基于动态惩罚因子的改进蚱蜢算法求解经济负荷调度和经济排放联合调度问题

电力生产装置运行中各种燃料的成本逐步增加,需要最小化成本函数以求解此类复杂经济负荷调度问题.鉴于此,提出一种基于动态惩罚因子的改进蚱蜢算法求解经济负荷调度(economic load dispatch, ELD)问题和经济排放联合调度(combined economic emission dispatch, CEED)问题.为了提高蚱蜢算法(grasshopper optimization algorithm, GOA)性能,提出一种改进的混合蚱蜢算法(hybrid grasshopper optimization algorithm, HGOA),将重力搜索算子和鸽群搜索算子-地标算子加入GOA中,增强算法的搜索能力,平衡算法的勘探和开发.同时,为了更好地解决ELD和CEED问题中的约束问题,提出6个惩罚函数,包括2个V型函数、反正切函数、反正弦函数、线性函数和二次函数,并使用动态惩罚策略代替传统的固定值惩罚策略.选取3个ELD问题案例和4个CEED问题案例验证所提出方法的有效性,实验结果表明, HGOA相较于其他元启发式算法在求解质量上表现更好,且动态惩罚策略比固定值惩罚策略效果更...     

A Solution to the Combined Economic and Emission Dispatch Using Hybrid PSOGSA Algorithm

This article presents a new hybrid algorithm based on particle swarm optimization (PSO) and the gravitational search algorithm (GSA) for solving the combined economic and emission dispatch (CEED) problem in power systems. Performance of this approach for the CEED problem is studied and evaluated on three test systems with 3, 6, and 40 generating units, with various cost curve nature and different constraints. The results obtained are compared to those reported in the recent literature. Those results show that the proposed algorithm provides an effective and robust high-quality solution of the CEED problem.     

Recurrent neural network for combined economic and emission dispatch

Recently, the combined economic and emission dispatch (CEED) problem, which aims to simultaneously decrease fuel cost and reduce environmental emissions of power systems, has been a widespread concern. To improve the utilization efficiency of primary energy, combined heat and power (CHP) units are likely to play an important role in the future. The goal of this study is to propose an approach to solve the CEED problems in a CHP system which consists of eight power generators (PGs), two CHP units and one heat only unit. Owing to the existence of power loss in power transmission line and the non-convex feasible region of CHP units, the proposed problem is a nonlinear, multi-constraints, non-convex multi-objectives (MO) optimization problem. To deal with it, a recurrent neural network (RNN) combined with a novel technique is developed. It means that the feasible region is separated into two convex regions by using two binary variables to search for different regions. In the frame of the neurodynamic optimization, existence and convergence of the dynamic model are analyzed. It shows that the convergence solution obtained by RNN is the optimal solution of CEED problem. Numerical simulation results show that the proposed algorithm can generate solutions efficiently.     

A hybrid non-linear time-varying double-weighted particle swarm optimization for solving non-convex combined environmental economic dispatch problem

Fossil-fuel based power sources cause environmental pollution such as the degradation of air quality and climate change, which negatively impacts the life on the earth. Consequently, this demands that the power generation should consider the optimal management of thermal sources that are aimed at minimizing the emission of gasses in the generation mix. The production volume of multi-pollutant gasses (SO₂, NO_x, and CO₂) can be reduced through a combined environmental economic dispatch (CEED) approach. This study has proposed a hybrid algorithm based on a novel combination of a modified genetic algorithm and an improved version of particle swarm optimization abbreviated as MGAIPSO to solve CEED problem. The study utilizes three robust operators to enhance the performance of the proposed hybrid algorithm. In GA, a uniformly weighted arithmetic crossover and a normally distributed mutation operator have been implemented to produce elite off-springs in each iteration and diversify the solutions in the search space. In the case of PSO, a non-linear time-varying double-weighted (NLTVDW) technique is developed to obtain a substantial balance between exploration and exploitation. To further enhance the exploitation ability of the MGAIPSO, this study has implemented two movements correctional methods to continuously monitor and amend the position and velocity of the particles. Several numerical case studies ranging from small to large-scale are carried out to validate the practicality of the proposed algorithm.     

基于目标分解的高维多目标并行进化优化方法

高维多目标优化问题普遍存在且难以解决, 到目前为止, 尚缺乏有效解决该问题的进化优化方法. 本文提出一种基于目标分解的高维多目标并行进化优化方法, 首先, 将高维多目标优化问题分解为若干子优化问题, 每一子优化问题除了包含原优化问题的少数目标函数之外, 还具有由其他目标函数聚合成的一个目标函数, 以降低问题求解的难度; 其次, 采用多种群并行进化算法, 求解分解后的每一子优化问题, 并在求解过程中, 充分利用其他子种群的信息, 以提高Pareto非被占优解的选择压力; 最后, 基于各子种群的非被占优解形成外部保存集, 从而得到高维多目标优化问题的Pareto 最优解集. 性能分析表明, 本文提出的方法具有较小的计算复杂度. 将所提方法应用于多个基准优化问题, 并与NSGA-II、PPD-MOEA、ε-MOEA、HypE和MSOPS等方法比较, 实验结果表明, 所提方法能够产生收敛性、分布性, 以及延展性优越的Pareto最优解集.     

改进聚合树的高维多目标降维优化算法

对于高维多目标优化问题,降维优化算法通过去除或融合冗余目标的方法解决算法耗时过多的问题,但同时也会导致算法分布性能下降。聚合树算法定义非参数秩冲突从而可以快速计算出各目标间冲突度,但聚合树算法鲁棒性有待提高,且需要用户自行决策去除冗余目标。针对这些问题,提出数组叠加机制并定义冲突趋势和冲突度误差,以提高算法鲁棒性;通过合并冲突度较低的冗余目标的方法来进行目标降维,并定义降维截止冲突度;与NSGA-III算法结合,以达到对高维多目标问题进行完整降维优化的目的。为检验该算法性能,与其他经典高维算法进行对DTLZ测试函数集的优化对比,实验结果表明,该算法在耗时更少的同时,也具有较为优秀的分布性能和收敛性能。     

融合指标分组的高维混合多目标进化优化

高维混合多目标优化问题因包含多个不同类型指标,目前尚缺乏有效求解该问题的进化优化方法。提出一种基于目标分组的高维混合多目标并行进化优化方法。采用深度学习神经网络预测种群隐式性能指标;基于指标相关性,将高维混合多目标优化问题分解为若干子优化问题;采用多种群并行进化算法,求解分解后的每一子优化问题,并基于各子种群的非被占优解构建外部保存集;采用聚合函数对外部保存集个体进一步优化,得到Pareto最优解集。在室内布局优化问题中验证所提方法,实验结果表明,所提方法的Pareto最优解在收敛性、分布性以及延展性等方面均优于对比方法。     

Using objective reduction and interactive procedure to handle many-objective optimization problems

A number of practical optimization problems are posed as many-objective (more than three objectives) problems. Most of the existing evolutionary multi-objective optimization algorithms, which target the entire Pareto-front are not equipped to handle many-objective problems. Though there have been copious efforts to overcome the challenges posed by such problems, there does not exist a generic procedure to effectively handle them. This paper presents a simplify and solve framework for handling many-objective optimization problems. In that, a given problem is simplified by identification and elimination of the redundant objectives, before interactively engaging the decision maker to converge to the most preferred solution on the Pareto-optimal front. The merit of performing objective reduction before interacting with the decision maker is two fold. Firstly, the revelation that certain objectives are redundant, significantly reduces the complexity of the optimization problem, implying lower computational cost and higher search efficiency. Secondly, it is well known that human beings are not efficient in handling several factors (objectives in the current context) at a time. Hence, simplifying the problem a priori addresses the fundamental issue of cognitive overload for the decision maker, which may help avoid inconsistent preferences during the different stages of interactive engagement. The implementation of the proposed framework is first demonstrated on a three-objective problem, followed by its application on two real-world engineering problems.     

An improved evolutionary algorithm for handling many-objective optimization problems

It has been shown that the multi-objective evolutionary algorithms (MOEAs) act poorly in solving many-objective optimization problems which include more than three objectives. The research emphasis, in recent years, has been put into improving the MOEAs to enable them to solve many-objective optimization problems efficiently. In this paper, we propose a new composite fitness evaluation function, in a novel way, to select quality solutions from the objective space of a many-objective optimization problem. Using this composite function, we develop a new algorithm on a well-known NSGA-II and call it FR-NSGA-II, a fast reference point based NSGA-II. The algorithm is evaluated for producing quality solutions measured in terms of proximity, diversity and computational time. The working logic of the algorithm is explained using a bi-objective linear programming problem. Then we test the algorithm using experiments with benchmark problems from DTLZ family. We also compare FR-NSGA-II with four competitive algorithms from the extant literature to show that FR-NSGA-II will produce quality solutions even if the number of objectives is as high as 20.     

基于环境经济调度问题的空间自适应划分多目标优化

提出一种基于空间自适应划分的多目标优化算法. 为了增强种群的收敛性和多样性, 多维搜索空间被划分成多个网格, 网格内的粒子通过共享“引导”粒子的经验信息调整自身的速度和位置, 并引入年龄观测器实时记录引导粒子对Pareto 解集所做的贡献, 及时更新引导粒子, 以增强算法的全局搜索能力. 对多目标测试函数以及环境经济调度问题进行了仿真实验, 实验结果表明, 所提出算法能对解空间进行更加全面、充分的探索, 快速找到一组分布具有较好的逼近性、宽广性和均匀性的最优解集合.

     

A survey on evolutionary computation for complex continuous optimization

Complex continuous optimization problems widely exist nowadays due to the fast development of the economy and society. Moreover, the technologies like Internet of things, cloud computing, and big data also make optimization problems with more challenges including Many-dimensions, Many-changes, Many-optima, Many-constraints, and Many-costs. We term these as 5-M challenges that exist in large-scale optimization problems, dynamic optimization problems, multi-modal optimization problems, multi-objective optimization problems, many-objective optimization problems, constrained optimization problems, and expensive optimization problems in practical applications. The evolutionary computation (EC) algorithms are a kind of promising global optimization tools that have not only been widely applied for solving traditional optimization problems, but also have emerged booming research for solving the above-mentioned complex continuous optimization problems in recent years. In order to show how EC algorithms are promising and efficient in dealing with the 5-M complex challenges, this paper presents a comprehensive survey by proposing a novel taxonomy according to the function of the approaches, including reducing problem difficulty, increasing algorithm diversity, accelerating convergence speed, reducing running time, and extending application field. Moreover, some future research directions on using EC algorithms to solve complex continuous optimization problems are proposed and discussed. We believe that such a survey can draw attention, raise discussions, and inspire new ideas of EC research into complex continuous optimization problems and real-world applications.

     

An economic load dispatch and multiple environmental dispatch problem solution with microgrids using interior search algorithm

Microgrid is a novel small-scale system of the centralized electricity for a small-scale community such as villages and commercial area. Microgrid consists of micro-sources like distribution generator, solar and wind units. A microgrid is consummate specific purposes like reliability, cost reduction, emission reduction, efficiency improvement, use of renewable sources and continuous energy source. In the microgrid, the Energy Management System is having a problem of Economic Load Dispatch (ELD) and Combined Economic Emission Dispatch (CEED) and it is optimized by meta-heuristic techniques. The key objective of this paper is to solve the Combined Economic Emission Dispatch (CEED) problem to obtain optimal system cost. The CEED is the procedure to scheduling the generating units within their bounds together with minimizing the fuel cost and emission values. The newly introduced Interior Search Algorithm (ISA) is applied for the solution of ELD and CEED problem. The minimization of total cost and total emission is obtained for four different scenarios like all sources included all sources without solar energy, all sources without wind energy and all sources without solar and wind energy. In both scenarios, the result shows the comparison of ISA with the Reduced Gradient Method (RGM), Ant Colony Optimization (ACO) technique and Cuckoo Search Algorithm (CSA) for the two different cases which are ELD without emission and CEED with emission. The results are calculated for different Power Demand of 24 h. The results obtained to ISA give comparatively better cost reduction as compared with RGM, ACO and CSA which shows the effectiveness of the given algorithm.

     

基于参考点的高维多目标粒子群算法

高维多目标优化问题一般指目标个数为4个 或以上时的多目标优化问题.由于种群中非支配解数量随着目标数量的增加而急剧增多,导致进化算法的进化压力严重降低,求解效率低.针对该问题,提出一种基于粒子群的高维多目标问题求解方法,在目标空间中引入一系列的参考点,根据参考点筛选出能兼顾多样性和收敛性的非支配解作为粒子的全局最优,以增大选择压力.同时,提出了基于参考点的外部档案维护策略,以保持最后所得解集的多样性.在标准测试函数DTLZ2上的仿真结果表明,所提方法在求解高维多目标问题时能够得到收敛性和分布性都较好的解集.     

Modified neo-fuzzy neuron-based approach for economic and environmental optimal power dispatch

At the central energy management center in a power system, the real time controls continuously track the load changes and endeavor to match the total power demand with total generation in such a manner that the operating cost is minimized while all the operating constraints are satisfied. However, due to the strict government regulations on environmental protection, operation at minimum cost is no longer the only criterion for dispatching electrical power. The idea behind the environmentally constrained economic dispatch formulation is to estimate the optimal generation schedule of generating units in such a manner that fuel cost and harmful emission levels are both simultaneously minimized for a given load demand. Conventional optimization techniques become very time consuming and computationally extensive for such complex optimization tasks. These methods are hence not suitable for on-line use. Neural networks and fuzzy systems can be trained to generate accurate relations among variables in complex non-linear dynamical environment, as both are model-free estimators. The existing synergy between these two fields has been exploited in this paper for solving the economic and environmental dispatch problem on-line. A multi-output modified neo-fuzzy neuron (NFN), capable of real time training is proposed for economic and environmental power generation allocation.This model is found to achieve accurate results and the training is observed to be faster than other popular neural networks. The proposed method has been tested on medium-sized sample power systems with three and six generating units and found to be suitable for on-line combined environmental economic dispatch (CEED).     

Comparison of many-objective evolutionary algorithms using performance metrics ensemble

In this study, we have thoroughly researched on performance of six state-of-the-art Multiobjective Evolutionary Algorithms (MOEAs) under a number of carefully crafted many-objective optimization benchmark problems. Each MOEA apply different method to handle the difficulty of increasing objectives. Performance metrics ensemble exploits a number of performance metrics using double elimination tournament selection and provides a comprehensive measure revealing insights pertaining to specific problem characteristics that each MOEA could perform the best. Experimental results give detailed information for performance of each MOEA to solve many-objective optimization problems. More importantly, it shows that this performance depends on two distinct aspects: the ability of MOEA to address the specific characteristics of the problem and the ability of MOEA to handle high-dimensional objective space.     

Modified non-dominated sorting genetic algorithm III with fine final level selection

Dominance resistance is a challenge for Pareto-based multi-objective evolutionary algorithms to solve the high-dimensional optimization problems. The Non-dominated Sorting Genetic Algorithm III (NSGA-III) still has such disadvantage even though it is recognized as an algorithm with good performance for many-objective problems. Thus, a variation of NSGA-III algorithm based on fine final level selection is proposed to improve convergence. The fine final level selection is designed in this way. The θ-dominance relation is used to sort the solutions in the critical layer firstly. Then I_SDE index and favor convergence are employed to evaluate convergence of individuals for different situations. And some better solutions are selected finally. The effectiveness of our proposed algorithm is validated by comparing with nine state-of-the-art algorithms on the Deb-Thiele-Laumanns-Zitzler and Walking-Fish-Group test suits. And the optimization objectives are varying from 3 to 15. The performance is evaluated by the inverted generational distance (IGD), hypervolume (HV), generational distance (GD). The simulation results show that the proposed algorithm has an average improvement of 55.4%, 60.0%, 63.1% of 65 test instances for IGD, HV, GD indexes over the original NSGA-III algorithm. Besides, the proposed algorithm obtains the best performance by comparing 9 state-of-art algorithms in HV, GD indexes and ranks third for IGD indicator. Therefore, the proposed algorithm can achieve the advantages over the benchmarks.

     

Symbiotic organisms search optimization algorithm for economic/emission dispatch problem in power systems

This paper presents symbiotic organisms search (SOS) algorithm to solve economic emission load dispatch (EELD) problem for thermal generators in power systems. The basic objective of the EELD is to minimize both minimum operating costs and emission levels, while satisfying the load demand and all equality–inequality constraints. In other research direction, this multi-objective problem is converted into single-objective function by using price penalty factor approach in order to solve it with SOS. The proposed algorithm has been implemented on various test cases, with different constraints and various cost curve nature. In order to see the effectiveness of the proposed algorithm, its results are compared to those reported in the recent literature. The results of the algorithms indicate that SOS gives good results in both systems and very competitive with the state of the art for the solution of the EELD problems.

     

HWOA: an intelligent hybrid whale optimization algorithm for multi-objective task selection strategy in edge cloud computing system

Edge computing is a popular computing modality that works by placing computing resources as close as possible to the sensor data to relieve the burden of network bandwidth and data centers in cloud computing. However, as the volume of data and the scale of tasks processed by edge terminals continue to increase, the problem of how to optimize task selection based on execution time with limited computing resources becomes a pressing one. To this end, a hybrid whale optimization algorithm (HWOA) is proposed for multi-objective edge computing task selection. In addition to the execution time of the task, economic profits are also considered to optimize task selection. Specifically, a fuzzy function is designed to address the uncertainty of task’s economic profits and execution time. Five interactive constraints among tasks are presented and formulated to improve the performance of task selection. Furthermore, some improved strategies are designed to solve the problem that the whale optimization algorithm (WOA) is subject to local optima entrapment. Finally, an extensive experimental assessment of synthetic datasets is implemented to evaluate the multi-objective optimization performance. Compared with the traditional WOA, the diversity metric (Δ-spread), the hypervolume (HV) and other evaluation metrics are significantly improved. The experiment results also indicate the proposed approach achieves remarkable performance compared with other competitive methods.

     

Variable space diversity, crossover and mutation in MOEA solving many-objective knapsack problems

In this work, we analyze variable space diversity of Pareto optimal solutions (POS) and study the effectiveness of crossover and mutation operators in evolutionary many-objective optimization. First we examine the diversity of variables in the true POS on many-objective 0/1 knapsack problems with up to 20 items (bits), showing that variables in POS become noticeably diverse as we increase the number of objectives. We also verify the effectiveness of conventional two-point and uniform crossovers, Local Recombination that selects mating parents based on proximity in objective space, and two-point and uniform crossover operators which Controls the maximum number of Crossed Genes (CCG). We use NSGA-II, SPEA2, IBEA _??+? and MSOPS, which adopt different selection methods, and many-objective 0/1 knapsack problems with $n=\{100,250,500,750,\mbox{1,000}\}$ items (bits) and m?=?{2,4,6,8,10} objectives to verify the search performance of each crossover operator. Simulation results reveal that Local Recombination and CCG operators significantly improve search performance especially for NSGA-II and MSOPS, which have high diversity of genes in the population. Also, results show that CCG operators achieve higher search performance than Local Recombination for m?≥?4 objectives and that their effectiveness becomes larger as the number of objectives m increases. In addition, the contribution of CCG and mutation operators for the solutions search is analyzed and discussed.