Random Search Optimization Research Articles

Conjunctive Use Management under Uncertainty Conditions in Aquifer Parameters

Given that conjunctive use operation policies play a vital role in the sustainability of water resources and their optimal allocation, applying realistic conditions of water resource system in management models lead operating rules to be close to natural conditions. In this study, the combined fuzzy logic and direct search optimization technique has been used to account for the uncertainty associated with parameters affecting groundwater table level fluctuations. The mentioned effective parameters include specific yields and inflow recharge and outflow discharge from the aquifer which are often observed trivially or transitorily in management models. Using the hydrogeological area information and piezometric data, the fluctuation range of each parameter is specified to determine the membership function. Applying fuzzy cuts (numbers between zero and one) on each effective parameter and corresponding interval production, random search optimization model is implemented to find the minimum and maximum value of the groundwater table level fluctuations. The fuzzy number of the output parameter can be determined through replicating the above steps. To compare the results of applying uncertainty in providing optimal allocation values, a conjunctive use model was formulated with the aim of minimizing the shortage rate in supplying water demands given the water resources constraints. In this model, the area under study is divided into zones and given the priorities for each zone and considering the importance of the consumption and source types, optimal allocations are determined. The results of the proposed model show that if real conditions are considered in conjunctive use model, the reliability of system will be capable in handling the water supply demands. The results of the proposed model also indicate that it present reliable allocations compared to the static conventional models and that it performs more desirably and practically in allocating supplies to water demands as it duly includes the opinions of the decision-makers involved.

A modified probability collectives optimization algorithm based on trust region method and a new temperature annealing schedule

This article presents a distributed random search optimization method, the trust region probability collectives (TRPC) method, for unconstrained optimization problems without closed forms. Through analyzing the framework of the original probability collectives (PC) algorithm, three potential requirements on solving the original PC model are first identified. Then an interior point trust region method for bound constrained minimization is adopted to satisfy these requirements. Besides, the temperature annealing schedule is also redesigned to improve the algorithmic performance. Since the new annealing schedule is linked to the gradient, it is much more flexible and efficient than the original one. Ten benchmark functions are used to test the modified algorithm. Numerical results show that TRPC is superior to the PC algorithm in iteration times, accuracy, and robustness.

Reinforcement learning of ball screw feed drive controllers

Feedback controllers for ball screw feed drives may provide great accuracy in positioning, but have no close analytical solution to derive the desired controller. Reinforcement Learning (RL) is proposed to provide autonomous adaptation and learning of them. The RL paradigm allows different approaches, which are tested in this paper looking for the best suited for the ball screw drivers. Specifically, five algorithms are compared on an accurate simulation model of a commercial device, with and without a noisy disturbance on the state observation values. Benchmark results are provided by a double-loop PID controller, whose parameters have been tuned by a random search optimization. Action-critic methods with continuous action space (Policy-Gradient and CACLA) outperform the PID controller in the computational experiments, encouraging future research.

Automated Shape Optimization of Orienting Devices for Vibratory Bowl Feeders

Orienting devices for vibratory bowl feeders are still the most widely used system for the automated sorting and feeding of small parts. The design process of these orienting devices has recently been supported by simulation methods. However, this merely shifts the well-known trial-and-error-based adaption of the orienting device's geometry into virtual world. Yet, this does not provide optimal design and, furthermore, requires strong involvement of the developer due to manual shape variation. This paper proposes an optimization algorithm for the automated simulation-based shape optimization of orienting devices for vibratory bowl feeders. First, general formalisms to state the multiobjective optimization problem for arbitrary types of orienting devices and feeding parts are provided. Then, the implementation of the algorithm is described based on Bullet Physics Engine and random search optimization technique. Finally, comparison of simulation results with experimental data point out good accuracy and, thus, great potential of the developed shape optimization software.

Control of a fuel cell based on the SIRMs fuzzy inference model

A typical working mode for the fuel cell hybrid system is that the fuel cell produces constant power output while the auxiliary storage energy device such as ultracapacitor or battery provides the deviation between the desired power demand and the value of the actual operation. This paper concentrates on the control of the fuel cell flow system. The system which is like an under-actuated mechanical system needs to control two objects (the cathode pressure and the air flow) with one manipulated variable (the set voltage of the air mass flow controller). A SIRMs-based fuzzy inference model is successfully implemented in the system. Online random search optimization algorithm based on Simulink C-S functions is developed to adjust the parameters in the model. By alternative control of the two objects, experimental results demonstrate the realization of the control strategy with one adjustment means.

Professor Ryszard Zieliński's contribution to Monte Carlo methods and random number generators. Uniform asymptotics in statistics

The aim of the paper is to summarize contributions of Ryszard Zielinski to two important areas of research. First, we discuss his work related to Monte Carlo methods. Ryszard Zielinski was particularly interested in Monte Carlo optimization. About 10 of his papers concerned stochastic algorithms for seeking extrema. He examined methods related to stochastic approximation, random search and global optimization. We stress that Zielinski often considered computational problems from a statistical perspective. In several articles he explicitly indicated that optimization can be reformulated as a statistical estimation problem. We also discuss relation between the family of Simulated Annealing algorithms on the one hand and some procedures examined earlier by Ryszard Zielinski on the other. Another topic belonging to Monte Carlo methods, in which Ryszard Zielinski has achieved interesting results, is construction of random number generators and examination of their statistical properties. Zielinski proposed an aperiodic generator based on Weil sequences and showed how it can be efficiently implemented. Later he constructed an algorithm which uses several such generators and produces pseudo-random sequences with better statistical properties. The second area of Zielinski’s work discussed here is related to uniform limit theorems of mathematical statistics. We stress the methodological motivation behind the research in this direction. In Zielinski’s view, asymptotic results should hold uniformly with respect to the family of probability distributions under consideration. In his opinion, this requirement comes from the very nature of statistical models and the needs of practical applications. Zielinski examined uniform versions the Weak Law of Large Numbers, Strong Law of Large Numbers and Central Limit Theorem in several statistical models. Some results were rather unexpected. He also gave a necessary and sufficient condition for uniform consistency of sample quantiles. Two papers of Ryszard Zielinski were devoted to uniform consistency of smoothed versions of empirical cumulative distribution function. In one of them he proved a version of Dvoretzky-Kiefer-Wolfowitz inequality.

A Fuzzy Goal Programming Approach for Optimal Product Family Design of Mobile Phones and Multiple-Platform Architecture

Competitiveness of any manufacturing industry depends on its ability to respond quickly to market niches and to produce a variety of high-utility products at relatively low costs. The promising tool to achieve aforesaid goals is the development of an efficient product family design strategy. The collection of shared components across the product family is termed as a platform that allows the saving in additional cost. Unfortunately, a single platform is advantageous only up to a certain extent; firms have sensed the requirement of multiple platforms. In this context, this paper deals with the exploration of product family design and multiple-platform architecture with a view to maximize the overall utility and to minimize the total production cost. This multiobjective problem has two conflicting and incommensurate objectives; therefore, a fuzzy goal programming model is adopted for modeling. The adoption of fuzzy goal programming model aids in combining the two objectives as well as captures the inherent uncertainty involved in decision making. The problem is formulated as a mixed integer program, and, additionally, random search optimization techniques, namely, genetic algorithm, simulated annealing, and Tabu search are being used to resolve the underlying issues. Moreover, in order to illustrate the proposed framework, a hypothetical case study-a family of mobile phones-is considered. Extensive experiments are performed on the underlying case study, and computational results are reported to validate the efficacy of multiple platforms over the single platform.

Optimization of beam line parameters for space charge dominated multi-species beam using random search method

In this Letter we present a method based on random search optimization technique to transport and match a space charge dominated multi-species beam using the recently developed beam envelope equations. This technique optimizes the transport of primary species and maximizes the loss of other unwanted species. To illustrate the utility of the procedure, we have studied and optimized the transport of proton beam in the presence of H2+ and H3+ in a solenoid based transport line. Numerical results of the beam selection and optimized transport parameters have been presented for various values of the total beam current and different fractions of p, H2+, and H3+ species.

Using inverse analysis to find optimum nano-scale radiative surface patterns to enhance solar cell performance

Nano-scale surface patterning can provide highly spectral-directional absorption properties for thin film solar cells. Achieving optimal surface patterning is an inverse optimization problem that requires a numerical procedure capable of scrutinizing the space of geometry parameters to search for an optimal solution. In this paper, 2-D and 3-D thin film amorphous silicon (a-Si) solar cells with periodic structures are considered, whereby the surface of the solar cell is textured with rectangular metallic nano-patterns for enhancing the solar absorption spectrum. We use FDTD simulations to solve Maxwell’s equations inside the cell area when subject to standard optical irradiation. By means of several numerical optimization techniques such as the Quasi-Newton BFGS method, random search Simulated Annealing, and Tabu Search, we determine optimal specifications for surface nano-patterns. Invoking constrained optimization tools, we incorporate various types of practical constraints into the optimization programs. The resulting cell structures found by the inverse solvers illustrate enhancement factors as high as 1.52 in solar absorption when silver nano-patterns are used, compared to bare a-Si cells. Results demonstrate the efficiency of the selected optimization techniques and their computational efficiency in contrast with the naïve brute force alternative and provide a benchmark for comparing the performances of various local and global optimization methods. The global random search optimization techniques (Simulated Annealing and Tabu Search) tend to perform better than the local method (Quasi-Newton), especially for higher problem dimensions.

OPTIMAL PLACEMENT OF PILES IN REAL GRILLAGES: EXPERIMENTAL COMPARISON OF OPTIMIZATION ALGORITHMS

The aim of the article is to choose algorithms suited for optimal placement of piles in real grillages by performing experimental comparison of different global optimization algorithms. The comparison includes several algorithms: random search, metaheuristics (simulated annealing and genetic algorithm) and local optimization combined with random search. The algorithms are compared using the results of optimization of pile placement schemes of 10 practical grillages of small-to-medium scale with data obtained from several design bureaus. The best results have been achieved with simulated annealing and nonlinear optimization algorithm NEWUOA combined with heuristic random search. http://dx.doi.org/10.5755/j01.itc.40.2.427

Design of optimized diffusion-controlled transdermal drug delivery systems

Background: We describe a systematic approach to designing multilayer transdermal patches based on therapeutically relevant specifications of the drug. Method: Random search optimization techniques are used to optimize maximum drug release from the patch subject to the therapeutic specifications. Barrier layer thickness and relative concentrations of the drug in the drug-containing layers are used as key design parameters. Results: A patch made of two drug-containing layers of equal thicknesses and relative drug concentrations of 20% and 80%, and a barrier layer with thickness of 14% compared to the total thickness of drug-containing layers was found to be the most optimum design. Conclusion: The proposed design is almost universally applicable and satisfies therapeutically relevant specifications while maximizing drug utilization.

An incorporate genetic algorithm based back propagation neural network model for coal and gas outburst intensity prediction

The traditional GABP model used in complex coal and gas outbursts prediction, which trains the back-propagation neural networks (BPNN) by Genetic Algorithm (GA), is provided with some limitations, such as massive time-consuming, optimal stop condition of GA pretreatment indeterminacy, independency and complex task of great importance. To overcome these problems, a new method of coal and gas outbursts intensity prediction by Incorporate Genetic Algorithm Based Back Propagation Neural Network (IGABP) is applied to determine parameters of BPNN automatically and propose an efficient GA which reduces its iterative computation time for enhancing the training capacity of BPNN. First, improved GA is based on single population model among continuous generation model and used the modified self-adapted crossover rate, crossover strategy, self-adapted stop criterion, as well as special survival condition. Second, BP operator is introduced into the evolution of GA operations, improving the standard GA optimization of random search and self-guiding optimization searching. To show the validity of the proposed method, we compare it with traditional GABP and IGABP using a dataset. The results show that the IGABP model can effectively overcome the inadequacies of the traditional model, its operating efficiency and forecast performance are improved significantly.

Multi-objective resource assignment problem in a product-driven supply chain using a Taguchi-based DNA algorithm

This paper conceptualises the integration of tangible and intangible factors into the design consideration of a resource assignment problem for a product-driven supply chain. The problem is formulated mathematically as a multi-objective optimisation model to maximise the broad objectives of profit, ahead of time of delivery, quality, and volume flexibility. Product characteristics are associated with the design requirements of a supply chain. Different types of resources are considered, each differing in its characteristics, thereby providing various alternatives during the design process. The aim is to design integrated supply chains that maximise the weighted sum of the objectives, the weights being decided by the desired product characteristics. The problem is solved through the proposed Taguchi-based DNA algorithm that draws its traits from random search optimisation and the statistical design of experiments. In order to minimise the effect of the causes of variations, the fundamental Taguchi method is integrated with the DNA-metaheuristic. The suggested methodology exhibits the global exploration capability to exploit the optimal or near-optimal DNA strands with a faster convergence rate. In order to authenticate the performance of the proposed solution methodology, a set of ten problem instances are considered and the results obtained are compared with that of the basic DNA, particle swarm optimisation (PSO) and its variant (PSO — time varying acceleration coefficients). The results demonstrate the benefits of the proposed algorithm for solving this type of problem.

The Luus-Jaakola algorithm applied to a nuclear reactor core design optimisation

The Luus-Jaakola (LJ) algorithm is a random search optimisation method that has been successfully employed mainly in chemical engineering problems. In this paper, we apply this algorithm to an optimisation problem solved previously with genetic algorithms, particle swarm optimisation and Metropolis algorithms. This problem consists of adjusting several reactor cell parameters, such as dimensions, enrichment and materials, in order to minimise the average peak factor in a three-enrichment-zone reactor, considering restrictions on the average thermal flux, criticality and submoderation. LJ is compared with the aforementioned optimisation algorithms and is shown to perform well, thus demonstrating its potential for other applications.

A strategic planning model for natural gas transmission networks

The design and development of natural gas transmission pipeline networks are multidisciplinary problems that require various engineering knowledge. In this problem, the type, location, and installation schedule of major physical components of a network including pipelines and compressor stations are decided upon over a planning horizon with least cost goal and subject to network constraints. Practically, this problem has been viewed as a conceptual design case and not as an optimization problem that tries to select the best design option among a set of possible solutions. Consequently, conceptual design approaches are usually suboptimal and work only for short-run development planning. We propose an integrated nonlinear optimization model for this problem. This model provides the best development plans for an existing network over a long-run planning horizon with least discounted operating and capital costs. A heuristic random search optimization method is also developed to solve the model. We show the application of the model through a simple case study and discuss how non-economic objectives may also be incorporated into model.

On the convergence rate of the Markov homogeneous monotone optimization method

An estimate of the convergence rate of some homogeneous Markov monotone random search optimization algorithms is obtained.

Generalized DEA model of fundamental analysis and its application to portfolio optimization

Fundamental analysis is used in asset selection for equity portfolio management. In this paper, a generalized data envelopment analysis (DEA) model is developed to analyze a firm’s financial statements over time in order to determine a relative financial strength indicator (RFSI) that is predictive of firm’s stock price returns. RFSI is based on maximizing the correlation between the DEA-based score of financial strength and the stock market performance. This maximization involves a difficult binary nonlinear program that requires iterative re-configuration of parameters of financial statements as inputs and outputs. We utilize a two-step heuristic algorithm that combines random sampling and local search optimization. The proposed approach is tested with 230 firms from various US technology-industries to determine optimized RFSI indicators for stock selection. Then, those selected stocks are used within portfolio optimization models to demonstrate the usefulness of the scheme for portfolio risk management.

Adaptive optics for enhanced signal in CARS microscopy

We report the use of adaptive optics with coherent anti-Stokes Raman scattering (CARS) microscopy for label-free deep tissue imaging based on molecular vibrational spectroscopy. The setup employs a deformable membrane mirror and a random search optimization algorithm to improve signal intensity and image quality at large sample depths. We demonstrate the ability to correct for both system and sample-induced aberrations in test samples as well as in muscle tissue in order to enhance the CARS signal. The combined system and sample-induced aberration correction increased the signal by an average factor of approximately 3x for the test samples at a depth of 700 microm and approximately 6x for muscle tissue at a depth of 260 microm. The enhanced signal and higher penetration depth offered by adaptive optics will augment CARS microscopy as an in vivo and in situ biomedical imaging modality.

Solving Part-Type Selection and Operation Allocation Problems in an FMS: An Approach Using Constraints-Based Fast Simulated Annealing Algorithm

Production planning of a flexible manufacturing system (FMS) is plagued by two interrelated problems, namely 1) part-type selection and 2) operation allocation on machines. The combination of these problems is termed a machine loading problem, which is treated as a strongly NP-hard problem. In this paper, the machine loading problem has been modeled by taking into account objective functions and several constraints related to the flexibility of machines, availability of machining time, tool slots, etc. Minimization of system unbalance (SU), maximization of system throughput (TH), and the combination of SU and TH are the three objectives of this paper, whereas two main constraints to be satisfied are related to time and tool slots available on machines. Solutions for such problems even for a moderate number of part types and machines are marked by excessive computational complexities and thus entail the application of some random search optimization techniques to resolve the same. In this paper, a new algorithm termed as constraints-based fast simulated annealing (SA) is proposed to address a well-known machine loading problem available in the literature. The proposed algorithm enjoys the merits of simple SA and simple genetic algorithm and is designed to be free from some of their drawbacks. The enticing feature of the algorithm is that it provides more opportunity to escape from the local minimum. The application of the algorithm is tested on standard data sets, and superiority of the same is witnessed. Intensive experimentations were carried out to evaluate the effectiveness of the proposed algorithm, and the efficacy of the same is authenticated by efficiently testing the performance of algorithm over well-known functions

Using the correlation criterion to position and shape RBF units for incremental modelling

A novel technique is proposed for the incremental construction of sparse radial basis function (RBF) networks. The correlation between a RBF regressor and the training data is used as the criterion to position and shape the RBF node, and it is shown that this is equivalent to incrementally minimise the modelling mean square error. A guided random search optimisation method, called the repeated weighted boosting search, is adopted to append RBF nodes one by one in an incremental regression modelling procedure. The experimental results obtained using the proposed method demonstrate that it provides a viable alternative to the existing state-of-the-art modelling techniques for constructing parsimonious RBF models that generalise well.