A review of meta-heuristic algorithms for reactive power planning problem <s> The best compromise solution over Pareto solutions <s> This paper proposes an application of the Differential Evolution optimization algorithm to reactive power planning. This problem could be formulated mathematically as a nonlinear, non smooth, mixed-integer, multiobjective optimization problem. One of the objectives deals with the minimization of the real power losses that result in a reduction of the operational costs and improving the voltage profile across the system. The other objective minimizes the allocation of additional reactive power sources throughout the system. The proposed approach has been tested in a modified version of the IEEE 30-bus test system with satisfactory results. These results were compared with those obtained by another evolutionary computation technique (Evolutionary Programming). <s> BIB001 </s> A review of meta-heuristic algorithms for reactive power planning problem <s> The best compromise solution over Pareto solutions <s> Abstract People have paid more attention to enhancing voltage stability margin since voltage collapses happened in some power systems recently. This paper proposes an optimal reactive power flow (ORPF) incorporating static voltage stability based on a multi-objective adaptive immune algorithm (MOAIA). The main idea of the proposed algorithm is to add two parts to an existing immune algorithm. The first part defines both partial affinity and global affinity to evaluate the antibody affinity to the multi-objective functions. The second part uses adaptive crossover, mutation and clone rates for antibodies to maintain the antibodies diversity. Hence, the proposed algorithm can achieve a dynamic balance between individual diversity and population convergence. The paper describes ORPF’s multi-objective functional mathematical model and the constraint conditions. The problems associated with the antibody are also discussed in detail. The proposed method has been tested in the IEEE-30 system and compared with IGA (immune genetic algorithm). The results show that the proposed algorithm has improved performance over the IGA. <s> BIB002 </s> A review of meta-heuristic algorithms for reactive power planning problem <s> The best compromise solution over Pareto solutions <s> The optimal Reactive Power Dispatch (RPD) problem is a nonlinear constrained optimization problem. This paper presents true multi-objective solution set for multi-objective RPD problem. The objective functions are real power loss minimization and control variable adjustment costs. In this paper, a Modified Non-Dominated Sorting Genetic Algorithm version II (MNSGA-II) is proposed for solving RPD problem. For maintaining good diversity in the performance of NSGA-II, the concept of Dynamic Crowding Distance (DCD) is implemented in NSGA-II algorithm and given name as MNSGA-II. The standard IEEE 30-bus and IEEE 118 bus test systems are used. The results obtained using MNSGA-II are compared with NSGA-II and validated with reference Pareto front generated by conventional weighted sum method using Covariance Matrix Adapted Evolution Strategy (CMA-ES). The performance of NSGA-II and MNSGA-II are compared with respect to best, mean, worst and standard deviation of multi-objective performance measures.The results show the effectiveness of MNSGA-II and confirm its potential to solve the multi-objective RPD problem. <s> BIB003 </s> A review of meta-heuristic algorithms for reactive power planning problem <s> The best compromise solution over Pareto solutions <s> Abstract This paper addresses an application of modified NSGA-II (MNSGA-II) by incorporating controlled elitism and dynamic crowding distance (DCD) strategies in NSGA-II to multiobjective optimal reactive power dispatch (ORPD) problem by minimizing real power loss and maximizing the system voltage stability. To validate the Pareto-front obtained using MNSGA-II, reference Pareto-front is generated using multiple runs of single objective optimization with weighted sum of objectives. For simulation purposes, IEEE 30 and IEEE 118 bus test systems are considered. The performance of MNSGA-II, NSGA-II and multiobjective particle swarm optimization (MOPSO) approaches are compared with respect to multiobjective performance measures. TOPSIS technique is applied on obtained non-dominated solutions to determine best compromise solution (BCS). Karush–Kuhn–Tucker (KKT) conditions are also applied on the obtained non-dominated solutions to substantiate a claim on optimality. Simulation results are quite promising and the MNSGA-II performs better than NSGA-II in maintaining diversity and authenticates its potential to solve multiobjective ORPD effectively. <s> BIB004 </s> A review of meta-heuristic algorithms for reactive power planning problem <s> The best compromise solution over Pareto solutions <s> This paper presents a multi-objective optimization methodology to solve the Optimal Reactive Power Flow (ORPF) problem. The e-constraint approach is implemented for the Multi-objective Mathematical Programming (MMP) formulation. The solution procedure uses Mixed Integer Non-Linear Programming (MINLP) model due to discrete variables, such as the tap settings of transformers and the reactive power output of capacitor banks. The optimum tap settings of transformers are directly determined in terms of the admittance matrix of the network since the admittance matrix is constructed in the optimization framework as additional equality constraints. The optimization problem is modeled in General Algebraic Modeling System (GAMS) software and solved using DICOPT solver. Simulation results are implemented on the IEEE 14-, 30-, and 118-bus test systems to simultaneously optimize the total fuel cost, power losses and the system loadability as objective functions. The simulation results show that the proposed algorithm is suitable and effective for the reactive power planning. <s> BIB005 </s> A review of meta-heuristic algorithms for reactive power planning problem <s> The best compromise solution over Pareto solutions <s> This paper discusses the application of Modified Non-Dominated Sorting Genetic Algorithm-II (MNSGA-II) to multi-objective Reactive Power Planning (RPP) problem. The three objectives considered are minimization of combined operating and VAR allocation cost, bus voltage profile improvement and voltage stability enhancement. For maintaining good diversity in nondominated solutions, Dynamic Crowding Distance (DCD) procedure is implemented in NSGA-II and it is called as MNSGA-II. The standard IEEE 30-bus test system, practical 69-bus Indian system and IEEE 118-bus system are considered to analyze the performance of MNSGA-II. The results obtained using MNSGA-II are compared with NSGA-II and validated with reference pareto-front generated by conventional weighted sum method using Covariance Matrix Adapted Evolution Strategy (CMA-ES). The performance of NSGA-II and MNSGA-II are compared with respect to best, mean, worst and standard deviation of multi-objective performance measures namely gamma, spread, minimum spacing and Inverted Generational Distance (IGD) in 15 independent runs. The results show the effectiveness of MNSGA-II and confirm its potential to solve the multi-objective RPP problem. A decision-making procedure based on Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method is used for finding best compromise solution from the set of pareto-solutions obtained through MNSGA-II. <s> BIB006
Determination of a single optimal solution that simultaneously optimizes all multi-objective functions is difficult. However, the decision makers can perform a trade-off analysis and select among the set of the non-dominated solutions BIB003 BIB001  . The fuzzy decision-making tool has been presented to determine the best compromise solution for the RPP problem BIB005 16(Ch. 4) ,17]. Each objective F i is fuzzified with a membership function l i as in Eq. (16) and Fig. 3 shows its related fuzzy modeling. Then, the best solution is selected, which achieves the maximum membership l k which is defined in Eq.  or the maximum normalizing membership l k which is defined in Eq. (18) BIB005 : where k refers to each non-dominated solution, M is the number of objectives, n is the total number of the non-dominated solutions, and x i refers to weight value of the ith objective function. This method suffers from the problem of how to select the weight values x i . In BIB005 , the weight values x i has been selected based on the importance of economic and technical aspects. Moreover, the best compromise solution could be obtained using the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method BIB006 BIB004  (Chs. 7 and 8)] as a multiple criteria decision making approach. In this technique, the relative performance of each non-dominated solution with respect to each criterion is identified and the geometric distance between each solution and the ideal solution in each criterion is calculated. Finally, the best compromise solution can be determined according to the maximum relative closeness to the ideal solution. In BIB004 , TOPSIS approach has been used to rank the obtained MNSGA-II solutions for the reactive power dispatch to minimize two objectives, real power losses and L-index. The best compromise solution has been determined by a single decision maker. In BIB006 , TOPSIS approach has been also used to find the best compromise for the RPP problem to minimize the combined operating and VAR allocation cost improves the voltage profile and enhances the voltage stability. In spite of its simplicity, TOPSIS approach does not take the relationships of different criteria into consideration. On the other hand, Pareto concept has been incorporated to the immune algorithm in BIB002 to define the partial affinity of an antibody (solution) to each antigen (objective). Then, the best compromise solution was based on the global affinity (sum of partial affinities).