Global Optimal Point Research Articles

FTDZOA: An Efficient and Robust FS Method with Multi-Strategy Assistance.

Feature selection (FS) is a pivotal technique in big data analytics, aimed at mitigating redundant information within datasets and optimizing computational resource utilization. This study introduces an enhanced zebra optimization algorithm (ZOA), termed FTDZOA, for superior feature dimensionality reduction. To address the challenges of ZOA, such as susceptibility to local optimal feature subsets, limited global search capabilities, and sluggish convergence when tackling FS problems, three strategies are integrated into the original ZOA to bolster its FS performance. Firstly, a fractional order search strategy is incorporated to preserve information from the preceding generations, thereby enhancing ZOA's exploitation capabilities. Secondly, a triple mean point guidance strategy is introduced, amalgamating information from the global optimal point, a random point, and the current point to effectively augment ZOA's exploration prowess. Lastly, the exploration capacity of ZOA is further elevated through the introduction of a differential strategy, which integrates information disparities among different individuals. Subsequently, the FTDZOA-based FS method was applied to solve 23 FS problems spanning low, medium, and high dimensions. A comparative analysis with nine advanced FS methods revealed that FTDZOA achieved higher classification accuracy on over 90% of the datasets and secured a winning rate exceeding 83% in terms of execution time. These findings confirm that FTDZOA is a reliable, high-performance, practical, and robust FS method.

Minimisation of losses of consumer quality during storage of cherry fruits under the influence of hydrocooling and protective composition

The need for consumption of fruit products, in particular sweet cherries and cherries, is growing every year in Ukraine. This is driven by national traditions, stakeholder needs, and the population's demand for healthy eating. Cherries are a nutritious fruit that contains such functional ingredients as essential amino acids, vitamins, minerals, dietary fiber, etc. Unfortunately, in terms of long-term storage, cherries quickly lose their quality and have a short harvest and processing period. To increase the shelf life of products, it is advisable to develop and improve methods of storage and processing of cherries. Optimisation of chilling methods for cherries before storage increases the shelf life of fresh fruit and the suitability for fresh consumption. Improving the methods of chilling cherries will help to increase the demand for its fruits by all stakeholders in the European market. The aim of the research was to establish the optimal concentration of acetic and lactic organic acids, which are included in the protective composition for processing cherry fruits, and to determine the level of daily losses of cherry fruits during hydrocooling while maintaining the global optimum point. To establish an effective cooling method, fruit losses caused by diseases of microbiological origin and physiological disorders were determined. During storage, the effect of the concentrations of the protective composition on the indicators of weight loss and the average level of daily fruit loss was studied. A regression model was built and the optimal values of the indicators were determined by stages: a regression model was built on the basis of experimental data and the global optimum point was determined on the basis of the model and a confidence interval for the optimum was built. According to the results of the research, the lowest rate of daily fruit losses at the level of 0,117%-0,121% was recorded during hydrocooling of cherry fruits using organic compositions of lactic and acetic acids in the ratio of their components of 1,25-2,25:1,50-2,25 and 1,75-2,25% with the amount of acetic acid at 1,25%, respectively. The regression analysis showed the optimal value of the average level of daily losses during storage of cherry fruits of the model variety ‘Vstrecha’ – 0,106% at the value of factors x1=2,217 and x2=1,966.

Parameters Estimation of Photovoltaic Modules Using Differential Evolution Metaheuristic Method

This paper presents the analysis of the differential evolution (DE) metaheuristic method, which is used to estimate some parameters employed in the equivalent electrical circuit that represents the photovoltaic (PV) cell model. The DE algorithm is an evolutionary algorithm that can be designed to search global optimal points with fast convergence time and present accurate results, requiring few control variables to be set. The accuracy of reproducing the characteristics of the PV module depends on the knowledge of some PV cell model parameters, such as series and shunt resistances, diode ideality factor, and diode reverse saturation current. Once the referred parameters are not usually given in the manufacturers' datasheet, their determination can be achieved by the DE algorithm, employing data and the current-voltage (I-V) characteristic curve provided by the PV module manufacturers. The technique is designed to minimize the error between the reference I-V curve and the I-V curve reproduced by the DE algorithm. Through simulation results, the feasibility of the DE algorithm to estimate the desired parameters of a PV cell is validated, and the algorithm's performance to reach the best solution with fast convergence and a small iteration number is evaluated.

Bluefin Trevally Optimizer (BTO): A Metaheuristic Algorithm Using Fuzzy Logic Controller for Feature Selection Problem

Metaheuristic algorithms are increasingly used for feature selection (FS) problems due to their robustness and searchability. This study presents a unique optimization technique called fuzzy bluefin trevally optimizer (BTO). BTO draws its inspiration from bluefin’s cooperative nature and sudden ambush behavior. The trevally will jump out of the water and attack its food in the air or even snag it off the water when it is sufficiently close to it. This study uses mathematical modeling to create an optimization algorithm to replicate dynamic patterns and behaviors. Since parameters play a critical role in optimization, we use the fuzzy concept for dynamic parameter adaptation in fuzzy BTO. By introducing the idea of signature and demonstrating that fuzzy BTO converges to the global optimal point, the mathematical basis for the proposed algorithm is provided. The convergence of fuzzy BTO is proved using the Markov chain property. On benchmark functions (BF), the effectiveness of the suggested strategies is evaluated and compared with other metaheuristic algorithms. Then the proposed algorithms are applied to a fuzzy FS problem. Then they are compared with traditional and recent metaheuristic algorithms on the UCI machine learning repository datasets. Finally, the statistical significance is examined using the Kruskal–Wallis test (KWT).

Application of the Parabola Method in Nonconvex Optimization

We consider the Golden Section and Parabola Methods for solving univariate optimization problems. For multivariate problems, we use these methods as line search procedures in combination with well-known zero-order methods such as the coordinate descent method, the Hooke and Jeeves method, and the Rosenbrock method. A comprehensive numerical comparison of the obtained versions of zero-order methods is given in the present work. The set of test problems includes nonconvex functions with a large number of local and global optimum points. Zero-order methods combined with the Parabola method demonstrate high performance and quite frequently find the global optimum even for large problems (up to 100 variables).

Using multi-threshold non-local means joint distribution method to analysis the spatial distribution patterns of binder and fibers in gas diffusion layers of fuel cells

The gas diffusion layer (GDL) in fuel cell plays a crucial role in mass transfer, electron conduction and structural support. The distribution of binder and hydrophobic agent directly affects the mass transfer and conductivity of the fuel cell. In this study, a multi-threshold segmentation-based image processing method was used to distinguish between pores, fibers, and binder in the GDL. The relationship between binder distribution and fiber density as well as the thickness of the binder layer was investigated. Specifically, the study first utilized a joint distribution map based on grayscale values and non-local means values, with global Rényi entropy as the optimization objective. A bee algorithm was employed to search for the global optimal point, achieving threshold segmentation of micro-scale images. Subsequently, by comparing the results of element segmentation using one-dimensional and multi-dimensional segmentation methods, a three-dimensional convolutional kernel of different sizes was used to obtain the distance from each point in the structure to the edge, effectively separating adherent fibers. Finally, convolutional methods were used to analyze the relationship between the thickness of the binder layer and fiber density. It was found that there is a positive correlation between thickness and spatial density of fibers when the fiber layer is thin. These research findings provide theoretical basis for the content and distribution of binder in the basal layer process of GDL fabrication, and contribute to a more accurate description of the microstructure and properties of actual materials, enhancing the understanding of the preparation process and microstructure properties of GDL in fuel cells. The image processing method utilized in this study enables the computation of crucial parameters within the GDLs' multi-component segmentation algorithm, utilizing a limited sample size. Additionally, it offers valuable insights into the spatial distribution characteristics of fibers and the presence of thin matrix layers. These findings highlight the potential of this method for future applications in the realm of realistic three-dimensional structural reconstructions, thus holding promising prospects for further advancements in this field.

A group decision making approach based on the multi-dimensional Steiner point

<abstract> <p>The social division of labor has become increasingly specialized, and there are more and more group decision-making problems participated by multiple decision-makers. With respect to the multi-attribute group decision making problem, including two-tuple linguistic information, based on the theory and method of group decision making, Steiner point constraint and plant growth simulation algorithm, we establish a novel multi-attribute group decision making approach based on two-tuple linguistic information aggregation. We introduce Steiner points into group consensus decision making and use the PGSA algorithm to seek the global optimal point. The method seeks set points that are both mathematically and geometrically meaningful to reduce set bias. In this paper, to begin with, according to the constraints of multi-dimensional Steiner point, we map the evaluation vectors of the group experts over the alternatives into multi-dimensional space and then we propose a two-tuple linguistic information aggregation model. Moreover, we construct a comprehensive evaluation decision making approach and then design a plant growth simulation algorithm to select the optimal alternative. Finally, a case verifies the validity and rationality of the proposed model.</p> </abstract>

Quantized Zeroth-Order Gradient Tracking Algorithm for Distributed Nonconvex Optimization Under Polyak-Łojasiewicz Condition.

This article focuses on distributed nonconvex optimization by exchanging information between agents to minimize the average of local nonconvex cost functions. The communication channel between agents is normally constrained by limited bandwidth, and the gradient information is typically unavailable. To overcome these limitations, we propose a quantized distributed zeroth-order algorithm, which integrates the deterministic gradient estimator, the standard uniform quantizer, and the distributed gradient tracking algorithm. We establish linear convergence to a global optimal point for the proposed algorithm by assuming Polyak-Łojasiewicz condition for the global cost function and smoothness condition for the local cost functions. Moreover, the proposed algorithm maintains linear convergence at low-data rates with a proper selection of algorithm parameters. Numerical simulations validate the theoretical results.

Disturbance rejection controller design based on adaptive nonlinear FOPID controller and chaotic WOA with a neuro-fuzzy approximation for URV robot

This paper presents an adaptive neuro-fuzzy-based nonlinear fractional order proportional integral derivative (ANF-NLFOPID) controller to stabilize six degrees of freedom (6-DOF) underwater robotic vehicle (URV). Generally, the stability of the URV system is jammed due to internal and external variations related to unknown uncertainties and disturbances in the URV model, which lead to trajectory tracking problems. Thus, to solve unknown uncertainties and disturbances problems, an ANF network is proposed to estimate unknown uncertainties and disturbances. At the same time, an NLFOPID controller is proposed to minimize the error effect generated by the variation of the URV model parameters. Considering the unknown and unpredictable behavior of the URV system in the presence of uncertainties and disturbances, the ANF-NLFOPID controller parameters are tuned continuously using an improved whale optimization algorithm based on chaotic theory (IWOA-CT). The main working principle of the IWOA-CT is to solve the local minimum (optimum) problem and achieve the global optimum points to deliver the best parameter values for the ANF-NLFOPID controller. A simulation and experimental results are conducted to measure the performance of the ANF-NLFOPID controller compared to other existing works. MATLAB software is used to simulate four trajectory tracking cases, where the first case proved the superiority of the ANF-NLFOPID controller by 52.559%, 70.028%, and 73.83%, the second case shows that the ANF-NLFOPID improves the trajectory tracking performance by 34.399%, 46.094%, and 59.143%, the third case demonstrates the effectiveness of the ANF-NLFOPID controller by 41.922%, 51.205%, and 62.252%, and the fourth case shows that the ANF-NLFOPID enhance the overall trajectory tracking efficiency by 29.356%, 38.413%, and 44.795% compared to adaptive neural network-based nonlinear FOPID (ANNFOPID), adaptive fuzzy-based nonlinear PID (AFNLPID), and disturbance rejection based on adaptive neural network (DR-ANN) controllers respectively. In the end, the experimental results were conducted using a real-world URV model and showed that the ANF-NLFOPID controller presents superior in solving trajectory tracking problems compared to the ANNFOPID controller.

Big data decision tree for continuous-valued attributes based on unbalanced cut points

The decision tree is a widely used decision support model, which can quickly mine effective decision rules based on the dataset. The decision tree induction algorithm for continuous-valued attributes, based on unbalanced cut points, is efficient for mining decision rules; however, extending it to big data remains an unresolved. In this paper, two solutions are proposed to solve this problem: the first one is based on partitioning instance subsets, whereas the second one uses partitioning attribute subsets. The crucial of these two solutions is how to find the global optimal cut point from the set of local optimal cut points. For the first solution, the calculation of the Gini index of the cut points between computing nodes and the selection of the global optimal cut point by communication between these computing nodes is proposed. However, in the second solution, the division of the big data into subsets using attribute subsets in a way that all cut points of an attribute are on the same map node is proposed, the local optimal cut points can be found in this map node, then the global optimal cut point can be obtained by summarizing all local optimal cut points in the reduce node. Finally, the proposed solutions are implemented with two big data platforms, Hadoop and Spark, and compared with three related algorithms on four datasets. Experimental results show that the proposed algorithms can not only effectively solve the scalability problem, but also have lowest running time, the fastest speed and the highest efficiency under the premise of preserving the classification performance.

Study of cooperative wake control for multiple wind turbines under variable wind speeds/directions

In the wind farm control field, wind turbines are normally manipulated to maximize the individual power production which is named the greedy control. However, this greedy control method can lead to massive losses of total wind farm power production, mainly caused by the wake interference between multiple wind turbines. To this end, the cooperative wake control, which seeks the maximum total power production by coordinating each individual wind turbine at the global optimum operation point, can greatly improve the wind farm output performance. In this paper, we investigate the effectiveness of two different cooperative wake control strategies, i.e., instantaneous control and wind-interval based (WIB) control under variable wind speeds/directions scenario. These two cooperative control strategies are achieved based on the power de-rating operation to the upstream wind turbines. Taking three in-line wind turbines as an example, the control parameters of the two upstream wind turbines are cooperatively optimized while the downstream third wind turbine operates at the maximum power coefficient. To account for the multiple wind turbines wake interference, an artificial neural network (ANN) wake model characterized by the fast computational efficiency and great accuracy, in combination with the best wake superposition model chosen to quantify multiple wake effect, is proposed for the control optimization. By comparing to the baseline greedy control, it shows that both cooperative control strategies are effective in improving the power production of the wind farm. More specifically, the WIB control can maintain the power production at the same level of instantaneous control with a maximum difference less than 3%, while it reduces the operating difficulty to a large extent which greatly facilitates its application under realistic more complex wind scenarios.

Artificial ecosystem optimization by means of fitness distance balance model for engineering design optimization

Optimization techniques have contributed to significant strides in complex real-world engineering problems. However, they must overcome several difficulties, such as the balance between the capacities for exploitation and exploration and avoiding local optimum. An enhanced Artificial Ecosystem Optimization (AEO) is proposed incorporating Fitness Distance Balance Model (FDB) for handling various engineering design optimization problems. In the proposed optimizer, the combined FDB design aids in selecting individuals who successfully contribute to population-level searches. Therefore, the FDB model is integrated with the AEO algorithm to increase the solution quality in nonlinear and multidimensional optimization situations. The FDBAEO is developed for handling six well-studied engineering optimization tasks considering the welded beam, the rolling element bearing, the pressure vessel, the speed reducer, the planetary gear train, and the hydrostatic thrust bearing design problems. The simulation outcomes were evaluated compared to the systemic AEO algorithm and other recent meta-heuristic approaches. The findings demonstrated that the FDBAEO reached the global optimal point more successfully. It has demonstrated promising abilities. Also, the proposed FDBAEO shows greater outperformance compared to several recent algorithms of Atomic Orbital Search, Arithmetic-Trigonometric, Beluga whale, Chef-Based, and Artificial Ecosystem Optimizers. Moreover, it declares great superiority compared to various reported optimizers.

Optimization of a solar-based PEM methanol/water electrolyzer using machine learning and animal-inspired algorithms

This contribution scrutinizes the performance of the integrated photovoltaic thermal (PVT) system with the proton exchange membrane methanol electrolyzer (PEMME) and water electrolyzer (PEMWE) as sustainable ways to produce hydrogen. Artificial neural networks (ANNs), are adopted to evaluate the effect of various operating parameters on the performance of the systems. The adopted ANNs are radial basis function (RBF), extreme learning machine (ELM), long short-term memory (LSTM), and gated recurrent unit (GRU). Moreover, to obtain the optimum performances of the systems, the multi-objective whale optimization algorithm (MOWOA) and multi-objective bat algorithm (MOBA) are implemented. It is found that solar radiation is the most influential parameter on the hydrogen production rate of the systems, followed by ambient temperature, inlet temperature, working fluid mass flow rate, and wind speed. According to the machine learning outputs, the highest hydrogen production rate for the PVT-PEMWE and PVT-PEMME systems are around 2.45 mol h−1 m−2 and 5.44 mol h−1 m−2, respectively. Moreover, the MOBA shows that the hydrogen production rate and electrical efficiency of the PVT-PEMWE and PVT-PEMME systems are 2.29 mol h−1 m−2 and 18.74%, and 5.06 mol h−1 m−2, and 18.77%, respectively, at their global optimum point by considering hydrogen production rate and electrical efficiency as the objective functions. This study reveals that although at the same working conditions, the electrical and thermal output of the water-based PVT system is superior to that of the water/methanol-based PVT system, the PVT-PEMME system outperforms the PVT-PEMWE system from the hydrogen production viewpoint, due to the higher efficiency of the PEM methanol electrolyzer.

Improved Electro Search Algorithm with Intelligent Controller Control System: ESPID Algorithm

Studies have established that hybrid models outperform single models. The particle swarm algorithm (PSO)-based PID (proportional-integral-derivative) controller control system is used in this study to determine the parameters that directly impact the speed and performance of the Electro Search (ESO) algorithm to obtain the global optimum point. ESPID algorithm was created by integrating this system with the ESO algorithm. The improved ESPID algorithm has been applied to 7 multi-modal benchmark test functions. The acquired results were compared to those derived using the ESO, PSO, Atom Search Optimization (ASO), and Vector Space Model (VSM) algorithms. As a consequence, it was determined that the ESPID algorithm’s mean score was superior in all functions. Additionally, while comparing the mean duration value and standard deviations, it is observed that it is faster than the ESO algorithm and produces more accurate results than other algorithms. ESPID algorithm has been used for the least cost problem in the production of pressure vessels, which is one of the real-life problems. Statistical results were compared with ESO, Genetic algorithm and ASO. ESPID was found to be superior to other methods with the least production cost value of 5885.452.

Distributed Fixed-Time Optimal Resource Management for Microgrids

This article studies the problem of distributed cooperative resource management for Microgrids. In order to maximize the social welfare, a distributed fixed-time consensus algorithm is first proposed to integrate economic dispatch and demand response, which optimally assigns the energy between generation participants and load participants. Based on the designed algorithm, each participant is able to quickly obtain its optimal operation and only requires partial calculation and communication without a central control coordination, thus it offers high flexibility, strong robustness, and better privacy. Moreover, compared with the existing distributed optimization algorithms, the proposed algorithm simultaneously possesses the advantages of fixed-time consensus, no initialization conditions, and supporting switching topology, etc. Furthermore, it is proved that each participant can achieve consensus in a fixed-time manner and converge to the global optimal point if the parameters of the algorithm satisfy some conditions. Finally, numerical simulations in the 6-Bus and the IEEE 30-Bus systems are provided to validate the effectiveness of the presented algorithm. Note to Practitioners—This article is motivated by the problem of distributed cooperative resource management for Microgrids to make the system economical and safe operation. The existing distributed methods only converge in an infinite time horizon. However, asymptotic convergence is undesirable in practice, especially in multiperiod optimisation problems. To address this issue and integrate more distributed resources in the future, in this article, we first propose a distributed fixed-time consensus method, where each participant can achieve consensus in a fixed time and obtain its optimal operation locally. Moreover, the proposed method is robust to communication failures and adaptive to topology changes. Our future work will aim at considering more practical constraints, such as power flow constraints, ramping rate constraints, etc.

Multi-objective optimization of metal hydride hydrogen storage tank with phase change material

• Transient simulation and optimization of a metal hydride storage tank. • Application of a phase change material to the metal hydride tank for heat recovery. • Appropriate selection of design parameters for the optimization purpose. • Consideration of hydrogen to metal ratio and the absorption time as the objective functions. • Finding the design parameters that reasonably satisfies both objective functions. The use of hydrogen as a future energy source to supply world fuel is essential. The storage problem is one of the main challenges facing the use of hydrogen as a fuel. In this study, we model and optimize the transient operation of a 2D metal hydride storage tank. A phase change material (PCM) is attached to a metal hydride tank for heat recovery during hydrogen absorption and heat supply during desorption. Four parameters, porosity and diameter of the metal hydride tank, initial temperature and melting temperature of the PCM, are selected to optimize hydrogen absorption. An advanced optimization algorithm is applied to increase the hydrogen to metal ratio and decrease the absorption reaction time. The hydrogen to metal ratio and the absorption time, when system pressure equals equilibrium pressure, are considered as the two objective functions. The optimization and appropriate selection of design parameters result in a significant increase in the hydrogen to metal ratio. For better understanding, five particular points in the ranges of high, mediocre and low values of hydrogen to metal ratio are selected on the optimized Pareto front. The effects of the different parameters on the objective functions are discussed for the optimal points. A final (global) optimum point is obtained based on the LINMAP method that reasonably satisfies both objective functions and the results in this point are presented and discussed separately.

Distributed neurodynamic-based economic dispatch strategy for we-energy

This paper investigates the distributed collaborative energy management of distributed cyber-energy system with consideration of multiple types of coupled energy sources and loads. Firstly, the energy structure of We-Energy (WE) and the characteristics of multi-energy interconversion are studied. With this effort, the concept of general loads are modeled based on transform loss and compensation coefficient, which enables multiple controllable loads interconverting with each other to reduce energy consumption. As a result, the system capacity costs can be greatly reduced. Furthermore, a new fully distributed neurodynamics-based algorithm is proposed to solve the economic dispatch problem of multiple WEs. The proposed method can only use seldom shared variables to obtain the optimal solutions and does not require the objective function to be strictly convex and smooth in solving convex optimization problems. Meanwhile, the proposed possesses faster convergence speed by employing application-specific integrated circuits. Moreover, we prove that the proposed neurodynamics-based algorithm can asymptotically converge to the global optimal point based on Lyapunov analysis method. Finally, simulation results demonstrate the validity of the algorithm and the effect of general load on the overall operating cost of the WE system.

A Hybrid Stochastic Deterministic Algorithm for Solving Unconstrained Optimization Problems

In this paper, a new deterministic method is proposed. This method depends on presenting (suggesting) some modifications to existing parameters of some conjugate gradient methods. The parameters of our suggested method contain a mix of deterministic and stochastic parameters. The proposed method is added to a line search algorithm to make it a globally convergent method. The convergence analysis of the method is established. The gradient vector is estimated by a finite difference approximation approach, and a new step-size h of this approach is generated randomly. In addition, a set of stochastic parameter formulas is constructed from which some solutions are generated randomly for an unconstrained problem. This stochastic technique is hybridized with the new deterministic method to obtain a new hybrid algorithm that finds an approximate solution for the global minimization problem. The performance of the suggested hybrid algorithm is tested in two sets of benchmark optimization test problems containing convex and non-convex functions. Comprehensive comparisons versus four other hybrid algorithms are listed in this study. The performance profiles are utilized to evaluate and compare the performance of the five hybrid algorithms. The numerical results show that our proposed hybrid algorithm is promising and competitive for finding the global optimum point. The comparison results between the performance of our suggested hybrid algorithm and the other four hybrid algorithms indicate that the proposed algorithm is competitive with, and in all cases superior to, the four algorithms in terms of the efficiency, reliability, and effectiveness for finding the global minimizers of non-convex functions.

Optimal Granularity Selection for Indoor Localization Detection with Wireless IoT Networks

Indoor localization detection acts as an important issue and has wide applications with wireless Internet of Things (IoT) networks. In recent years, the WiFi-based localization by using the latest artificial intelligence methods for improving the detection accuracy has attracted attention of many researchers. Granular computing is a newly emerged computing paradigm in artificial intelligence, which focuses on the structured thinking based on multiple levels of granularity. Thus, we introduce granular computing approaches to the task of wireless indoor localization detection, and a novel heuristic data discretization method is proposed based on the binary ant colony optimization and rough set (BACORS) for the selection of optimal granularity. For BACORS, the global optimal cut point set is searched based on the binary ant colony optimization to simultaneously discretize multiple attributes. Meanwhile, the accuracy of approximation classifications coined from rough sets is used to determine the consistent of multiple attribute data. To validate the effectiveness of BACORS, it is applied to a wireless indoor localization data set, and the experimental results indicate that it has promising performance.

Fitness-distance balance based artificial ecosystem optimisation to solve transient stability constrained optimal power flow problem

ABSTRACT The Transient Stability Constrained Optimal Power Flow (TSCOPF) has become an important tool for power systems today. TSCOPF is a nonlinear optimisation problem, making its solution difficult, especially for small power systems. This paper presents a new optimisation method that incorporates Fitness-Distance Balance (FDB) with the Artificial Ecosystem Optimisation (AEO) algorithm to improve the solution quality in multi-dimensional and nonlinear optimisation problems. The proposed method, named the Fitness-Distance Balance Artificial Ecosystem Optimisation (FDBAEO), also has the capacity to solve the TSCOPF problem efficiently. In order to evaluate the proposed algorithm, it was tested on IEEE CEC benchmarks and on an IEEE 30-bus test system for the TSCOPF problem. Simulation results were compared with the basic AEO algorithm and other current meta-heuristic methods reported in the literature. The results showed that the proposed method was more effective in converging at the global optimum point in solving the TSCOPF problem compared to the other algorithms. This situation indicates that the design changes made in the decomposition phase of the AEO were more suitable for simulating the operation of the algorithm in the real world. The FDBAEO has exhibited a promising performance in solving both single-objective optimisation and constrained real-world engineering design problems.