Multidimensional Optimization Problem Research Articles

Evolutionary calibration of fractional fuzzy controllers

Fuzzy controllers (FCs) that are based on integer schemes have demonstrated their performance in an extensive variety of applications. However, several dynamic systems can be more accurately controlled by fractional controllers yielding an increased interest in generalizing the design of FCs with fractional operators. In the design stage of fractional FCs, the parameter calibration process is transformed into a multidimensional optimization problem where fractional orders, as well as the controller parameters of the fuzzy system, are considered as decision variables. Under this approach, the complexity of the optimization problem tends to produce multimodal error surfaces for which their respective cost functions are significantly difficult to minimize. Several algorithms based on evolutionary computation principles have been successfully applied to identify the optimal parameters of fractional FCs. However, most of them still exhibit serious limitation since they frequently obtain sub-optimal solutions after an improper equilibrium between exploitation and exploration in their search strategies. This paper presents an algorithm for the optimal parameter calibration of fractional FCs. In order to determine the best parameters, the proposed method uses a new evolutionary method called Social Spider Optimization (SSO), which is inspired on the emulation of the collaborative behavior of social-spiders. In SSO, solutions imitate a set of spiders, which cooperate to each other by following the natural laws of a cooperative colony. Unlike most of the existing evolutionary algorithms, the method explicitly evades the concentration of individuals in the best positions, avoiding critical flaws such as the premature convergence to sub-optimal solutions and the limited balance of exploration-exploitation. Numerical simulations have been conducted on several plants to show the effectiveness of the proposed scheme.

Parameter estimation for chaotic systems via a hybrid flower pollination algorithm

Parameter estimation is a fundamental research issue which has attracted great concern in the control and synchronization of chaotic systems. This problem can be mathematically described as a multi-dimensional continuous optimization problem through constructing an appropriate fitness function, and then solved via meta-heuristic algorithms. A hybrid flower pollination algorithm is proposed in this paper for solving this problem more efficiently. The proposed algorithm well combines the good global exploration ability of the original flower pollination algorithm and the powerful local exploitation ability of the Nelder–Mead simplex method together by integrating these two methods in a very simple way. The experimental results tested on three typical chaotic system parameter estimation problems with three unknown system parameters, including the Lorenz system, the Rossler system, and the Lorenz system under the noise condition, demonstrate that the algorithm can estimate the unknown parameters efficiently and accurately. The comparisons with the basic flower pollination algorithm and some other four reported methods including the quantum particle swarm optimization, the hybrid adaptive cuckoo search optimization algorithm, the oppositional backtracking search optimization algorithm, and the hybrid algorithm combining differential evolution with artificial bee colony suggest that the proposed algorithm is energy efficient and superior. The proposed algorithm can be used as a new and effective choice for parameter estimation of chaotic systems.

An Orthogonal Multi-Swarm Cooperative PSO Algorithm with a Particle Trajectory Knowledge Base

A novel orthogonal multi-swarm cooperative particle swarm optimization (PSO) algorithm with a particle trajectory knowledge base is presented in this paper. Different from the traditional PSO algorithms and other variants of PSO, the proposed orthogonal multi-swarm cooperative PSO algorithm not only introduces an orthogonal initialization mechanism and a particle trajectory knowledge base for multi-dimensional optimization problems, but also conceives a new adaptive cooperation mechanism to accomplish the information interaction among swarms and particles. Experiments are conducted on a set of benchmark functions, and the results show its better performance compared with traditional PSO algorithm in aspects of convergence, computational efficiency and avoiding premature convergence.

Vibration Analysis for Monitoring of Ancient Tie-Rods

This paper presents an application of vibration analysis to the monitoring of tie-rods. An algorithm for the axial load estimation based on experimentally measured natural frequencies is introduced and its application to a case study is reported. The proposed model of a tie-rod incorporates elastic bed-type boundary conditions that represent the contact between stonework and the tie-rod. The weighed differences between experimentally and numerically determined frequencies are minimized with respect to the parameters of the model, the main being the axial load and the stiffness at the tie-rod/wall interface. Thus, the multidimensional optimization problem is solved. Results are analysed in comparison to a model with simple fixed-end boundary conditions. In addition, the analytical formulation of the problem is delivered.

Global Optimization of Multivariate Holderian Functions Using Overestimators

This paper deals with the global optimization of several variables Holderian functions. An algorithm using a sequence of overestimators of a single variable objective function was developed converging to the maximum. Then by the use of α-dense curves, we show how to implement this algorithm in a multidimensional optimization problem. Finally, we validate the algorithm by testing it on some test functions.

Artificial bee colony algorithmbased parameter estimation of fractional-order chaotic system with time delay

It is an important issue to estimate parameters of fractional-order chaotic systems in nonlinear science, which has received increasing interest in recent years. In this paper, time delay and fractional order as well as system’s parameters are concerned by treating the time delay and fractional order as additional parameters. The parameter estimation is converted into a multi-dimensional optimization problem. A new scheme based on artificial bee colony U+0028 ABC U+0029 algorithm is proposed to solve the optimization problem. Numerical experiments are performed on two typical time-delay fractional-order chaotic systems to verify the effectiveness of the proposed method.

Joint Downlink/Uplink Design for Wireless Powered Networks With Interference

This paper jointly investigates the downlink/uplink of wireless powered networks (WPNs), which are exposed to the effect of the cascaded near-far problem , i.e., the asymmetric overall degradation of the users’ performance, due to different path-loss values. More specifically, assuming that the users are able to harvest energy both from interference and desired signals, higher path loss reduces the downlink rate of the far user, while it also negatively affects its uplink rate, since less energy can be harvested during downlink. Furthermore, if the far user is located at the cell edge, its performance is more severely impaired by interference, despite the potential gain due to energy harvesting from interference signals. To this end, we fairly maximize the downlink/uplink users’ rates, by utilizing corresponding priority weights. Two communication protocols are taken into account for the downlink, namely, time division multiple access and non-orthogonal multiple access (NOMA), while NOMA with time sharing is considered for the uplink. The formulated multidimensional non-convex optimization problems are transformed into the equivalent convex ones and can be solved with low complexity. Simulations results illustrate that: 1) a relatively high downlink rate can be achieved, while the required energy is simultaneously harvested by the users for the uplink and 2) dowlink NOMA is a more appropriate option with respect to the network topology, especially when a high downlink rate is desired.

The Method for Optimisation of Gas Compressors Performance in Gas Storage Systems

We present a computational method for achieving an optimal operation of compressor units used in industrial gas storage systems. The proposed method is capable to operate with a mix of compressor types (i.e., with different operational parameters, different power drives, and different types of construction, e.g., reciprocal and turbocompressors). The goal of the optimisation is to find an optimal compressors configuration and distribution of the compressor loads for each instance of time. The proposed method is based on conversion of a multidimensional discrete-continuous optimisation problem into a set of independent combinatorial and nonlinear optimisation problems. We derive the mathematical foundations of the algorithms. The exemplary results of the application are presented. [Received: May 4, 2016; Accepted: December 2, 2016]

Design of image enhancement filters using a novel parallel particle swarm optimisation algorithm

Designing image enhancement filters with arbitrary frequency response subject to stability constraints is a complex multidimensional optimisation problem. In this paper a novel parallel particle swarm optimisation algorithm (PPSO) is proposed and applied to the design of infinite impulse response image filters. The proposed PPSO consists of two phases: in the first phase, the particle swarm in the classical PSO algorithm is divided into subpopulations that evolve on separate cores of a multi-core machine. Best solutions from each sub population are then interchanged between cores. In the second phase a local search using Nelder-Mead simplex is done to refine the solution. Classical PSO is used for global exploration to explore multiple local minima whereas Nelder-Mead helps refine the solution computed by the PSO. The PPSO outperformed other global optimisation algorithms in terms of the mean square error between the ideal and designed filter frequency responses and CPU usage.

A Novel Modification of PSO Algorithm for SML Estimation of DOA.

This paper addresses the issue of reducing the computational complexity of Stochastic Maximum Likelihood (SML) estimation of Direction-of-Arrival (DOA). The SML algorithm is well-known for its high accuracy of DOA estimation in sensor array signal processing. However, its computational complexity is very high because the estimation of SML criteria is a multi-dimensional non-linear optimization problem. As a result, it is hard to apply the SML algorithm to real systems. The Particle Swarm Optimization (PSO) algorithm is considered as a rather efficient method for multi-dimensional non-linear optimization problems in DOA estimation. However, the conventional PSO algorithm suffers two defects, namely, too many particles and too many iteration times. Therefore, the computational complexity of SML estimation using conventional PSO algorithm is still a little high. To overcome these two defects and to reduce computational complexity further, this paper proposes a novel modification of the conventional PSO algorithm for SML estimation and we call it Joint-PSO algorithm. The core idea of the modification lies in that it uses the solution of Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT) and stochastic Cramer-Rao bound (CRB) to determine a novel initialization space. Since this initialization space is already close to the solution of SML, fewer particles and fewer iteration times are needed. As a result, the computational complexity can be greatly reduced. In simulation, we compare the proposed algorithm with the conventional PSO algorithm, the classic Altering Minimization (AM) algorithm and Genetic algorithm (GA). Simulation results show that our proposed algorithm is one of the most efficient solving algorithms and it shows great potential for the application of SML in real systems.

Consistent Synchronization of Action Order with Least Noticeable Delays in Fast-Paced Multiplayer Online Games

When running multiplayer online games on IP networks with losses and delays, the order of actions may be changed when compared to the order run on an ideal network with no delays and losses. To maintain a proper ordering of events, traditional approaches either use rollbacks to undo certain actions or local lags to introduce additional delays. Both may be perceived by players because their changes are beyond the just-noticeable-difference (JND) threshold. In this article, we propose a novel method for ensuring a strongly consistent completion order of actions, where strong consistency refers to the same completion order as well as the same interval between any completion time and the corresponding ideal reference completion time under no network delay. We find that small adjustments within the JND on the duration of an action would not be perceivable, as long as the duration is comparable to the network round-trip time. We utilize this property to control the vector of durations of actions and formulate the search of the vector as a multidimensional optimization problem. By using the property that players are generally more sensitive to the most prominent delay effect (with the highest probability of noticeability P notice or the probability of correctly noticing a change when compared to the reference), we prove that the optimal solution occurs when P notice of the individual adjustments are equal. As this search can be done efficiently in polynomial time ( ∼ 5ms) with a small amount of space ( ∼ 160KB), the search can be done at runtime to determine the optimal control. Last, we evaluate our approach on the popular open-source online shooting game BZFlag.

A set of novel continuous action-set reinforcement learning automata models to optimize continuous functions

Learning automata (LA) as a powerful tool for reinforcement learning which belongs to the subject of Artificial Intelligence, could search for the optimal state adaptively in a random environment. In the past decades quite a few FALA algorithms are maturely developed but exposing critical defects, when they are applied to optimize continuous functions. In order to overcome their shortcomings and explore a higher-performance LA, we propose a novel CALA algorithm to solve the function optimization problems via one kind of LA prototypes, i.e, the continuous action-set reinforcement learning automata, which is abbreviated as CARLA. The key mechanism of the proposed algorithm lies in a combination of equidistant discretization and linear interpolation. Specifically, four categories of application models are constructed. Two of them are created to obtain continuous actions when the priori information is finite ones, thus avoiding the drawbacks of FALA. The realization of this functionality recourses to the so-called cumulative distribution function (CDF) and a new concept of area surrounded by curves (AsbC) respectively. The other two models are modified versions to balance the trade-off between accuracy and speed. Moreover, these models are expanded to their generalized versions so that multidimensional function optimization problems can be handled as well. A massive amount of experiments including four benchmarks and three scenarios are designed to demonstrate the effectiveness and efficiency of the proposed application models. The proposed algorithm outperforms the state of the arts of LA as well as optimization algorithms, with a high accuracy rate, a fast convergence speed, and a competitive time consumption, especially in noised environments.

Conjunctive Operation of Reservoirs and Ponds Using a Simulation-Optimization Model of Irrigation Systems

Water resource management in arid agricultural irrigation regions is a great challenge for managers and decision makers. In some of those regions, many ponds have been built to ensure an adequate water supply for irrigation. Therefore, reservoirs and ponds should be managed conjunctively to minimize shortages of water. In this study, a new integrated mathematical model of conjunctive, or integrated, operation of reservoirs and ponds to maximize the water supply has been proposed for a reservoir-pond irrigation system. This objective has been achieved via the use of two models: an optimal model, which is used to determine the optimal discharge of reservoirs, and a simulation model, which considers the regulatory role of ponds and reservoirs and simulates their water supply to the irrigation system. An adaptive genetic algorithm has been employed in this study to solve the nonlinear and multi-dimensional reservoirs optimization problem. This methodology has been applied to the Yarkant River Basin to demonstrate its applicability, and three scenarios are presented. The main objective of the simulation-optimization model in the Yarkant River Basin is to minimize shortages in meeting irrigation demands for nine sub-irrigation systems subject to the constraint of ecological water transfer to the Tarim River. The optimizing effect of the model was particularly prominent under the third scenario, i.e., the XBD, MMK, and ART Reservoirs and 16 ponds conjunctively operated to meet the water demand of the YKB. The frequency of success (FS) in meeting agricultural water demands reaches up to 75%, and the value for ecological demand is 50.98%. The results demonstrate the importance of the conjunctive combined use approach for management of water resources in irrigation system of arid regions.

A Method for Decomposition of the Basic Reaction of Biological Macromolecules into Exponential Components.

The structural and dynamical properties of biological macromolecules under non-equilibrium conditions determine the kinetics of their basic reaction to external stimuli. This kinetics is multiexponential in nature. This is due to the operation of various subsystems in the structure of macromolecules, as well as the effect of the basic reaction on the structure of macromolecules. The situation can be interpreted as a manifestation of the stationary states of macromolecules, which are represented by monoexponential components of the basic reaction (Monod-Wyman-Changeux model) Monod et al. (J Mol Cell Biol 12:88–118, 1965). The representation of multiexponential kinetics of the basic reaction in the form of a sum of exponential functions left(A(t)={displaystyle {sum}_{i=1}^n{a}_i{e}^{-{k}_it}}right) is a multidimensional optimization problem. To solve this problem, a gradient method of optimization with software determination of the amount of exponents and reasonable calculation time is developed. This method is used to analyze the kinetics of photoinduced electron transport in the reaction centers (RC) of purple bacteria and the fluorescence induction in the granum thylakoid membranes which share a common function of converting light energy.

Decoupling linear and nonlinear regimes: an evaluation of efficiency for nonlinear multidimensional optimization

Solving a large subset of multidimensional nonlinear optimization problems can be significantly improved by decoupling their intrinsically linear and nonlinear parts. This effectively decreases the dimensionality of the problem, reduces the search space and improves the efficiency of the optimization. This decoupled approach is generalized with mathematical formalism and its superiority over standard methods empirically verified and quantified on a couple of examples involving $$\chi ^2$$ź2 curve fitting to data.

Monotone Comparative Statics for Cut-Offs

I show that by taking path integral along the so-called diagonally increasing path, the interval dominance order proposed by Quah and Strulovici (2009) can be applied to a class of multi-dimensional optimization problems with cut-off rules. Two applications are included: optimal switching time and monotone pragmatics.

A novel two-stage evolutionary optimization method for multiyear expansion planning of distribution systems in presence of distributed generation

In this paper, a new approach for multiyear expansion planning of distribution systems (MEPDS) is presented. The proposed MEPDS model optimally specifies the expansion schedule of distribution systems including reinforcement scheme of distribution feeders as well as sizing and location of distributed generations (DGs) during a certain planning horizon. Moreover, it can determine the optimal timing (i.e. year) of each investment/reinforcement. The objective function of the proposed MEPDS model minimizes the total investment, operation and emission costs while satisfying various technical and operational constraints. In order to solve the presented MEPDS model as a complicated multi-dimensional optimization problem, a new two-stage solution approach composed of binary modified imperialist competitive algorithm (BMICA) and Improved Shark Smell Optimization (ISSO), i.e. BMICA+ISSO, is presented. The performance of the suggested MEPDS model and also two-stage solution approach of BMICA+ISSO is verified by applying them on two distribution systems including a classic 34-bus and a real-world 94-bus distribution system as well as a well-known benchmark function. Additionally, the achieved results of BMICA+ISSO are compared with the obtained results of other two-stage solution methods.

A MODEL FOR PROFIT PATTERN MINING BASED ON GENETIC ALGORITHM

Mining profit oriented patterns is a novel technique of association rule mining in data mining, which basically focuses on important issues related with business. As it is well known that every business aims to generate the profit and find the ways to improve the same. In earlier days association rule mining was used for market basket analysis and targeted only some of the business and commercial aspects. Afterwards the researchers started to aim the most prominent element of any business i.e. Profit, and determined the innovative way to generate the association rules based on profit. Profit oriented patterns mining approach combines the statistic based pattern mining with value-based decision making to generate those patterns with the maximum profit and some ways to generate recommenders for future strategy. To achieve the desired goal the traditional association rule mining alone is not effectual, so we combine the strength of genetic algorithm with association rule mining to enhance its capability. The study shows that Genetic Algorithm improves the effectiveness and efficiency of association rule mining outcome, since genetic algorithms are competent to handle the problems related with the uncertainty, multi-dimensional, non-differential, non-continuous, and non-parametrical, non-linearity constraint and multi-objective optimization problems. In this paper we apply the concept of profit pattern mining with genetic algorithm to generate profit oriented pattern which help out in future business expansion and fulfill the business objective.

Array Factor Optimization of an Active Planar Phased Array Using Evolutionary Algorithm

Evolutionary algorithms (EAs) have the potential to handle complex, multi-dimensional optimization problems in the field of phased array. Out of different EAs, particle swarm optimization (PSO) is a popular choice. In a phased array, antenna element failure is a common phenomenon and this leads to degradation of the array factor (AF) pattern, primarily in terms of increased side lobe levels (SLLs), displacement of nulls and reduction in the null depths. The recovery of a degraded pattern using a cost and time-effective approach is on demand. In this context, an attempt made to obtain an optimized AF pattern after fault in a 49 elements quasi-circular aperture equilateral triangular grid active planar phased array using PSO. In the paper, multiple cases on recovery are discussed having a maximum 20% element failure. Each recovery is also further evaluated by different statistical analyses. A dedicated software tool was developed to carry out the work presented in this paper.

Application-Oriented Stochastic Energy Management for Plug-in Hybrid Electric Bus With AMT

Taking the complex but regular characteristics of bus routines into account, the stochastic dynamic programming (SDP) might be a method with more potential to optimize the energy management of a plug-in hybrid electric bus (PHEB). However, the discrete transmission system and the continuous power system make it a complicated multidimensional optimal problem, particularly for PHEB with automated mechanical transmission (AMT), and the optimal decisions, which are obtained based on historical data, might not always well satisfy the driver's expectation to vehicle maneuverability under various driving conditions. To solve these problems, an adaptive approach based on the SDP is proposed in this paper. Exhaustively, the SDP is propelled into the input of the transmission to only optimize the torque split under the special gearshift logic, which reduces the dimensions of optimization and obtains more applicable optimal sequences. Then, an adaptive factor, which trades off the vehicle fuel economy and drivability in real time by dynamically adjusting the gearshift points and the torque split, is developed for the variation of the complicated bus driving cycles. The simulation results demonstrate that the proposed method could well respond to the variations of the driving conditions (e.g., road grade and vehicle load). Furthermore, the performance of the proposed method is discussed in detail by comparisons with different control strategies. More importantly, the proposed approach has great potential to be applied in practice.