procedures and show the utility of the latter.

MSO: a framework for bound-constrained black-box global optimization algorithms

This paper addresses a class of algorithms for solving bound-constrained black-box global optimization problems. These algorithms partition the objective function domain over multiple scales in search for the global optimum. For such algorithms, we provide a generic procedure and refer to as multi-scale optimization (MSO). Furthermore, we propose a theoretical methodology to study the convergence of MSO algorithms based on three basic assumptions: (a) local Holder continuity of the objective function f, (b) partitions boundedness, and (c) partitions sphericity. Moreover, the worst-case finite-time performance and convergence rate of several leading MSO algorithms, namely, Lipschitzian optimization methods, multi-level coordinate search, dividing rectangles, and optimistic optimization methods have been presented.

Derivative-Free Augmented Lagrangian for Global Optimization: Cost Minimization in a Simplified Activated Sludge System Model

A methodology for finding the optimal values of the decision variables from an efficient simplified mathematical model of an activated sludge system is addressed in this paper. The work herein presented arises in a wastewater treatment plant design context, where investment and operational costs are to be minimized and computational effort is to be reduced. To achieve the best design, a non-linear optimization solution method based on an augmented Lagrangian approach is proposed. At each iteration, a subproblem is globally solved by a derivative-free recursive branching technique, known as the multilevel coordinate search algorithm of Huyer and Neumaier [20]. The presented technique has been shown to work quite well when solving the herein proposed non-convex and non-smooth constrained optimization model. The numerical results show the reliability of the obtained solutions at a reduced computational cost.

Prestiction friction compensation in direct-drive mechatronics systems

LuGre model has been widely used in friction modeling and compensation. However, the new friction regime, named prestiction regime, cannot be accurately characterized by LuGre model in the latest research. With the extensive experimental observations of friction behaviors in the prestiction, some variables were abstracted to depict the rules in the prestiction regime. Based upon the knowledge of friction modeling, a novel friction model including the presliding regime, the gross sliding regime and the prestiction regime was then presented to overcome the shortcomings of the LuGre model. The reason that LuGre model cannot estimate the prestiction friction was analyzed in theory. Feasibility analysis of the proposed model in modeling the prestiction friction was also addressed. A parameter identification method for the proposed model based on multilevel coordinate search algorithm was presented. The proposed friction compensation strategy was composed of a nonlinear friction observer and a feedforward mechanism. The friction observer was designed to estimate the friction force in the presliding and the gross sliding regimes. And the friction force was estimated based on the model in the prestiction regime. The comparative trajectory tracking experiments were conducted on a simulator of inertially stabilization platforms among three control schemes: the single proportional-derivative (PD) control, the PD with LuGre model-based compensation and the PD with compensator based on the presented model. The experimental results reveal that the control scheme based on the proposed model has the best tracking performance. It reduces the peak-to-peak value (PPV) of tracking error to 0.2 mrad, which is improved almost 50% compared with the PD with LuGre model-based compensation. Compared to the single PD control, it reduces the PPV of error by 66.7%.

Detection of flaws in piezoelectric structures using extended FEM

SUMMARYAn iterative method to treat the inverse problem of detecting cracks and voids in two‐dimensional piezoelectric structures is proposed. The method involves solving the forward problem for various flaw configurations, and at each iteration, the response of piezoelectric material is minimized at known specific points along the boundary to match measured data. Extended finite element method (XFEM) is employed for solving the forward problem as it allows the use of a single regular mesh for a large number of iterations with different flaw geometries. The minimization of cost function is performed by multilevel coordinate search (MCS) method. The algorithm is an intermediate between purely heuristic methods and methods that allow an assessment of the quality of the minimum obtained and is in spirit similar to the direct method for global optimization. In this paper, the XFEM‐MCS methodology is applied to two‐dimensional electromechanical problems where flaws considered are straight cracks and elliptical voids. The results show that this methodology can be effectively employed for damage detection in piezoelectric materials. Copyright © 2013 John Wiley & Sons, Ltd.

Parameter identification of inertially stabilized platforms using current command design

Accurate parameter identification is essential when designing controllers for inertially stabilized platforms (ISPs). But traditional identification methods suffer from observation measurement noise and operating restrictions of ISPs. To address this issue, a novel identification method based on current command design and multilevel coordinate search (MCS) algorithm without any higher order measurement differentiations was proposed. The designed current commands were adopted to obtain parameter decoupled models with the platform operating under allowable conditions. MCS algorithm was employed to estimate the parameters based on parameter decoupled models. A comparison experiment between the proposed method and non-linear least square method was carried out and most of the relative errors of identified parameters obtained by the proposed method were below 10%. Simulation and experiment based on identified parameters were conducted. A velocity control structure was also developed with disturbance observer (DOB) for application in disturbance compensation control system of an ISP. Experimental results show that the control scheme based on the identified parameters with DOB has the best disturbance rejection performance. It reduces the peak to peak value (PPV) of velocity error integral to 0.8 mrad which is much smaller than the value (10 mrad) obtained by the single velocity controller without DOB. Compared with the control scheme based on sweep model with DOB compensation, the proposed control scheme improves the PPV of velocity error integral by 1.625 times.

LuGre-Model-Based Friction Compensation in Direct-Drive Inertially Stabilized Platforms

A Trajectory tracking problem for direct-drive inertially stabilized platforms suffered from nonlinear friction was considered in this paper. The dynamic characteristics of the system was study. A parameter identification method for LuGre model based on multilevel coordinate search algorithm was presented. Furthermore, nonlinear friction observer was designed to estimate the unmeasurable internal state of LuGre model. The comparative trajectory tracking experiments were conducted on a simulator of direct-drive systems between the single proportional–derivative (PD) control and the PD with LuGre model-based compensation. The experimental results revealed that the control scheme based on LuGre-model-based friction compensation reduced 3δ tracking error to 0.2mrad which is improved almost 66.7% compared with the PD control. At last, the ‘fake non-dissipativity phenomenon’ of LuGre in simulation and the digital implementation of LuGre friction compensation were discussed.

Estimating hysteresis in the soil water retention curve from monolith experiments

Water movement in unsaturated soils is commonly affected by hysteresis, a phenomenon often ignored as to keep the mathematical description of water flow and solute transport simple. In this study, the importance of hysteresis was quantified at lysimeter scale on two Belgian soils, a loamy and a sandy loam soil. Undisturbed soil monoliths (79cm diameter by 105cm height) were collected in each soil and the flow studied for various boundary conditions. Each monolith was equipped with different measuring devices to monitor online soil water content, pressure head, and outlet water fluxes. Four unsaturated steady state flow experiments were conducted on each monolith. Hydraulic properties were obtained by inverting the governing flow equation of Richards, using a global multilevel coordinate search inversion algorithm. Measured soil water contents, pressure heads, and outlet water fluxes were used in the objective function. First soil hydraulic parameters in the retention and hydraulic conductivity functions were estimated neglecting hysteresis and compared with the functions obtained using approaches considering hysteresis in their analysis. Hysteresis was incorporated in the retention curve using the simple empirical model proposed by Scott et al. (1983) and using the universal conceptual model of Mualem (1977). Hysteresis in both soils was characterized by a relative large difference between the main drying and wetting soil water retention curves. However, results showed that the effect of hysteresis was different on various components of water flow in the two studied soils. The Scott's model considerably improved pressure head estimates in the loamy soil and Mualem's model somewhat improved the soil water content estimates in the sandy loam soil. Outlet water fluxes in both soils were less sensitive to hysteresis. In general, the simple hysteretic model of Scott was more successful in studying hysteresis in both studied soils.

A new heuristic for plant-wide schedule coordination problems: The intersection coordination heuristic

This work addresses the coordination heuristics of two large-scale flexible multi-stage batch (flow shop) scheduling problems, which are currently solved independently by tailored algorithms that consist of mixed-integer linear optimization and heuristics. The approach is motivated by an industrial-scale steel making process that consists of a melt shop as the first production section and a hot rolling mill as the second production section. The first section produces intermediate products, i.e. slabs, which are stored in an intermediate storage area and which are consumed by the second section. The coordination objective is to reduce the storage time of the slabs or, more generally, the storage time between two sections taking into account the objectives of the two distributed scheduling solutions. A generic model formulation for multi-stage batch schedule coordination problems is presented. Three different schedule coordination heuristics are discussed and compared for simplified case studies: the heuristic based on Lagrangean decomposition (LD), a derivative-free optimization algorithm – Multilevel Coordinate Search (MCS), the new intersection coordination heuristic (IC) and monolithic MILP model solved by CPLEX (MONO). The proposed bi-level intersection coordination heuristic uses the knowledge on the bottlenecks of the two processes to build a simplified model for the upper-level coordinator which coordinates the lower-level distributed MILP schedulers via coordination variables iteratively. The numerical comparisons show the advantage of the IC among these three coordination approaches in terms of solution quality and computational effort. The limitations of LD, MCS, MONO and IC for the plant-wide schedule coordination problem are discussed in view of the requirements of large-scale industrial schedule coordination problems.

Optimal experiment design for time-lapse traveltime tomography

Geophysical monitoring techniques offer the only noninvasive approach capable of assessing the spatial and temporal dynamics of subsurface fluid processes. Increasingly, permanent sensor arrays in boreholes and on the ocean floor are being deployed to improve the repeatability and increase the temporal sampling of monitoring surveys. Because permanent arrays require a large up-front capital investment and are difficult (or impossible) to reconfigure once installed, a premium is placed on selecting a geometry capable of imaging the desired target at minimum cost. We have taken a simple approach to optimizing downhole sensor configurations for monitoring experiments making use of differential seismic traveltimes. We used a design quality metric based on the accuracy of tomographic reconstructions for a suite of imaging targets. By not requiring an explicit singular value decomposition of the forward operator, evaluation of this objective function scaled to problems with a large numberof unknowns. We restricted the design problem by recasting the array geometry into a low-dimensional form more suitable for optimization at a reasonable computational cost. We tested two search algorithms on the design problem: the Nelder-Mead downhill simplex method and the multilevel coordinate search algorithm. The algorithm was tested for four crosswell acquisition scenarios relevant to continuous seismic monitoring, a two-parameter array optimization, several scenarios involving four-parameter length/offset optimizations, and a comparison of optimal multisource designs. In the last case, we also examined trade-offs between source sparsity and the quality of tomographic reconstructions. Asymmetrical array lengths improved localized image quality in crosswell experiments with a small number of sources and a large number of receivers. Preliminary results also suggested that high-quality differential images could be generated using only a small number of optimally positioned sources in tandem with a more extensive receiver array.

Uniqueness and stability analysis of hydrogeophysical inversion for time‐lapse ground‐penetrating radar estimates of shallow soil hydraulic properties

Precise measurement of soil hydraulic properties at field scales is one of the prerequisites to simulate subsurface flow and transport processes, which is crucial in many research and engineering areas. In our study, we numerically analyze uniqueness and stability for integrated hydrogeophysical inversion of time‐lapse, off‐ground ground‐penetrating radar (GPR) data in estimating the unsaturated soil hydraulic properties. In the inversion, hydrodynamic modeling based on the one‐dimensional (1‐D) Richards equation is used to physically constrain a full‐waveform radar electromagnetic model. Synthetic GPR data, in terms of 3‐D multilayered media Green's functions, were generated for three different textured soils (coarse, medium, and fine) and assuming different infiltration events. Inversion was performed iteratively to estimate three key soil hydraulic parameters (α, n, and Ks) of the Mualem‐van Genuchten model using the global multilevel coordinate search optimization algorithm. For the coarse‐ and medium‐textured soils, inversions converged to the actual solution for all scenarios. For the fine soil, estimation errors occurred, mainly because of the higher attenuation of the electromagnetic waves in such a soil (high electric conductivity). The procedure appeared to be generally stable with respect to possible errors in the hydrodynamic and petrophysical model parameterization. However, we found that particular attention should be given to an accurate estimation of the saturated water content and infiltration flux for real field applications. The results from our numerical experiments suggest that, in theory, the proposed method is promising for the noninvasive identification of the shallow soil hydraulic properties at the field scale with a high spatial resolution.

Joint Dynamics Modeling and Parameter Identification for Space Robot Applications

Long-term mission identification and model validation for in-flight manipulator control system in almost zero gravity with hostile space environment are extremely important for robotic applications. In this paper, a robot joint mathematical model is developed where several nonlinearities have been taken into account. In order to identify all the required system parameters, an integrated identification strategy is derived. This strategy makes use of a robust version of least-squares procedure (LS) for getting the initial conditions and a general nonlinear optimization method (MCS—multilevel coordinate search—algorithm) to estimate the nonlinear parameters. The approach is applied to the intelligent robot joint (IRJ) experiment that was developed at DLR for utilization opportunity on the International Space Station (ISS). The results using real and simulated measurements have shown that the developed algorithm and strategy have remarkable features in identifying all the parameters with good accuracy.

EFFICIENT MAGNETIC LOCALIZATION AND ORIENTATION TECHNIQUE FOR CAPSULE ENDOSCOPY

To build a new wireless robotic capsule endoscope with external guidance for controllable and interactive GI tract examination, a sensing system is needed for tracking 3D location and 2D orientation of the capsule endoscope movement. An appropriate sensing method is to enclose a small permanent magnet in the capsule. The intensities of the magnetic field produced by the magnet in different spatial points can be measured by the magnetic sensors outside the patient's body. With the sensing data of magnetic sensor array, the 3D location and 2D orientation of the capsule can be calculated. Higher calculation accuracy can be obtained if more sensors and optimal algorithm are applied. In this paper, different nonlinear optimization algorithms were evaluated to solve the magnet's 5D parameters, e.g. Powell's, Downhill Simplex, DIRECT, Multilevel Coordinate Search, and Levenberg Marquardt method. We have found that Levenberg-Marquardt method provides satisfactory calculation accuracy and faster speed. Simulations were done for investigating the de-noise ability of this algorithm based on different sensor arrays. Also the real experiment shows that the results are satisfactory with high accuracy (average localization error is 5.6 mm).

Estimating soil electric properties from monostatic ground‐penetrating radar signal inversion in the frequency domain

A new integrated approach for identifying the shallow subsurface electric properties from ground‐penetrating radar (GPR) signal is proposed. It is based on an ultrawide band (UWB) stepped frequency continuous wave (SFCW) radar combined with a dielectric filled transverse electric and magnetic (TEM) horn antenna to be used off the ground in monostatic mode; that is, a single antenna is used as emitter and receiver. This radar configuration is appropriate for subsurface mapping and allows for an efficient and more realistic modeling of the radar‐antenna‐subsurface system. Forward modeling is based on linear system response functions and on the exact solution of the three‐dimensional Maxwell equations for wave propagation in a horizontally multilayered medium representing the subsurface. Subsurface electric properties, i.e., dielectric permittivity and electric conductivity, are estimated by model inversion using the global multilevel coordinate search optimization algorithm combined sequentially with the local Nelder‐Mead simplex algorithm (GMCS‐NMS). Inversion of synthetic data and analysis of the corresponding response surfaces proved the uniqueness of the inverse solution. Laboratory experiments on a tank filled with a homogeneous sand subject to different water content levels further demonstrated the stability and accuracy of the solution toward measurement and modeling errors, particularly those associated with the dielectric permittivity. Inversion for the electric conductivity led to less satisfactory results. This was mainly attributed to the characterization of the frequency response of the antenna and to the high frequency dependence of the electric conductivity.

Influence of material properties on sliding contact braking applications

In sliding contact, conditions such as pressure and temperature are affected by geometry as well as by material properties and boundary conditions. Simulations have been performed to investigate the effects of material properties and geometry on pressure and temperature. In addition, a favourable set of material parameters has been obtained using an optimisation method called multilevel coordinate search (MCS). The design parameters were found to affect the contact conditions to varying degrees. The ones that were found to have the most significant effect on contact temperature were the coefficient of friction, and specific heat. The pressure, on the other hand, is most affected by thermal expansion and the coefficient of wear. Assessing the effects that different parameters may have on the contact pressure and temperature of sliding bodies has become increasingly important, due to constantly increasing demands on brake performance. The thermal aspects of a friction couple then play an important role, and are often a restricting factor for the braking capabilities of a system. More specifically, a thermoelastic instability (TEI) phenomenon is believed to be the driving force in terms of excessive pressure and temperature. TEI in friction material appears as slowly moving contact points. The cause of this is an interaction between wear and thermal expansion. Moreover, in this paper the sliding material has been modelled as a smooth, but thermally conductive rigid surface. A continuum thermomechanical model was used to calculate the interface pressure and temperature. The model incorporates temperature dependent variables, such as friction and wear. The thermomechanical model was discretized with finite elements, and Newton method was used to solve the resulting system of equations.