Programming Global Optimization Research Articles

PGA: A new particle swarm optimization algorithm based on genetic operators for the global optimization of clusters.

We have developed a global optimization program named PGA based on particle swarm optimization algorithm coupled with genetic operators for the structures of atomic clusters. The effectiveness and efficiency of the PGA program can be demonstrated by efficiently obtaining the tetrahedral Au20 and double-ring tubular B20, and identifying the ground state clusters through the comparison between the simulated and the experimental photoelectron spectra (PESs). Then, the PGA was applied to search for the global minimum structures of (n = 3-30) clusters, new structures have been found for sizes n = 6, 7, 12, 14, and medium-sized 21-30 were first determined. The high consistency between the simulated spectra and the experimental ones once again demonstrates the efficiency of the PGA program. Based on the ground-state structures of these (n = 3-30) clusters, their structural evolution and electronic properties were subsequently explored. The performance on Au20, B20, , and (n = 3-30) clusters indicates the promising potential of the PGA program for exploring the global minima of other clusters. The code is available for free upon request.

Parameter global optimization and climatic adaptability analysis of PCM glazed system for long-term application

Filling phase change material (PCM) in the glazed system is crucial to achieving thermal inertia enhancement and solar radiation regulation. However, most previous investigations focused on the energy performance of the PCM glazed system (PCMGS) in typical periods, and the optimization of PCMGS was mainly conducted by control variables to obtain the optimal value of a single parameter, which cannot accurately guide for the long-term application of PCMGS. In this paper, a global optimization program coupled with a numerical model of PCMGS and differential evolution algorithm (DEA) was developed. The annual energy performance of PCMGS was simulated as the objective function to obtain the optimal values of 11 parameters. Subsequently, the climatic applicability of PCMGS was demonstrated by comparing the annual energy performance with that of the traditional double-glazed system (TDGS). The results indicate that the objective function value converges to optimal after 2000 iterations. PCMGS performs preeminent adaptability in hot regions, followed by intermediate regions. The energy consumption of the building when PCMGS is used is reduced by 13.80% and 1.58% respectively compared to the TDGS. However, in cold regions, PCMGS reveals deplorable adaptability, as the energy consumption increased by 36.58% compared to the TDGS.

Two-dimensional photonic crystals as selective filters for thermophotovoltaic applications.

The optical properties and performance of the two-dimensional photonic crystal (2D PhC) filters at normal incidence were simulated, and the best geometric parameters were obtained with the help of a global optimization program. The honeycomb structure has better performance, including high in-band transmittance, high out-band reflectance, and low parasitic absorption. The power density performance and conversion efficiency can reach 80.6% and 62.5%. Furthermore, the deeper cavity structure and multi-layer structure were designed to improve the performance of the filter. The deeper one can reduce the influence of transmission diffraction, increases the power density performance and conversion efficiency. The multi-layer structure reduces the parasitic absorption significantly and increases the conversion efficiency to 65.5%. These filters have both high efficiency and high power density, avoid the challenge of high-temperature stability faced by emitters, also easier and cheaper to fabricate compared to the 2D PhC emitters. These results suggest that the 2D PhC filters can be used in thermophotovoltaic systems for long-duration missions to improve the conversion efficiency.

Solving non-monotone equilibrium problems via a DIRECT-type approach

A global optimization approach for solving non-monotone equilibrium problems (EPs) is proposed. The class of (regularized) gap functions is used to reformulate any EP as a constrained global optimization program and some bounds on the Lipschitz constant of such functions are provided. The proposed global optimization approach is a combination of an improved version of the DIRECT algorithm, which exploits local bounds of the Lipschitz constant of the objective function, with local minimizations. Unlike most existing solution methods for EPs, no monotonicity-type condition is assumed in this paper. Preliminary numerical results on several classes of EPs show the effectiveness of the approach.

Fuel consumption reduction by introducing best-mode controller for hybrid electric vehicles

In this paper, a power management system for hybrid electric vehicles is developed and shown to improve the vehicle fuel consumption in various working conditions. A best-mode concept is defined based on the results of the dynamic programming global optimization strategy. It is shown that the use of exclusive control relations for each working mode improves fuel saving. The working state of the engine and one electric motor is used to determine the best-mode of powertrain operation. The best-mode classification also considers the battery state of charge. This enables the controller to specify near optimal working points in a wide range of state of charge. The control rule for each different work-mode is developed based on the dynamic programming results and applying the particle swarm optimization algorithm. The results show that the best-mode controller is capable of achieving fuel consumptions around 97% of that of the offline dynamic programming.

RETRACTED ARTICLE: The energy management strategy for parallel hybrid electric vehicles based on MNN

The energy management of the hybrid electric vehicle is still the research hotspot. In order to improve the fuel economy of the parallel hybrid electric vehicle, a new energy management design method based on the kernel fuzzy C clustering (KFCM) for multi neural network (MNN) is proposed. The global optimal solution is obtained by the dynamic programming global optimization off-line simulation, and the KFCM algorithm is used to cluster the global optimal data set according to the vehicle running mode, and the neural network is established for each cluster. The MNN model structure after training is used as the output of the energy management strategy to realize the real-time optimal allocation of engine and motor torque according to the real-time condition. The simulation results show that the energy management strategy based on KFCM-MNN has good learning simulation ability for dynamic planning energy management strategy, and it is a quasi-optimal control strategy.

Contrastive Study on Torque Distribution of Distributed Drive Electric Vehicle under Different Control Methods

This paper uses certain hub motor distributed electric vehicle driving system as the research object, using several control strategies, such as dynamic programming global optimization algorithm, fuzzy control, and torque equal distribution and realizing the distribution control of the distributed power of the electric drive system. The simulation results show that, under the NEDC road condition, using the dynamic programming algorithm to optimize the torque distribution, the energy consumption of the electric drive system is 8041 kJ, decreased by 4.77% compared to the average torque distribution control and decreased by 3.5% compared to the fuzzy control strategy. The power consumption of the electric vehicle is 20.25 kWh per 100 km, decreased by 1.01 kWh compared to the average torque distribution control strategy and decreased by 0.72 kWh compared to the fuzzy control strategy. Under the fixed working condition, the energy efficiency of power system can be improved effectively when the distributed dynamic system torque is optimized by the dynamic programming algorithm. Without considering the global optimization, the fuzzy control can effectively improve the energy efficiency of the power system compared to the torque average distribution strategy.

Examination and Optimization of a Heating Circuit for Energy‐Efficient Buildings

AbstractThe conference center darmstadtium in Darmstadt is a prominent example of energy efficient buildings. Its heating system consists of different source and consumer circuits connected by a Zortström reservoir. Our goal was to reduce the energy costs of the system as much as possible. Therefore, we analyzed its supply circuits. The first step towards optimization is a complete examination of the system: 1) Compilation of an object list for the system, 2) collection of the characteristic curves of the components, and 3) measurement of the load profiles of the heat and volume‐flow demand. Instead of modifying the system manually and testing the solution by simulation, the second step was the creation of a global optimization program. The objective was to minimize the total energy costs for one year. We compare two different topologies and show opportunities for significant savings.

Hybrid electric vehicle modeling accuracy verification and global optimal control algorithm research

Vehicle modeling and simulation is a very important part in the design and development of electric and hybrid vehicles. To precisely simulate the powertrain running status, many commercial software products are applied into the development of control strategy. However, these models cost too much time in the simulation analysis, which would be difficult to apply in the control strategy optimization. Therefore, vehicle dynamic system model is built by the software of matlab/Simulink and this vehicle model is compared with the commercial vehicle simulation model. Simulation results show that this model has relatively high simulation accuracy, which lays the foundation for further vehicle performance optimization. In this study, dynamic programming global optimization algorithm is applied on the hybrid electric vehicle to search the optimal solution in the determinate speed cycle. Obviously, this method can obtain the minimum fuel economy while keep the balance of battery state of charge (SOC), but it is difficult to apply in the real-time control system. Therefore, the optimal gear-shifting rules, vehicle operation mode control rules and engine torque control rules under the different of battery SOC are extracted into the rule-based control algorithm. Simulation results show that rule-based optimized control based on the DP control rules can reduce about 13.20% of fuel consumption when compared to original logic rule control algorithm under the China's urban driving cycle. It could obtain better fuel economy under the Beijing driving cycle and easily be implemented in a vehicle prototype.

Optimal Control of Saccharomyces cerevisiae. Fermentation Process

This article demonstrates the existence of multiple optimal control profiles for the fermentation process involving Saccharomyces cerevisiae. The Jones–Kompala model is used to model the dynamics of the fermentation process. Both dilution rate and the oxygen mass transfer coefficient are used as the control variables individually and together. While it was demonstrated recently that the steady-state optimization for the Jones–Kompala model would reveal multiple optimum solutions, this work demonstrates the existence of multiple optimum control profiles when dynamic optimization is performed. To perform the dynamic optimization, the differential equations were converted to a nonlinear program (NLP) using Radau collocation with finite elements and the state-of-the-art optimization program CONOPT (constrained optimizer) was used to obtain the local optimum profiles. The global solution was confirmed using the deterministic global optimization program branch-and-reduce optimization navigator. Both the programs were accessed through the network enabled optimization system (NEOS) server.

A Mathematical Approach To Demand Estimation In Multi-Segment Oligopoly Markets - With An Application To The Automobile Market

<p class="MsoNormal" style="text-align: justify; line-height: normal; margin: 0in 0.5in 0pt;"><span style="font-size: 10pt;"><span style="font-family: Times New Roman;">The purpose of this paper is to develop a purely mathematical approach to determining consumer demand. The model developed allows the researcher to derive demand in an oligopoly market from observed firm output and market prices using only assumptions about each firm, modest restrictions on consumer behavior, and limitations on market structure. The advantage of this revealed demand approach is that it does not require the specification of the consumer’s utility function or any firm’s production function. In addition, this mathematical approach allows for the estimation of own price and cross price elasticities of demand without statistical regression. </span></span></p><p class="MsoNormal" style="text-align: justify; line-height: normal; margin: 0in 0.5in 0pt;"><span style="font-size: 10pt;"><span style="font-family: Times New Roman;"> </span></span></p><p class="MsoNormal" style="text-align: justify; line-height: normal; margin: 0in 0.5in 0pt;"><span style="font-size: 10pt;"><span style="font-family: Times New Roman;">The mathematical model developed is applied to the automobile industry assuming a market characterized by Cournot-Nash behavior and divided into five homogenous vehicle segments. A global optimization program is used to mathematically determine the range of values the coefficients of demand must take in each segment to satisfy market equilibrium. These coefficients can be used to estimate own and cross price elasticities of demand and construct demand equations. </span></span></p><p class="MsoNormal" style="text-align: justify; line-height: normal; margin: 0in 0.5in 0pt;"><span style="font-size: 10pt;"><span style="font-family: Times New Roman;"> </span></span></p><p class="MsoNormal" style="text-align: justify; line-height: normal; margin: 0in 0.5in 0pt;"><span style="font-size: 10pt;"><span style="font-family: Times New Roman;">The elasticity estimates generated by the mathematical model of the automobile industry are compared to other estimates of elasticity found by statistical estimation. It is shown that the mathematical model generates results that are consistent with the statistical methods of the automobile market used by other researchers.<span style="mso-spacerun: yes;">  </span></span></span></p>

Per Mile Emissions Taxes And Lump Sum Emissions Taxes: A Comparative Study Using A Mathematical Approach To Demand Estimation

The primary purpose of this study was to utilize the mathematical approach to demand estimation developed in Culp (2004) to compare two common emissions based taxes. The model assumes Cournot-Nash behavior and divides the automobile market into five homogenous segments. A global optimization program is utilized to mathematically determine the range of values the coefficients of demand must take in each segment to satisfy market equilibrium. Simulations were performed to examine the comparative impact on social welfare of both the per mile emission tax (PMET) and the lump sum emission tax (LSET) in the automotive and travel markets. In the simulations, a global optimization program allows market conditions to change while holding constant the level of pollution reduction, satisfying the other constraints of the model, and satisfying each firm’s first order profit-maximizing conditions. The simulation found that in five of the thirty-two quarters examined, and regardless of market conditions, that the LSET produced more gains from trade. In simulations of the remaining quarters, the outcomes varied depending upon the cross price elasticity of vehicle demand and upon the sensitivity of consumers to vehicle operating cost. The simulations also show that an approximately 20 percent reduction in emissions from new vehicles is achieved by the LSET with a median tax rate of $155.74 per gram of average CO emissions per mile. Consequently, a vehicle that emits an average of two grams of CO per mile would pay a one-time fee of $311.48. The median tax rate required by the PMET is $0.00666 per gram per mile. Accordingly, a vehicle that emits two grams of CO per mile on average would pay $0.0103 per mile or $1332.46 for every 100,000 miles traveled. The difference between the two tax rates, required to achieve the same pollution reduction goal, is likely the result of consumer’s insensitivity to the rise in vehicle operating costs caused by the PMET. This result is consistent with the view that consumers highly discount future payments.

Optimization of Uniaxial Multilayer Cylinders Used for Invisible Cloak Realization

Uniaxial cylindrical cloaks have recently been proposed to prevent scattering of electromagnetic waves, i.e., to render objects invisible. While it is possible to achieve that the rays follow the proper path inside the cloak, the proposed cloaks with reduced variation of constitutive parameters suffer from nonzero reflectance. The purpose of this paper is to improve invisibility performance of the original cloak structure in terms of total scattering width reduction and the operating frequency bandwidth. Therefore, the program for analyzing uniaxial cylindrical structures is merged with the global optimization program based on the particle swarm optimization algorithm. The results show that it is possible either to obtain the “perfect” cloak at the expense of bandwidth or to improve the operating frequency bandwidth at the expense of limited reduction of total scattering width.

MEM Calculations on Apatites Containing Peroxide Using BAYMEM and TOPAS

A set of macros for the powerful least squares and global optimization program TOPAS has been written in order to create a user friendly interface to the maximum entropy method (MEM) program BayMem. As a case study, the crystal structures of pure strontium hydroxyl apatite and strontium hydroxyl apatite with approximately 10% of the hydroxyl anions substituted by peroxide anions were analyzed by TOPAS and BayMem. Although the concentration of peroxide is relatively small, distinct differences in the two crystal structures could be made visible by the MEM.

An application of a global optimization parametrization method on macromolecular structure problem

In this paper, we propose a new parametrization auxiliary function approach on solving global optimization programming of macromolecular potential energy problem that received world wide attention in recent years in terms of the characteristic of the model. Numerical experiments show the method is not only feasible but much more efficient than current method on solving potential energy optimization problem.

An optimization methodology of alkaline–surfactant–polymer flooding processes using field scale numerical simulation and multiple surrogates

After conventional waterflood processes the residual oil in the reservoir remains as a discontinuous phase in the form of oil drops trapped by capillary forces and is likely to be around 70% of the original oil in place (OOIP). The EOR method so-called alkaline–surfactant–polymer (ASP) flooding has proved to be effective in reducing the oil residual saturation in laboratory experiments and field projects through the reduction of interfacial tension and mobility ratio between oil and water phases. A critical step to make ASP floodings more effective is to find the optimal values of design variables that will maximize a given performance measure (e.g., net present value, cumulative oil recovery) considering a heterogeneous and multiphase petroleum reservoir. Previously reported works using reservoir numerical simulation have been limited to sensitivity analyses at core and field scale levels because the formal optimization problem includes computationally expensive objective function evaluations (field scale numerical simulations). This work presents a surrogate-based optimization methodology to overcome this shortcoming. The proposed approach estimates the optimal values for a set of design variables (e.g., slug size and concentration of the chemical agents) to maximize the cumulative oil recovery from a heterogeneous and multiphase petroleum reservoir subject to an ASP flooding. The surrogate-based optimization approach has been shown to be useful in the optimization of computationally expensive simulation-based models in the aerospace, automotive, and oil industries. In this work, we improve upon this approach along two directions: (i) using multiple surrogates for optimization, and (ii) incorporating an adaptive weighted average model of the individual surrogates. The cited approach involves the coupled execution of a global optimization algorithm and fast surrogates (i.e., based on Polynomial Regression, Kriging, Radial Basis Functions and a Weighted Average Model) constructed from field scale numerical simulation data. The global optimization program implements the DIRECT algorithm and the reservoir numerical simulations are conducted using the UTCHEM program from the University of Texas at Austin. The effectiveness and efficiency of the proposed methodology is demonstrated using a field scale case study.

A model for designing callable bonds and its solution using tabu search

Abstract We formulate the problem of designing callable bonds as a non-linear, global, optimization problem. The data of the model are obtained from simulations of holding-period returns of a given bond design, which are used to compute a certainty equivalent return, viz., some target assets. The design specifications of the callable bond are then adjusted so that the certainty equivalent return is maximized. The resulting problem is multi-modal, and a tabu search procedure, implemented on a distributed network of workstations, is used to optimize the bond design. The model is compared with the classical portfolio immunization model, and the tabu search solution technique is compared with simulated annealing for solving the global optimization program. It is shown that the global optimization model yields higher returns than portfolio immunization. It is also shown that tabu search is computationally more efficient than simulated annealing in solving the model, and it produces better solutions.

Mathematical modeling of a parallel global optimization algorithm

We describe the formation of a mathematical model of a reasonably complex parallel global optimization program, and the use of this model to assist in the development and understanding of the underlying parallel algorithm. First we discuss the formation of a model that accurately matched execution times of the parallel program on an Intel hypercube. Then we discuss the use of this model to simulate the behavior of our parallel algorithm in a variety of new situations, in order to detect weaknesses in the parallel algorithm and analyze possible improvements to it. We believe that this combination of parallel computer implementation and mathematical modeling is a useful approach in parallel algorithm development.