Multidimensional Optimization Problem Research Articles

A modified ABC algorithm based on improved-global-best-guided approach and adaptive-limit strategy for global optimization

Artificial bee colony (ABC) is a novel biological-inspired optimization algorithm which has been shown to be more effective for global optimization of multimodal and multidimensional optimization problems, than some other conventional biological-inspired optimization algorithms, such as genetic algorithm (GA) and particle swarm optimization (PSO), for its good exploration capability and the efficient balance between the local search and the global search processes. It has drawn widely attentions from scholars and was applied to various fields for its advantages of excellent global optimization ability and it is easy to implement. However, the basic ABC has some drawbacks such as poor exploitation, slow to converge and hard to find the best solution from all feasible solutions in some cases. In this paper, a modified ABC algorithm based on improved-global-best-guided approach and adaptive-limit strategy for global optimization problems called IGAL-ABC algorithm is proposed. An improved-global-best-guided term with a nonlinear adjusting factor is employed in the update equation. Two nonlinear adjusting factors are applied to control the convergence speed and balance the exploration and exploitation abilities. Multiple dimensions of solution are perturbed each time for generating new candidate food sources. In addition, an adaptive-limit strategy is applied to adjust the limit which controls the frequency that the employed bee abandons its food source, to improve the performance of the algorithm further. Results of experiments tested on multiple benchmark functions show that the proposed method is effective and has good performance. The comparison experiments illustrate that the proposed algorithm has better solution quality and convergence characteristics.

K-Bit-Swap: a new operator for real-coded evolutionary algorithms

There have been a variety of crossover operators proposed for real-coded genetic algorithms (RCGAs). Such operators recombine values from pairs of strings to generate new solutions. In this article, we present a recombination operator for RCGAs that selects the string locations for change separately randomly in the parent and offspring, enabling solution parts to move within a string, and compare it to mainstream crossover operators in a set of experiments on a range of standard multidimensional optimization problems and a real-world clustering problem. We present two variants of the operator, either selecting bits uniformly at random in both strings or sampling the second bit from a normal distribution centered at the selected location in the first string. While the operator is biased toward exploitation of fitness space, the random selection of the second bit for swapping reduces this bias slightly. Statistical analysis of the experimental results using a nonparametric test shows the advantage of the new recombination operators on our test optimization functions.

Induction Motor Parameter Identification Using a Gravitational Search Algorithm

The efficient use of electrical energy is a topic that has attracted attention for its environmental consequences. On the other hand, induction motors represent the main component in most industries. They consume the highest energy percentages in industrial facilities. This energy consumption depends on the operation conditions of the induction motor imposed by its internal parameters. Since the internal parameters of an induction motor are not directly measurable, an identification process must be conducted to obtain them. In the identification process, the parameter estimation is transformed into a multidimensional optimization problem where the internal parameters of the induction motor are considered as decision variables. Under this approach, the complexity of the optimization problem tends to produce multimodal error surfaces for which their cost functions are significantly difficult to minimize. Several algorithms based on evolutionary computation principles have been successfully applied to identify the optimal parameters of induction motors. However, most of them maintain an important limitation: They frequently obtain sub-optimal solutions as a result of an improper equilibrium between exploitation and exploration in their search strategies. This paper presents an algorithm for the optimal parameter identification of induction motors. To determine the parameters, the proposed method uses a recent evolutionary method called the gravitational search algorithm (GSA). Different from most of the existent evolutionary algorithms, the GSA presents a better performance in multimodal problems, avoiding critical flaws such as the premature convergence to sub-optimal solutions. Numerical simulations have been conducted on several models to show the effectiveness of the proposed scheme.

Using Taguchi-Fibonacci search method to optimize phase change materials enhanced buildings with integrated solar photovoltaic thermal collectors

This paper presents optimization of PCMs (phase change materials) enhanced buildings with integrated air-based solar PVT (photovoltaic thermal) collectors, where PCMs are embedded into building envelopes to increase local thermal mass, while the heated air from PVT collectors is directly used for space heating. The objective of the optimization is to maximize the S/N (Signal-to-Noise) ratio of CTPE (Coefficient of Thermal Performance Enhancement) of buildings. The factors optimized are the PVT air flow rate, PCM type, PCM layer thickness and additional wall insulation. Taguchi-Fibonacci search method integrating Taguchi method and Fibonacci search method is developed to solve this optimization problem with continuous and discrete variables. Analysis of Variance is used to determine the percentage contribution of each optimization factor. The simulation results based on a typical Australian house showed that the optimal PVT air flow rate, additional wall insulation, optimal PCM type among the PCMs studied and PCM layer thickness in the search ranges defined were 1640.4 kg/h, 3.0 m2 K/W, SP21E PCM and 30 mm, respectively. Compared to the results without optimization, the CTPEs of the house improved from 45.54 to 72.22%. Taguchi-Fibonacci search method can be useful for solving multi-dimensional design optimization problems with both discrete and continuous variables.

A multiyear DG-incorporated framework for expansion planning of distribution networks using binary chaotic shark smell optimization algorithm

In this paper, a new model for MEPDN (multiyear expansion planning of distribution networks) is proposed. By solving this model, the optimal expansion scheme of primary (i.e. medium voltage) distribution network including the reinforcement pattern of primary feeders as well as location and size of DG (distributed generators) during an ascertained planning period is determined. Furthermore, the time-based feature of proposed model allows it to specify the investments/reinforcements time (i.e. year). Moreover, a minimum load shedding-based analytical approach for optimizing the network's reliability is introduced. The associated objective function of proposed model is minimizing the total investment and operation costs. To solve the formulated MEPDN model as a complex multi-dimensional optimization problem, a new evolutionary algorithm-based solution method called BCSSO (Binary Chaotic Shark Smell Optimization) is presented. The effectiveness of the proposed MEPDN model and solution approach is illustrated by applying them on two widely-used test cases including 12-bus and 33-bus distribution network and comparing the acquired results with the results of other solution methods.

Parallel global optimization on GPU

This work considers a parallel algorithm for solving multidimensional multiextremal optimization problems. This algorithm uses Peano-type space filling curves for dimension reduction. Conditions of non-redundant parallelization of the algorithm are considered. Efficiency of the algorithm on modern computing systems with the use of graphics processing units (GPUs) is investigated. Speedup of the algorithm using GPU as compared with the same algorithm implemented on CPU only is demonstrated experimentally. Computational experiments are carried out on a series of several hundred multidimensional multiextremal problems.

Democracy-inspired particle swarm optimizer with the concept of peer groups

This article proposes to integrate the concept of governance in human society with the nature-inspired particle swarm optimization (PSO) algorithm. A population-based iterative global optimization algorithm, called Democracy-inspired particle swarm optimization with the concept of peer groups (DPG-PSO) has been developed for solving multidimensional, non-linear, non-convex, and multimodal optimization problems by exploiting the concept of the new peer-influenced topology. Here the particles, each of which model a candidate solution of the problem under consideration, are given a choice to follow two possible leaders who have been selected on the basis of a voting mechanism. The leader and the opposition have their influences proportional to the total number of votes polled in their favor. A detailed empirical study comprising tuning of DPG-PSO parameters and its optimizing mechanism has been presented in the paper. The algorithm is tested in a standard benchmark suite consisting of unimodal, multimodal, shifted and rotated functions. DPG-PSO is found to statistically outperform seven other well-known PSO variants in terms of final accuracy and robustness over majority of the test cases, thus, proving itself as an efficient algorithm.

Local Tuning in Peano Curves-based Global Optimization Scheme

This paper considers one of the methods to account for the local information on the objective function in Lipschitz global optimization problems. In the course of solving such problems, an issue arises regarding estimating the Lipschitz constant of the objective function arises. According to the classic scheme, this constant is a single estimate for the whole search domain. The method of accounting for local properties is based on building estimates of Lipschitz constants for the search subdomains, and has previously been investigated for the one-dimensional case. For solving multidimensional problems, dimension reduction is applied. A multidimensional optimization problem is reduced to a one-dimensional problem, for which the objective function satisfies the Hölder condition. In this paper, the application of building local Hölder constant estimates in reduced multidimensional optimization problems using the same scheme as is used in one-dimensional Lipschitzian problems is considered.

Parameter identification for fractional-order multi-scroll chaotic systems based on original dual-state transition algorithm

Parameter estimation for fractional-order chaotic systems is a multi-dimensional optimization problem, which is one of the important issues in fractional-order chaotic control and synchronization. With the orthogonal learning strategies and the original dual learning mechanism, the original dual-state transition algorithm is proposed for solving the problem of parameter estimation in fractional-order chaotic systems. The orthogonal learning strategy is presented which can increase the diversity of initial population and improve the convergence ability. And the original dual learning mechanism is presented which can increase the space ability of states, and also can improve the search capability of the algorithm. In the process of identification, we adopt Radau IIA method to solve the fractional-order differential equation. The simulation of the fractional-order multi-scroll chaotic systems with or without noise is conducted and the results demonstrate the e?ectiveness, robustness, and versatility of the proposed algorithm.

A Maximization Problem in Tropical Mathematics: A Complete Solution and Application Examples

A multidimensional optimization problem is formulated in the tropical mathematics setting as to maximize a nonlinear objective function, which is defined through a multiplicative conjugate transposition operator on vectors in a finite-dimensional semimodule over a general idempotent semifield. The study is motivated by problems drawn from project scheduling, where the deviation between initiation or completion times of activities in a project is to be maximized subject to various precedence constraints among the activities. To solve the unconstrained problem, we first establish an upper bound for the objective function, and then solve a system of vector equations to find all vectors that yield the bound. As a corollary, an extension of the solution to handle constrained problems is discussed. The results obtained are applied to give complete direct solutions to the motivating problems from project scheduling. Numerical examples of the development of optimal schedules are also presented.

Lifetime Enhancement of WSN using Energy-Balanced Distributed Clustering Algorithm with Honey Bee Optimization

Wireless sensor network consists of sensor nodes with sensing and communication capabilities. Typical communication model of wireless sensor network consists of several sensor nodes as group members, sensor head and sinks. Past few years have witnessed increased in the potential use of Wireless Sensor Network (WSN) such as military surveillance, tracking and monitoring, disaster management and combat field reconnaissance. Many issues in WSN are formulated as multidimensional optimization problem and solved through energy based distributed clustering techniques [1]. The main problem in WSN is the lifetime of network. To support scalability, nodes are often grouped in clusters having a leader, often referred as Sensor Head (SH). A SH is responsible for not only sending data to base station but also assists the general nodes to send sensed data to target nodes. The energy consumption of SH is greater than general nodes. Therefore SH selection will affect the lifetime of WSN and also support packet loss. This proposed approach is based on Energy-Balanced Distributed Clustering (EBDC) [2–3] algorithm. Honey bee optimization with some parameters is employed over EBDC algorithm for effective dynamic cluster head selection. This approach helps in increasing the energy consumption. This proposed technique works in three stages: Cluster nodes send data to SH, SH sends data directly to leader and leader sends data to Base Station (BS). Sensor Head (SH) has responsibility to select neighbor node as a Sub Sensor Head (SSH) to reduce overload. Simulations results demonstrate that EBDC-HBO algorithm improves the life time of network.

Efficient Generation of Models of Fed-Batch Fermentations for Process Design and Control

The paper presents a fast and efficient approach to the generation of process models for fed-batch fermentation processes. Elementary Modes (EM) with kinetic terms are used as macro-react ions in the model. A method based upon dynamic metabolic flux analysis (DMFA) is used to find an optimal selection of EM based on concentration measurements instead of reaction rates that must be calculated from the measurements. A multi-objective genetic algorithm is used to investigate the tradeoff between the number of EM and the difference of the estimated concentration profiles from the available measurements. Thus the number of macro-reactions for the model is kept small but the measured data are described sufficiently well by the selected EM. The influence of the process conditions on each macro-reaction rate are identified by a statistical analysis and kinetic expressions are fitted to the estimated evolutions by solving multiple simple optimization problems instead of a multi-dimensional large-scale nonlinear parameter optimization problem. The resulting process model provides a good fit of the measurement data. Provided that the data is generated by a systematic approach, e.g., using a design of experiments strategy, the modelling procedure provides models of adequate complexity that are valid within the so-called design space of the process.

A Parameter Estimation Method for Nonlinear Systems Based on Improved Boundary Chicken Swarm Optimization

Parameter estimation is an important problem in nonlinear system modeling and control. Through constructing an appropriate fitness function, parameter estimation of system could be converted to a multidimensional parameter optimization problem. As a novel swarm intelligence algorithm, chicken swarm optimization (CSO) has attracted much attention owing to its good global convergence and robustness. In this paper, a method based on improved boundary chicken swarm optimization (IBCSO) is proposed for parameter estimation of nonlinear systems, demonstrated and tested by Lorenz system and a coupling motor system. Furthermore, we have analyzed the influence of time series on the estimation accuracy. Computer simulation results show it is feasible and with desirable performance for parameter estimation of nonlinear systems.

Fitness Proportionate Random Vector Selection based DE Algorithm (FPRVDE)

Differential Evolution (DE) is a simple, powerful and easy to use global optimization algorithm. DE has been studied in detail by many researchers in the past years. In DE algorithm trial vector generation strategies have a significant influence on its performance. This research studies that whether performance of DE algorithm can be improved by incorporating selection advancement in effective trial vector generation strategies. A novel advancement in DE trial vector generation strategies is proposed in this research to speeds up the convergence speed of DE algorithm. The proposed fitness proportion based random vector selection DE (FPRVDE) is based on the proportion of individual fitness mechanism. FPRVDE reduces the role of poor performing individuals to enhance it performance capability of DE algorithm. To form a trial vector using FPRVDE, individual based on the proportion of their fitness are selected. FPRVDE mechanism is applied to most commonly used set of DE variants. A comprehensive set of multidimensional function optimization problems is used to access the performance of FPRVDE. Experimental result shows that proposed approach accelerates DE algorithm.

Efficient AM Algorithms for Stochastic ML Estimation of DOA

The estimation of direction-of-arrival (DOA) of signals is a basic and important problem in sensor array signal processing. To solve this problem, many algorithms have been proposed, among which the Stochastic Maximum Likelihood (SML) is one of the most concerned algorithms because of its high accuracy of DOA. However, the estimation of SML generally involves the multidimensional nonlinear optimization problem. As a result, its computational complexity is rather high. This paper addresses the issue of reducing computational complexity of SML estimation of DOA based on the Alternating Minimization (AM) algorithm. We have the following two contributions. First using transformation of matrix and properties of spatial projection, we propose an efficient AM (EAM) algorithm by dividing the SML criterion into two components. One depends on a single variable parameter while the other does not. Second when the array is a uniform linear array, we get the irreducible form of the EAM criterion (IAM) using polynomial forms. Simulation results show that both EAM and IAM can reduce the computational complexity of SML estimation greatly, while IAM is the best. Another advantage of IAM is that this algorithm can avoid the numerical instability problem which may happen in AM and EAM algorithms when more than one parameter converges to an identical value.

An affinity propagation-based multiobjective evolutionary algorithm for selecting optimal aiming points of missiles

When missiles attack the group targets, the selection of their optimal aiming points is a nonlinear, multi-dimensional and multimodal multiobjective optimization problem. To effectively address this problem, an affinity propagation-based multiobjective evolutionary algorithm called APMO is proposed in this article by introducing an affinity propagation and reproduction utility-based adaptive mating selection strategy named as AMS. In AMS, at each generation, an affinity propagation approach is firstly utilized to discover the neighborhood relationship of solutions. Afterward, parent selections for recombination are conducted on the neighborhoods or the whole population based on a mating restriction probability. Moreover, the mating restriction probability is updated at each generation according to the reproduction utility of the neighborhoods and the whole population over the last certain generations. Comprehensive experiments on benchmark instances denote that the proposed APMO significantly outperforms five popular multiobjective evolutionary algorithms, MOEA/D-DE, RM-MEDA, NSGA-II, SPEA2 and MOEA/D-STM. Practical application proves that APMO is promising to select the better optimal aiming points for missiles.

Parameter estimation of unknown fractional-order memristor-based chaotic systems by a hybrid artificial bee colony algorithm combined with differential evolution

In this paper, parameter estimation of unknown fractional-order memristor-based chaotic systems is concerned. Firstly, the parameter estimation is transformed into a multi-dimensional optimization problem, where the fractional orders are treated as independent variables. Then, a hybrid artificial bee colony algorithm combined with differential evolution and other searching mechanisms is put forward to solve the optimization problem. Finally, to demonstrate the effectiveness of the proposed method, numerical simulations based on two typical fractional-order memristor-based chaotic systems are conducted. The simulation results shows that the proposed approach for parameter estimation of unknown chaotic systems is a successful and promising method with higher calculation accuracy, faster convergence speed, and stronger robustness.

Master–slave model-based parallel chaos optimization algorithm for parameter identification problems

The parameter identification problem can be formalized as a multi-dimensional optimization problem, where an objective function is established minimizing the error between the estimated and measured data. In this article, a master–slave model (MSM)-based parallel chaos optimization algorithm (PCOA) (denoted as MSM-PCOA) is proposed for parameter identification problems. The MSM-PCOA is a novel global optimization algorithm, where twice carrier wave chaos search is employed as the master model, while the migration and crossover operation are used as the slave model. The MSM-PCOA is applied to the parameter identification of two different complex systems: bidirectional inductive power transfer system and chaotic systems. Simulation results, compared with other optimization algorithms, show that MSM-PCOA has better parameter identification performance.

Algebraic solutions of tropical optimization problems

We consider multidimensional optimization problems, which are formulated and solved in terms of tropical mathematics. The problems are to minimize (maximize) a linear or nonlinear function defined on vectors over an idempotent semifield, and may have constraints in the form of linear equations and inequalities. The aim of the paper is twofold: first to give a broad overview of known tropical optimization problems and solution methods, including recent results; and second, to derive a direct, complete solution to a new constrained optimization problem as an illustration of the algebraic approach recently proposed to solve tropical optimization problems with nonlinear objective functions.

An Application Adaptation Approach to Mitigate the Impact of Dynamic Thermal Management on Video Encoding

Due to limitations of cooling methods such as using fan and heat sink, dynamic thermal management (DTM) is being widely adopted to manage the temperature of computing systems. However, application of DTM can reduce the system performance and thereby affect the quality of real-time applications. Real-time video encoding, which has high computational need and hard deadlines, is a commonly used application that can be severely affected by the usage of DTM. We study the effect of DTM on a widely used H.264 video encoder and formulate a multidimensional optimization problem to maximize video quality and minimize bit rate while ensuring that the video encoder can run in real time in spite of DTM effects. We model the effects of adapting encoding parameters on video quality, bit rate, and encoder speed. We propose a dynamic application adaptation method to efficiently solve the optimization problem by optimally adapting the encoding parameters in response to DTM effects. In addition, we show that the proposed dynamic application adaptation method would reduce the need for cooling methods such as forced convection cooling. We implement the proposed approach on an Intel® Core™ 2 Duo platform where dynamic voltage and frequency scaling (DVFS) is used for DTM. Our measurements with several videos reveal that when DTM is applied, the video quality is affected significantly. However, using the proposed adaptation algorithm, the encoder can run in real time, and the quality loss is minimized with only a marginal increase in the bit rate.