Multi-objective optimal reactive power dispatch considering voltage stability in power systems using HFMOEA

This paper proposes a new hybrid fuzzy multi-objective evolutionary algorithm (HFMOEA) based approach for solving complex multi-objective, mixed integer nonlinear problems such as optimal reactive power dispatch considering voltage stability (ORPD-VS). In HFMOEA based optimization approach, the two parameters like crossover probability (P_C) and mutation probability (P_M) are varied dynamically through the output of a fuzzy logic controller. The fuzzy logic controller is designed on the basis of expert knowledge to enhance the overall stochastic search capability for generating better pareto-optimal solution. Two detailed case studies are presented: Firstly, the performance of HFMOEA is tested on five benchmark test problems such as ZDT1, ZDT2, ZDT3, ZDT4 and ZDT6 as suggested by Zitzler, Deb and Thiele; Secondly, HFMOEA is applied to multi-objective ORPD-VS problem. In both the case studies, the optimization results obtained from HFMOEA are analysed and compared with the same obtained from two versions of elitist non-dominated sorting genetic algorithms such as NSGA-II and MNSGA-II in terms of various performance metrics. The simulation results are promising and confirm the ability of HFMOEA for generating better pareto-optimal fronts with superior convergence and diversity.     

A multi-objective evolutionary algorithm based QoS routing in wireless mesh networks

The huge demand for real time services in wireless mesh networks (WMN) creates many challenging issues for providing quality of service (QoS). Designing of QoS routing protocols, which optimize the multiple objectives is computationally intractable. This paper proposes a new model for routing in WMN by using Modified Non-dominated Sorting Genetic Algorithm-II (MNSGA-II). The objectives which are considered here are the minimization of expected transmission count and the transmission delay. In order to retain the diversity in the non-dominated solutions, dynamic crowding distance (DCD) procedure is implemented in NSGA-II. The simulation is carried out in Network Simulator 2 (NS-2) and comparison is made using the metrics, expected transmission count and transmission delay by varying node mobility and by increasing number of nodes. It is observed that MNSGA-II improves the throughput and minimizes the transmission delay for varying number of nodes and higher mobility scenarios. The simulation clearly shows that MNSGA-II algorithm is certainly more suitable for solving multiobjective routing problem. A decision-making procedure based on analytic hierarchy process (AHP) has been adopted to find the best compromise solution from the set of Pareto-solutions obtained through MNSGA-II. The performance of MNSGA-II is compared with reference point based NSGA-II (R-NSGA-II) in terms of spread.     

Multi-objective reactive power market clearing in competitive electricity market using HFMOEA

This paper presents an application of a hybrid fuzzy multi-objective evolutionary algorithm (HFMOEA) for solving a highly constraint, mixed integer type, complex multi-objective reactive power market clearing (RPMC) problem for the competitive electricity market environment. In HFMOEA based multi-objective optimization approach, based on the output of a fuzzy logic controller crossover and mutation probabilities are varied dynamically. It enhances stochastic search capabilities of HFMOEA. In multi-objective RPMC optimization framework, two objective functions namely the total payment function (TPF) for reactive power support from generators and synchronous condensers and the total real transmission loss (TRTL) are minimized simultaneously for clearing the reactive power market. The proposed HFMOEA based multi-objective RPMC scheme is tested on a standard IEEE 24 bus reliability test system and its performance is compared with five other multi-objective evolutionary techniques such as MOPBIL, NSGA-II, UPS-EMOA and SPEA-2 and a new extended form of NSGA (ENSGA-II). Applying all these six evolutionary techniques, a detailed statistical analysis using T-test and boxplots is carried out on three performance metrics (spacing, spread and hypervolume) data for RPMC problem. The obtained simulation results confirm the overall superiority of HFMOEA to generate better Pareto-optimal solutions with higher convergence rate as compared to above mentioned algorithms. Further, TPF and TRTL values corresponding to the best compromise solutions are obtained using said multi-objective evolutionary techniques. These values are compared with one another to take better market clearing decisions in competitive electricity environment.     

Multi-objective robust PID controller tuning using two lbests multi-objective particle swarm optimization

In this paper, two lbests multi-objective particle swarm optimization (2LB-MOPSO) is applied to design multi-objective robust Proportional-integral-derivative (PID) controllers for two MIMO systems, namely, distillation column plant and longitudinal control system of the super maneuverable F18/HARV fighter aircraft. Multi-objective robust PID controller design problem is formulated by minimizing integral squared error (ISE) and balanced robust performance criteria. During the search, 2LB-MOPSO can focus on small regions in the parameter space in the vicinity of the best existing fronts. As the lbests are chosen from the top fronts in a non-domination sorted external archive of reasonably large size, the offspring obtained can be more diverse with good fitness. The performance of various optimal PID controllers is compared in terms of the sum of ISE and balanced robust performance criteria. For the purpose of comparison, 2LB-MOPSO, NSGA-II as well as earlier reported Riccati, IGA and OSA methods are considered. The performance of PID controllers obtained using 2LB-MOPSO is better than that of others. In addition, Hypervolume-based comparisons are carried out to show the superior performance of 2LB-MOPSO over NSGA-II. The results reveal that 2LB-MOPSO yields better robustness and consistency in terms of the sum of ISE and balanced robust performance criteria than various optimal PID controllers.     

A modified MOEA/D approach to the solution of multi-objective optimal power flow problem

This study presents a modified multi-objective evolutionary algorithm based decomposition (MOEA/D) approach to solve the optimal power flow (OPF) problem with multiple and competing objectives. The multi-objective OPF considers the total fuel cost, the emissions, the power losses and the voltage magnitude deviations as the objective functions. In the proposed MOEA/D, a modified Tchebycheff decomposition method is introduced as the decomposition approach in order to obtain uniformly distributed Pareto-Optimal solutions on each objective space. In addition, an efficiency mixed constraint handling mechanism is introduced to enhance the feasibility of the final Pareto solutions obtained. The mechanism employs both repair strategy and penalty function to handle the various complex constraints of the MOOPF problem. Furthermore, a fuzzy membership approach to select the best compromise solution from the obtained Pareto-Optimal solutions is also integrated. The standard IEEE 30-bus test system with seven different cases is considered to verify the performance of the proposed approach. The obtained results are compared with those in the literatures and the comparisons confirm the effectiveness and the performance of the proposed algorithm.     

Multi-objective multiagent credit assignment in reinforcement learning and NSGA-II

Multiagent systems have had a powerful impact on the real world. Many of the systems it studies (air traffic, satellite coordination, rover exploration) are inherently multi-objective, but are often treated as single-objective problems within the research. A key concept within multiagent systems is that of credit assignment: quantifying an individual agent’s impact on the overall system performance. In this work,we extend the concept of credit assignment into multi-objective problems. We apply credit assignment through difference evaluations to two different policy selection paradigms to demonstrate their broad applicability. We first examine reinforcement learning, in which using difference evaluations improves performance by (i) increasing learning speed by up to 10\(\times \), (ii) producing solutions that dominate all solutions discovered by a traditional team-based credit assignment schema and (iii) losing only 0.61 % of dominated hypervolume in a scenario where 20 % of agents act in their own interests instead of the system’s interests (compared to a 43 % loss when using a traditional global reward in the same scenario). We then derive multiple methods for incorporating difference evaluations into a state-of-the-art multi-objective evolutionary algorithm, NSGA-II. Median performance of the NSGA-II considering credit assignment dominates best-case performance of NSGA-II not considering credit assignment in a multiagent multi-objective problem. Our results strongly suggest that in a multiagent multi-objective problem, proper credit assignment is at least as important to performance as the choice of multi-objective algorithm.     

快速提高NSGA-Ⅱ算法双目标优化效率的方法

NSGA-Ⅱ是一种性能优良的多目标进化算法,近年来非常流行。为了进一步改进NSGA-Ⅱ在双目标优化时的效率,采取了按需分层的策略,提出了一种新的非支配前沿集分层方法以替代NSGA-II原有的分层方法。与NSGA-Ⅱ的时间复杂度O(N2)相比,新方法的时间复杂度减少为O(kN+NlogN),k为所分前沿层数(k<相似文献   

一种双链结构的多目标进化算法DCMOEA

提出一种双链结构的多目标进化算法(DCMOEA).该算法采用双链结构表示个体,执行过程中无需设置外部归档集合,并采用ε支配策略保持解群的多样性.DCMOEA与MOEA/D、NSGA-II、SPEA2和PAES一同在4个2-目标ZDT函数和4个3-目标DTLZ问题上进行实验,并从算法所获解集的收敛性、分布均匀性和宽广性3个方面进行比较,仿真实验结果表明了DCMOEA的综合性能最好,是一种颇具竞争力的多目标进化算法.     

C-PSA: Constrained Pareto simulated annealing for constrained multi-objective optimization

In recent years, evolutionary algorithms (EAs) have been extensively developed and utilized to solve multi-objective optimization problems. However, some previous studies have shown that for certain problems, an approach which allows for non-greedy or uphill moves (unlike EAs), can be more beneficial. One such approach is simulated annealing (SA). SA is a proven heuristic for solving numerical optimization problems. But owing to its point-to-point nature of search, limited efforts has been made to explore its potential for solving multi-objective problems. The focus of the presented work is to develop a simulated annealing algorithm for constrained multi-objective problems. The performance of the proposed algorithm is reported on a number of difficult constrained benchmark problems. A comparison with other established multi-objective optimization algorithms, such as infeasibility driven evolutionary algorithm (IDEA), Non-dominated sorting genetic algorithm II (NSGA-II) and multi-objective Scatter search II (MOSS-II) has been included to highlight the benefits of the proposed approach.     

A fast multi-objective evolutionary algorithm based on a tree structure

This paper proposes a fast evolutionary algorithm based on a tree structure for multi-objective optimization. The tree structure, named dominating tree (DT), is able to preserve the necessary Pareto dominance relations among individuals effectively, contains the density information implicitly, and reduces the number of comparisons among individuals significantly. The evolutionary algorithm based on dominating tree (DTEA) integrates the convergence strategy and diversity strategy into the DT and employs a DT-based eliminating strategy that realizes elitism and preserves population diversity without extra time and space costs. Numerical experiments show that DTEA is much faster than SPEA2, NSGA-II and an improved version of NSGA-II, while its solution quality is competitive with those of SPEA2 and NSGA-II.     

Multi-objective biogeography based optimization for optimal PMU placement

The paper proposes a multi-objective biogeography based optimization (MO-BBO) algorithm to design optimal placement of phasor measurement units (PMU) which makes the power system network completely observable. The simultaneous optimization of the two conflicting objectives such as minimization of the number of PMUs and maximization of measurement redundancy are performed. The Pareto optimal solution is obtained using the non-dominated sorting and crowding distance. The compromised solution is chosen using a fuzzy based mechanism from the Pareto optimal solution. Simulation results are compared with Non-dominated Sorting Genetic Algorithm-II (NSGA-II) and Non-dominated Sorting Differential Evolution (NSDE). Developed PMU placement method is illustrated using IEEE standard systems to demonstrate the effectiveness of the proposed algorithm.     

Structural design using multi-objective metaheuristics. Comparative study and application to a real-world problem

Many structural design problems in the field of civil engineering are naturally multi-criteria, i.e., they have several conflicting objectives that have to be optimized simultaneously. An example is when we aim to reduce the weight of a structure while enhancing its robustness. There is no a single solution to these types of problems, but rather a set of designs representing trade-offs among the conflicting objectives. This paper focuses on the application of multi-objective metaheuristics to solve two variants of a real-world structural design problem. The goal is to compare a representative set of state-of-the-art multi-objective metaheuristic algorithms aiming to provide civil engineers with hints as to what optimization techniques to use when facing similar problems as those selected in the study presented in this paper. Accordingly, our study reveals that MOCell, a cellular genetic algorithm, provides the best overall performance, while NSGA-II, the de facto standard multi-objective metaheuristic technique, also demonstrates a competitive behavior.     

Evolutionary trajectory planning for an industrial robot

This paper presents a novel general method for computing optimal motions of an industrial robot manipulator (AdeptOne XL robot) in the presence of fixed and oscillating obstacles. The optimization model considers the nonlinear manipulator dynamics, actuator constraints, joint limits, and obstacle avoidance. The problem has 6 objective functions, 88 variables, and 21 constraints. Two evolutionary algorithms, namely, elitist non-dominated sorting genetic algorithm (NSGA-II) and multi-objective differential evolution (MODE), have been used for the optimization. Two methods (normalized weighting objective functions and average fitness factor) are used to select the best solution tradeoffs. Two multi-objective performance measures, namely solution spread measure and ratio of non-dominated individuals, are used to evaluate the Pareto optimal fronts. Two multi-objective performance measures, namely, optimizer overhead and algorithm effort, are used to find the computational effort of the optimization algorithm. The trajectories are defined by B-spline functions. The results obtained from NSGA-II and MODE are compared and analyzed.     

Optimal DG placement by multi-objective opposition based chaotic differential evolution for techno-economic analysis

Placement of optimally sized distributed generator (DG) units at optimal locations in the radial distribution networks can play a major role in improving the system performance. The maximum economic and technical benefits can be extracted by minimizing various objectives including yearly economic loss which includes installation, operation and maintenance cost, power loss as well as voltage deviation throughout the buses. The present problem is analysed considering these multi-objective frameworks and presents the best compromise solution or Pareto-optimal solution. Several equality and inequality constraints are also considered for the multi-objective optimization problem. In this paper, a novel multi-objective opposition based chaotic differential evolution (MOCDE) algorithm is proposed for solving the multi-objective problem in order to avoid premature convergence. Performance of population based meta-heuristic techniques largely depends on the proper selections of control parameters. It is reported that wrong parameters selection may lead to premature convergence and even stagnation. The proposed technique uses logistic mapping to generate chaotic sequence for control parameters. The proposed algorithm is implemented on IEEE-33 and IEEE-69 bus radial distribution systems for verifying its effectiveness. A comparative analysis with other modern multi-objective algorithms like NSGA-II, SPEA2 and MOPSO is also presented in this work. It is observed that the proposed algorithm can produce better results in terms of power loss and yearly economic loss minimization as well as improvement of voltage profile.     

Solving a bi-objective unrelated parallel batch processing machines scheduling problem: A comparison study

Nowadays in competitive markets, production organizations are looking to increase their efficiency and optimize manufacturing operations. In addition, batch processor machines (BPMs) are faster and cheaper to carry out operations; thus the performance of manufacturing systems is increased. This paper studies a production scheduling problem on unrelated parallel BPMs with considering the release time and ready time for jobs as well as batch capacity constraints. In unrelated parallel BPMs, modern machines are used in a production line side by side with older machines that have different purchasing costs; so this factor is introduced as a novel objective to calculate the optimum cost for purchasing various machines due to the budget. Thus, a new bi-objective mathematical model is presented to minimize the makespan (i.e., C_max), tardiness/earliness penalties and the purchasing cost of machines simultaneously. The presented model is first coded and solved by the ε-constraint‌ method. Because of the complexity of the NP-hard problem, exact methods are not able to optimally solve large-sized problems in a reasonable time. Therefore, we propose a multi-objective harmony search (MOHS) algorithm. the results are compared with the multi-objective particle swarm optimization (MOPSO), non-dominated sorting genetic algorithm (NSGA-II), and multi-objective ant colony optimization algorithm (MOACO). To tune their parameters, the Taguchi method is used. The results are compared by five metrics that show the effectiveness of the proposed MOHS algorithm compared with the MOPSO, NSGA-II and MOACO. At last, the sensitivity of the model is analyzed on new parameters and impacts of each parameter are illustrated on bi- objective functions.     

A spam filtering multi-objective optimization study covering parsimony maximization and three-way classification

Classifier performance optimization in machine learning can be stated as a multi-objective optimization problem. In this context, recent works have shown the utility of simple evolutionary multi-objective algorithms (NSGA-II, SPEA2) to conveniently optimize the global performance of different anti-spam filters. The present work extends existing contributions in the spam filtering domain by using three novel indicator-based (SMS-EMOA, CH-EMOA) and decomposition-based (MOEA/D) evolutionary multi-objective algorithms. The proposed approaches are used to optimize the performance of a heterogeneous ensemble of classifiers into two different but complementary scenarios: parsimony maximization and e-mail classification under low confidence level. Experimental results using a publicly available standard corpus allowed us to identify interesting conclusions regarding both the utility of rule-based classification filters and the appropriateness of a three-way classification system in the spam filtering domain.     

A bi-objective continuous review inventory control model: Pareto-based meta-heuristic algorithms

In this paper, a bi-objective multi-product (r,Q) inventory model in which the inventory level is reviewed continuously is proposed. The aim of this work is to find the optimal value for both order quantity and reorder point through minimizing the total cost and maximizing the service level of the proposed model simultaneously. It is assumed that shortage could occur and unsatisfied demand could be backordered, too. There is a budget limitation and storage space constraint in the model. With regard to complexity of the proposed model, several Pareto-based meta-heuristic approaches such as multi-objective vibration damping optimization (MOVDO), multi-objective imperialist competitive algorithm (MOICA), multi-objective particle swarm optimization (MOPSO), non-dominated ranked genetic algorithm (NRGA), and non-dominated sorting genetic algorithm (NSGA-II) are applied to solve the model. In order to compare the results, several numerical examples are generated and then the algorithms were analyzed statistically and graphically.     

Robust multi-objective optimization for water distribution system design using a meta-metaheuristic

The design of an urban water distribution system (WDS) is a challenging problem involving multiple objectives. The goal of robust multi-objective optimization for WDS design is to find the set of solutions which embodies an acceptable trade-off between system cost and reliability, so that the ideal solution may be selected for a given budget. In addition to satisfying consumer needs, a system must be built to accommodate multiple demand loading conditions, withstand component failures and allow surplus capacity for growth. In a developmental setting, WDS robustness becomes even more crucial, owing to the limited availability of resources, especially for maintenance. Recent optimization studies have achieved success using multi-objective evolutionary algorithms, such as the Non-dominated Sorting Genetic Algorithm II (NSGA-II). However, the multi-objective design of a large WDS within a reasonable timeframe remains a formidable problem, owing to the extremely high computational complexity of the problem. In this paper, a meta-algorithm called AMALGAM is applied for the first time to WDS design. AMALGAM uses multiple metaheuristics simultaneously in an attempt to improve optimization performance. Additionally, a Jumping-gene Genetic Algorithm (NSGA-II-JG) is also applied for the first time to WDS design. These two algorithms were tested against some other metaheuristics (including NSGA-II and a new greedy algorithm) with respect to a number of benchmark systems documented in the literature, and AMALGAM demonstrated the best performance overall, while NSGA-II-JG fared worse than the ordinary NSGA-II. Large cost savings and reliability improvements are demonstrated for a real WDS developmental case study in South Africa.     

Optimizing a bi-objective multi-product EPQ model with defective items,rework and limited orders: NSGA-II and MOPSO algorithms

In this paper, a bi-objective multi-products economic production quantity (EPQ) model is developed, in which the number of orders is limited and imperfect items that are re-workable are produced. The objectives of the problem are minimization of the total inventory costs as well as minimizing the required warehouse space. The model is shown to be of a bi-objective nonlinear programming type, and in order to solve it two meta-heuristic algorithms namely, the non-dominated sorting genetic algorithm (NSGA-II) and multi-objective particle swarm optimization (MOPSO) algorithm, are proposed. To verify the solution obtained and to evaluate the performance of proposed algorithms, two-sample t-tests are employed to compare the means of the first objective value, the means of the second objective values, and the mean required CPU time of solving the problem using two algorithms. The results show while both algorithms are efficient to solve the model and the solution qualities of the two algorithms do not differ significantly, the computational CPU time of MOPSO is considerably lower than that of NSGA-II.     

基于NSGA-II 算法的平面并联机构动态性能多目标优化

针对高速高加速度的平面并联机构,采用面向控制系统的机构设计方法,对机械结构进行优化设计． 分别在运动学、动力学层面上提出多个性能指标,以其作为目标函数和约束条件建立了标准的多目标优化模型．基 于NSGA-II 算法求解多目标优化问题,进行尺度综合．最终结果表明,优化后的机构能较大程度上消除系统耦合, 提升动态性能,为高速控制系统设计提供良好的机械硬件平台．