Hooke-Jeeves Pattern Search Research Articles

Structural damage identification considering uncertainties based on a Jaya algorithm with a local pattern search strategy and L0.5 sparse regularization

This study develops an improved Jaya algorithm for structural damage identification considering various uncertainties using vibration data. Most studies consider uncertainties, such as measurement noise, modeling uncertainties, and temperature variations separately but few on their coupling effects. On the other hand, the Jaya algorithm may trap local minimums in optimizing complex objective functions. Therefore, a novel modified Jaya algorithm is developed by integrating the one-step K-means clustering, Hooke–Jeeves pattern search, and linear population reduction strategies. The three modification strategies greatly improve the global optimization performance of the standard Jaya algorithm, which is verified by a series of high-dimension test functions. An L0.5 regularization is applied to improve the ill-posedness of the damage identification problem and ensure the sparsity of the solution. Numerical and experimental studies on two structures show that the proposed algorithm can identify the structural damage accurately, even considering the coupling effects of various types of uncertainties.

A peak-period taxi scheme design problem: Formulation and policy implications

Taxis are one of the most important urban transportation modes which provide prompt and comfortable service to customers. It is commonly known that demand for and supply of taxis fluctuate at different times of a day, leading to peak periods when customer waiting time for taxis is longer and the quality of taxi service is lower than that of the off-peak periods. There have been real-world practices to mitigate the demand-supply imbalance and improve the service quality of taxis during peak periods. For example, a peak-period surcharge is imposed on taxi passengers in Singapore; the city of Perth in Australia introduces a fleet of peak-period taxis (PTs) which are allowed to operate within specific hours as the additional supply to the market. However, there lacks theoretical evidence to tell which means (or both) should be implemented and it is also unclear which factor(s) is determinant to the optimal surcharge and the optimal fleet size and shift of PTs. Moreover, there is no methodology to design the optimal shifts (the permitted operating hours) and fleet size of PTs and the optimal peak-period surcharge. To tackle the above issues, this paper proposes a peak-period taxi scheme design problem (PTSDP) that aims to determine the optimal fleet size/shifts of PTs and a peak-period taxi surcharge. The problem is formulated as a bi-level optimization model in which the upper level is the regulator (government) problem and the lower level stands for the taxi driver problem. The model is solved by a brute force method combined with the Hooke-Jeeves pattern search and the Frank-Wolfe algorithm. Numerical examples are given to give policy implications and managerial insights into the regulation of taxi markets.

Structural health monitoring based on the hybrid ant colony algorithm by using Hooke–Jeeves pattern search

Structural health monitoring is crucial for the timely damage diagnosis of civil infrastructure. This paper explores the damage detection method based on the ant colony algorithm (ACO) by using Hooke–Jeeves (HJ) pattern search for intensification. The HJ is incorporated into the ACO to improve its performance in detecting damages. The damage is simulated by reducing the stiffness of the structural members, via elastic modulus reduction factor. Four civil engineering structures of varying complexity are analysed for low- and high-level damage scenarios to test the efficacy of the proposed approach. An inverse problem is formulated to minimise the objective function based on the frequency response function rather than using the frequency and mode-shape-based approach. The analysis results indicate that the proposed method can locate damages and identify their severity with higher precision than previously used GA, SPSO, and UPSO can.

Maximal coverage hybrid search algorithm for deployment in wireless sensor networks

A vital design aspect in the setting up of a wireless sensor network is the deployment of sensors. One of the key metrics of the quality of deployment is the coverage as it reflects the monitoring capability of the network. Random deployment is a sub-optimal method as it causes unbalanced deployment and requires sensors in excess of the planned deployment to achieve the same level of coverage. To achieve maximum coverage with a limited number of sensors, planned deployment is a preferred choice. Maximizing the coverage of the region of interest with a given number and type of sensors is an optimization problem. A novel maximal coverage hybrid search algorithm (MCHSA) is proposed in this paper to solve this problem. The MCHSA is a hybrid search algorithm that achieves the balance between exploration and exploitation by applying the particle swarm optimization as a global search technique and using the Hooke–Jeeves pattern search method to improve the local search. The algorithm starts with a good initial population. The proposed MCHSA has low computational complexity and fast convergence. The performance of the MCHSA is analyzed by performing a comparison with the existing algorithms in the literature, in terms of coverage achieved and number of fitness function evaluations. The paper also discusses the tuning of parameters of the proposed algorithm.

Heuristic performance improvement of Hooke-Jeeves pattern search algorithm

Heuristic performance improvement of Hooke-Jeeves pattern search algorithm

Optimal design of borehole heat exchangers based on hourly load simulation

This paper proposes an optimization design methodology for borehole heat exchangers coupled with heat pump units by controlling maximum/minimum inlet fluid temperature in the life cycle of ground coupled heat pump system. Base on the hourly performance simulation of ground coupled heat pump system, the optimal combination of the distance between boreholes, borehole depth and borehole number under a given annual cooling/heating load is determined using the Hooke-Jeeves pattern search algorithm. A case study is presented to validate the effectiveness and feasibility of the proposed method for optimal design of borehole heat exchangers. When minimum inlet fluid temperature is decreased from 5 °C to 0 °C, total borehole lengths and total areas required for the installation of single U-pipe borehole heat exchangers are reduced by 13.3% and 75.4% respectively, for double U-pipes borehole heat exchangers, the corresponding reductions are 11.5% and 73.1% respectively. For the same minimum inlet fluid temperature (0 °C), the minimum reduction of total areas required for borehole heat exchangers installation is still up to 21% when the type of borehole heat exchangers is changed from single U-pipe to double U-pipes.

Adaptive backtracking search optimization algorithm with pattern search for numerical optimization

The backtracking search optimization algorithm (BSA) is one of the most recently proposed population-based evolutionary algorithms for global optimization. Due to its memory ability and simple structure, BSA has powerful capability to find global optimal solutions. However, the algorithm is still insufficient in balancing the exploration and the exploitation. Therefore, an improved adaptive backtracking search optimization algorithm combined with modified Hooke-Jeeves pattern search is proposed for numerical global optimization. It has two main parts: the BSA is used for the exploration phase and the modified pattern search method completes the exploitation phase. In particular, a simple but effective strategy of adapting one of BSA's important control parameters is introduced. The proposed algorithm is compared with standard BSA, three state-of-the-art evolutionary algorithms and three superior algorithms in IEEE Congress on Evolutionary Computation 2014 (IEEE CEC2014) over six widely-used benchmarks and 22 real-parameter single objective numerical optimization benchmarks in IEEE CEC2014. The results of experiment and statistical analysis demonstrate the effectiveness and efficiency of the proposed algorithm.

Some Aspects of Crystal Centering During X-ray High-throughput Protein Crystallography Experiment

A set of algorithms and procedures of a crystal loop centering during X-ray high-throughput protein crystallography experiment has been designed and developed. A simple algorithm of the crystal loop detection and preliminary recognition has been designed and developed. The crystal loop detection algorithm is based on finding out the crystal loop ending point (opposite to the crystal loop pin) using image cross section (digital image column) profile analysis. The crystal loop preliminary recognition procedure is based on finding out the crystal loop sizes and position using image cross section profile analysis. The crystal loop fine recognition procedure based on Hooke-Jeeves pattern search method with an ellipse as a fitting pattern has been designed and developed. The procedure of restoring missing coordinate of the crystal loop is described. Based on developed algorithms and procedures the optimal auto-centering procedure has been designed and developed. A procedure of optimal manual crystal centering (Two Clicks Procedure) has been designed and developed. Developed procedures have been integrated into control software system PCCS installed at crystallography beamlines Photon Factory BL5A and PF-AR NW12, KEK.

Production optimization using derivative free methods applied to Brugge field case

Recently production optimization has achieved increasing attention in upstream petroleum industry. Here, we evaluate derivative free optimization methods for determination of the optimal production strategy using a numerical reservoir model which was prepared for a comparative study at the SPE Applied Technology Workshop in Brugge, June 2008. The pattern search Hooke–Jeeves, the reflection simplex Nelder–Mead, a new line-search derivative-free and a generalized pattern search methods are applied to the optimization problem. The line-search derivative-free algorithm is developed based on the existing line-search derivative free algorithms in combination with the Hooke–Jeeves pattern search method. The derivative free optimization results are compared with a gradient based sequential quadratic programming algorithm, but we clearly identify some issues limiting the performance of gradient based algorithms. In real applications our optimization problem is facing very costly function evaluations and at the same time one might have limitations in the computational budget. Therefore we are interested in methods that can improve the objective function with few function evaluations. The line-search derivative-free method performs more efficient and better than the other optimization methods. Ranking among the other four methods is somewhat more difficult, except that the Nelder–Mead method clearly has the slowest performance among these methods. We also observed that optimization with sequential quadratic programming had a high risk of getting trapped in a local optimum, which could be explained by properties of the objective function.

Artificial bee colony algorithm and pattern search hybridized for global optimization

Artificial bee colony algorithm is one of the most recently proposed swarm intelligence based optimization algorithm. A memetic algorithm which combines Hooke–Jeeves pattern search with artificial bee colony algorithm is proposed for numerical global optimization. There are two alternative phases of the proposed algorithm: the exploration phase realized by artificial bee colony algorithm and the exploitation phase completed by pattern search. The proposed algorithm was tested on a comprehensive set of benchmark functions, encompassing a wide range of dimensionality. Results show that the new algorithm is promising in terms of convergence speed, solution accuracy and success rate. The performance of artificial bee colony algorithm is much improved by introducing a pattern search method, especially in handling functions having narrow curving valley, functions with high eccentric ellipse and some complex multimodal functions.

Sediment flux modeling: Calibration and application for coastal systems

Benthic–pelagic coupling in shallow estuarine and coastal environments is an important mode of particle and solute exchange and can influence lag times in the recovery of eutrophic ecosystems. Links between the water column and sediments are mediated by particulate organic matter (POM) deposition to the sediment and its subsequent decomposition. Some fraction of the regenerated nutrients are returned to the water column. A critical component in modeling sediment fluxes is the organic matter flux to the sediment. A method is presented for estimating POM deposition, which is especially difficult to measure, by using a combination of long term time series of measured inorganic nutrient fluxes and a mechanistic sediment flux model (SFM). A Hooke–Jeeves pattern search algorithm is used to adjust organic matter deposition to fit ammonium (NH4+) flux at 12 stations in Chesapeake Bay for up to 17 years.POM deposition estimates matched reasonably well with sediment trap estimates on average (within 10%) and were strongly correlated with previously published estimates based upon sediment chlorophyll-a (chl-a) distribution and degradation. Model versus field data comparisons of NH4+ flux, sediment oxygen demand (SOD), sulfate (SO42−) reduction rate, porewater NH4+, and sedimentary labile carbon concentrations further validated model results and demonstrated that SFM is a powerful tool to analyze solute fluxes. Monthly model-field data comparisons clearly revealed that POM decomposition in the original SFM calibration was too rapid, which has implications for lagged ecosystem responses to nutrient management efforts. Finally, parameter adjustments have been made that significantly improve model-field data comparisons and underscore the importance of revisiting and recalibrating models as long time series (>5 years) become available.

An algorithm for minimization of pumping costs in water distribution systems using a novel approach to pump scheduling

The operation of a water distribution system is a complex task which involves scheduling of pumps, regulating water levels of storages, and providing satisfactory water quality to customers at required flow and pressure. Pump scheduling is one of the most important tasks of the operation of a water distribution system as it represents the major part of its operating costs. In this paper, a novel approach for modeling of explicit pump scheduling to minimize energy consumption by pumps is introduced which uses the pump start/end run times as continuous variables, and binary integer variables to describe the pump status at the beginning of the scheduling period. This is different from other approaches where binary integer variables for each hour are typically used, which is considered very impractical from an operational perspective. The problem is formulated as a mixed integer nonlinear programming problem, and a new algorithm is developed for its solution. This algorithm is based on the combination of the grid search with the Hooke–Jeeves pattern search method. The performance of the algorithm is evaluated using literature test problems applying the hydraulic simulation model EPANet.

Post-Slicing Inspection of Silicon Wafers Using the HJ-PSO Algorithm Under Machine Vision

Producing silicon wafers is a complex and important process for semiconductor manufacturers. Optimally utilizing each wafer to overcome the quartz shortage is tantamount to achieving maximum total profit. This makes the post-slicing inspection task a crucial step. This paper found that determining post-sliced wafer reuse is equal to measuring the maximum inscribed circle (MIC). This can be considered a nonlinear optimization problem. Due to silicon wafer flatness and fragility, we propose a machine vision-based inspection approach that uses a heuristic method to facilitate solving this MIC problem. The proposed method incorporates the Hooke-Jeeves pattern search with particle swarm optimization (PSO) to achieve fast convergence and quality solution. An experimental design was conducted to first verify the feasibility and identify the feasible control parameters for both PSO and the proposed HJ-PSO. Thirty defective wafers were then used to validate the proposed scheme. The experimental results reveal that the proposed scheme is effective and efficient for wafer post-slice inspection.

Artificial Bee Colony Algorithm with Local Search for Numerical Optimization

Artificial bee colony (ABC) algorithm is one of the most recently proposed swarm intelligence algorithms for global numerical optimization. It performs well in most cases; however, there still exist some problems it cannot solve very well. This paper presents a novel hybrid Hooke Jeeves ABC (HJABC) algorithm with intensification search based on the Hooke Jeeves pattern search and the ABC. The main purpose is to demonstrate how the standard ABC can be improved by incorporating a hybridization strategy. The proposed algorithm is tested on a comprehensive set of 3 6 complex benchmark functions and a slope stability analysis problem including a wide range of dimensions. Comparisons are made with the basic ABC and some recent algorithms. Numerical results show that the new algorithm is promising in terms of convergence speed, success rate and solution accuracy .

A novel particle swarm optimization approach for product design and manufacturing

This paper presents a novel optimization approach that is a new hybrid optimization approach based on the particle swarm optimization algorithm and receptor editing property of immune system. The aim of the present research is to develop a new optimization approach and then to apply it in the solution of optimization problems in both the design and manufacturing areas. A single-objective test problem, tension spring problem, pressure vessel design optimization problem taken from the literature and two case studies for multi-pass turning operations are solved by the proposed new hybrid approach to evaluate performance of the approach. The results obtained by the proposed approach for the case studies are compared with a hybrid genetic algorithm, scatter search algorithm, genetic algorithm, and integration of simulated annealing and Hooke-Jeeves pattern search.

A combination method for reliability-redundancy optimization

This study looks at the system reliability optimization problem under different resource and design configuration constraints by providing a new combination method. From the point of view of logistics engineering, reliability optimization applied in the initial system development period plays a key role to affect system maintenance planning, logistics requirements, and related costs during a system’s planned life cycle. Generally, system reliability can be improved by increasing component reliability level or providing redundant components. Hooke–Jeeves pattern search and dynamic programming, applying dominating sequences are combined to develop a model for such a problem. Besides general design configuration and resource capacity constraints, some specific system and subsystem reliability performance constraints are also included in this model. The proposed combination method can be used to obtain the optimal allocations of component redundancy and reliability level by minimizing the total system cost. A couple of numerical examples for different system configurations are provided. The results show that this model can fit various types of problems and can be applied in the design process of system logistics engineering. Finally, the performance of this proposed method and other reliability-redundancy allocation approaches are closely compared and the results turn out to be promising in many aspects.

Empirical comparison of search algorithms for discrete event simulation

Discrete-event simulation is a significant analysis tool for designing complex systems. In the research literature, several deterministic search algorithms have been linked with simulation for industrial applications; but there are few empirical comparisons of the various algorithms. This paper compares the Hooke–Jeeves pattern search, Nelder–Mead simplex, simulated annealing, and genetic algorithm optimization algorithms on variations of four industrial case study simulation problems. The simulation models include combinations of real variables, integer variables, non-numeric variables, deterministic constraints, and stochastic constraints. The genetic algorithm was the most robust, as it found near best solutions for all 25 test problems. However, it required the most replications of all the algorithms. The pattern search algorithm also found near best solutions to small- and medium-sized problems with no non-numeric variables, while requiring fewer replications than the genetic algorithm.

A MODIFIED PATTERN SEARCH METHOD WITH RELAXED LEXICOGRAPHIC MINIMIZATION FOR ENGINEERING DESIGN

In engineering design, many design problems have multiple constraints and objectives, which may be non-differentiable. For this problem type, only zero-order solution methods are applicable. In this paper, a relaxed lexicographic pattern search method is presented for solving this design problem type, where the objectives are preferenced in either an Archimedean or preemptive formulation. The Hooke-Jeeves (HJ) pattern search method is the basis of this method, which is implemented as the MORPS (Multi-Objective Randomized Pattern Search) algorithm. The HJ pattern search method is used because it requires only function values and has an intuitive graphical interpretation through which to gain insight into the nature of complex design spaces. A relatively new class of simultaneous product/process design problem utilizing virtual prototypes to support design for disassembly is introduced to motivate the need for the MORPS algorithm. An example, based on the design of an automotive center console for disassembly, illustrates the application of the MORPS algorithm.

A stochastic optimization approach for roundness measurements

In this paper, we develop a vision-based inspection system for roundness measurements. A stochastic optimization approach has been proposed to compute the reference circles of MIC (maximum inscribing circle), MCC (minimum circumscribing circle) and MZC (minimum zone circle) methods. The proposed algorithm is a hybrid optimization method based on simulated annealing and Hooke–Jeeves pattern search. From the experimental results, it is noted that the algorithm can solve the roundness assessment problems effectively and efficiently. The developed vision-based inspection system can be an on-line tool for the measurement of circular components.

On the robustness of population-based versus point-based optimization in the presence of noise

Practical optimization problems often require the evaluation of solutions through experimentation, stochastic simulation, sampling, or even interaction with the user. Thus, most practical problems involve noise. We address the robustness of population-based versus point-based optimization on a range of parameter optimization problems when noise is added to the deterministic objective function values. Population-based optimization is realized by a genetic algorithm and an evolution strategy. Point-based optimization is implemented as the classical Hooke-Jeeves pattern search strategy and threshold accepting as a modern local search technique. We investigate the performance of these optimization methods for varying levels of additive normally distributed fitness-independent noise and different sample sizes for evaluating individual solutions. Our results strongly favour population-based optimization, and the evolution strategy in particular.