Multi-objective optimization of space adaptive division for environmental economic dispatch

Economic Environmental Dispatch (EED) problem is the most serious problem in power operations and management. Taking into consideration transmission losses, power balance constraint, and generator capacity constraint, the EED problem becomes a non convex optimization problem, which is a difficult task that cannot be solved with traditional techniques. Furthermore, with both the environmental issues and economic objectives, the EDD problem can be formulated as a constrained nonlinear multiobjective optimization problem. In the present work, an enhanced multiobjective particle swarm optimization algorithm (EMOPSO) is proposed and applied to solve the EED problem. The proposed approach EMOPSO extends the particle swarm optimization to deal with multiobjective continuous optimization problems, EMOPSO incorporates a crowding distance mechanism for leader selection and deletion in an external archive of non dominated solutions, this mechanism improves the diversity and uniformity of the pareto front. A mutation operator is used in the population to prevent the premature convergence of the algorithm. The simulations have been made on IEEE 30 bus test system with six generators. The results are satisfying, and show that the proposed EMOPSO method was capable of achieving better performance compared with other multiobjective algorithms in the literature.

The environmental/economic dispatch (EED) problem, as one of the most important optimization problems in power systems operations, is a highly constrained, nonlinear, multiobjective optimization problem. Multiobjective evolutionary algorithms have become effective tools for solving the EED problem. To obtain higher quality Pareto solutions for EED as well as further improve the uniformity and diversity of the Pareto set, this paper proposes a novel multiobjective evolutionary algorithm, namely multiobjective grey prediction evolution algorithm (MOGPEA). The MOGPEA first develops a novel grey prediction evolution algorithm (GPEA) based on the even grey model (EGM(1,1)). Unlike other evolutionary algorithms, the GPEA considers the population series of evolutionary algorithms as a time series and uses the EGM(1,1) model to construct an exponential function as a reproduction operator for obtaining offspring. In addition, the MOGPEA adopts two learning strategies to improve the uniformity and diversity of the Pareto optimal solutions of the EED. One is a leader-updating strategy based on the maximum distance of each solution in an external archive, and the other is a leader-guiding strategy based on one solution of each external archive. To validate the effectiveness of the MOGPEA, a standard IEEE 30-bus 6-generator test system (with/without considering losses) is studied with fuel cost and emission as two conflicting objectives to be simultaneously optimized. The experimental results are compared with those obtained using a number of algorithms reported in the literature. The results reveal that the MOGPEA generates superior Pareto optimal solutions of the multiobjective EED problem. Matlab_Codes of this article can be found in https://github.com/Zhongbo-Hu/Prediction-Evolutionary-Algorithm-HOMEPAGE.

There is an increasing trend in the use of multi-objective evolutionary algorithms (MOEAs) to solve multi-objective optimization problems of the allocation of water resources. However, typically the outcome is a set of Pareto optimal solutions which make up a trade-off surface between the objective functions. For decision makers to choose a satisfactory alternative from a set of Pareto-optimal solutions, this paper suggests a new method based on least squares support vector machine (LSSVM) and k-means clustering for ranking the optimal solutions for the multi-objective allocation of water resources. First, the k-means clustering method was adopted to reduce the large set of solutions to a few representative solutions. Then, to capture and represent the decision maker's preferences as well as to select the most desirable alternative, the LSSVM method was applied to obtain the utility value for each representative solution. According to the magnitude of the utility values, the final priority orders of the representative solutions were determined. Finally, this methodology was applied to rank the Pareto optimal solution set obtained from the multi-objective optimization problems of water resources allocation for the water-receiving areas of the South-to-North Water Transfer Project in Hebei Province, China. Moreover, the comparisons of the proposed method with the information entropy method and the artificial neural network (ANN) model were given. The results of the comparison indicate that the proposed method has the ability to rank the non-dominated solutions of the multi-objective operation optimization model and that it can be employed for decision-making on water allocation and management in a river basin.

Multimodal multiobjective optimization problems (MMOPs) have attracted wide attention in recent years. This kind of problem is very challenging since they need to locate different Pareto-optimal solution sets (PSs) that correspond to the same Pareto front. To resolve it, this article proposes a novel multimodal multiobjective differential evolution (DE) algorithm with species conservation, which develops a new way of locating different PSs. Specifically, the proposed algorithm adopts species conservation to determine different PSs in known areas, while it uses a variant of DE as the basic optimizer to explore new areas. There are three operators in species conservation: 1) species division; 2) seed determination; and 3) seed conservation. Species division mainly partitions the joint population of parents and children into various species in the decision space for retaining different PSs. Seed determination selects superior solutions from each species as seeds that need to be kept in the next generation. Seed conservation is to ensure that all species seeds are retained in the new generation by substituting no promising solutions with them, thereby guarantee not missing some known areas that may contain different PSs. Besides, the DE variant is utilized to produce diverse solutions to find new areas in the decision space where PSs may exist. The comparative experiments with ten state-of-the-art algorithms have been performed on the CEC 2019 MMOPs test set and two real-world problems. The experimental results have verified that the proposed algorithm has a competitive performance for MMOPs.

Hybrid multi-objective Harris Hawk optimization algorithm based on elite non-dominated sorting and grid index mechanism

In this paper, a hybrid multiobjective improved bacterial foraging algorithm with fuzzy dominance sorting FSIBF is proposed and used to solve environmental friendly economic load dispatch problem. The fuzzy dominance-based sorting procedure is used to select the non-dominated solutions in the Pareto front. The proposed algorithm is applied to nonlinear constrained multiobjective environmental friendly economic load dispatch problem. In the proposed work, we have considered the standard IEEE 30-bus six-generator test system with fuel cost and emission as two conflicting objectives to be optimised simultaneously satisfying the system's operational constraints. The constraints imposed from the operation point of view are the limits on generator real power and reactive power outputs, bus voltages and power flow in the transmission lines. The proposed work also includes the effect of having non-smooth cost characteristics of the thermal generators which arises because of the valve point loading effect. The practical generator constraints such as ramp rate limits and prohibited operating zones are also incorporated in this work suitably.

This paper presents a simultaneous multiobjective optimization of a direct-drive permanent magnet synchronous generator and a three-blade horizontal-axis wind turbine for a large scale wind energy conversion system. Analytical models of the generator and the turbine are used along with the cost model for optimization. Three important characteristics of the system i.e., the total cost of the generator and blades, the annual energy output and the total mass of generator and blades are chosen as objective functions for a multi-objective optimization. Genetic algorithm (GA) is then employed to optimize the value of eight design parameters including seven generator parameters and a turbine parameter resulting in a set of Pareto optimal solutions. Four optimal solutions are then selected by applying some practical restrictions on the Pareto front. One of these optimal designs is chosen for finite element verification. A circuit-fed coupled time stepping finite element method is then performed to evaluate the no-load and the full load performance analysis of the system including the generator, a rectifier and a resistive load. The results obtained by the finite element analysis (FEA) verify the accuracy of the analytical model and the proposed method.

This paper investigates a new approach of computation using particle swarm in order to resolve economic environmental dispatch problem. This approach is called accelerated multiobjective particle swarm optimization (AMOPSO) which incorporates vector function as objective function and uses matrix computation and updates solutions set, in each iteration, for developing the Pareto front unlike the existing multi-objective algorithms which use an external archive. We apply this approach to resolve the problem which treats fuel cost, NOx emissions and active power losses as competing objectives.

We develop a model-based algorithm for the optimization of multiple objective functions that can only be assessed through black-box evaluation. The algorithm iteratively generates candidate solutions from a mixture distribution over the solution space and updates the mixture distribution based on the sampled solutions' domination count such that the future search is biased towards the set of Pareto optimal solutions. The proposed algorithm seeks to find a mixture distribution on the solution space so that 1) each component of the mixture distribution is a degenerate distribution centered at a Pareto optimal solution and 2) each estimated Pareto optimal solution is uniformly spread across the Pareto optimal set by a threshold distance. We demonstrate the performance of the proposed algorithm on several benchmark problems.

Environmental/economic power dispatch with wind power

Land-use allocation is of great significance in urban development. This type of allocation is usually considered to be a complex multi-objective spatial optimization problem, whose optimized result is a set of Pareto-optimal solutions (Pareto front) reflecting different tradeoffs in several objectives. However, obtaining a Pareto front is a challenging task, and the Pareto front obtained by state-of-the-art algorithms is still not sufficient. To achieve better Pareto solutions, taking the grid-representative land-use allocation problem with two objectives as an example, an artificial bee colony optimization algorithm for multi-objective land-use allocation (ABC-MOLA) is proposed. In this algorithm, the traditional ABC’s search direction guiding scheme and solution maintaining process are modified. In addition, a knowledge-informed neighborhood search strategy, which utilizes the auxiliary knowledge of natural geography and spatial structures to facilitate the neighborhood spatial search around each solution, is developed to further improve the Pareto front’s quality. A series of comparison experiments (a simulated experiment with small data volume and a real-world data experiment for a large area) shows that all the Pareto fronts obtained by ABC-MOLA totally dominate the Pareto fronts by other algorithms, which demonstrates ABC-MOLA’s effectiveness in achieving Pareto fronts of high quality.

The multi-dimensional knapsack problem (MDKP) is a well-known NP-hard problem in combinatorial optimization. As it has various real-life applications, the MDKP has been intensively studied in the literature. On the other hand, far too little attention has been paid to the multi-objective version of the MDKP. In this chapter, we consider the bi-objective multi-dimensional knapsack problem (BOMDKP). We propose a Binary Genetic Algorithm (BGA) with an external archive for the problem. Our proposed BGA algorithm also employs a binary local search. The non-dominated solution sets are obtained for various bi-objective benchmark instances with 100, 250, 500 and 750 items, by employing the proposed BGA. Then, the performance of the BGA is compared with other multi-objective algorithms from the literature, i.e., MOEA/D and MOFPA. Furthermore, it is observed that the Pareto-optimal solution set provided by Zitzler and Laumans for 500 items and 2 knapsacks includes 30 dominated solutions. Also, the Pareto-optimal solutions for the scenario with 750 items are not reported in Zitzler and Thiele [43]. Hence, the true Pareto-optimal solution sets are found for all benchmark problem instances using Improved Augmented Epsilon Constraint (AUGMECON2) method. The non-dominated solution sets of the BGA, MOEA/D and MOFPA are compared with the Pareto-optimal solution sets for all test instances. The computational results indicate that the proposed BGA is more effective to solve the BOMDKP than the best-performing algorithms from the literature.

A systematic approach for watershed ecological restoration strategy making: An application in the Taizi River Basin in northern China

ABSTRACTThe paper targets an optimal soil cutting operation by considering economic and productive aspects. Three realistic objectives and three problem-specific constraints are developed, and the optimization problem is solved using a hybrid evolutionary multi-objective optimization (EMO) technique. In this technique, a set of non-dominated solutions is generated by using an existing EMO technique, and then a few of them are selected for local search using the -constraint method. These selected solutions are used for starting independent local searches using fmincon solver of Matlab. Results demonstrate that the local searches have improved the non-dominated solutions a little, thereby suggesting a closeness of evolved solutions from EMO technique with true Pareto-optimal (PO) solutions. The PO solutions are further validated using experimental data from the literature. Overall, this study offers a platform to choose an appropriate solution from the set of PO solutions. Moreover, the post-optimal analysis demonstrates the commonality principle of few decision variables, which is followed by all PO solutions. The rest of the decision variables decipher important relationships that are responsible for trade-off among the PO solutions. The relationships are later used for preparing guidelines for a practitioner in selecting an appropriate solution for the optimal operation.

This research is intended to develop a suspension parameter optimization approach based on a virtual prototype surrogate model of rail vehicles considering the coupling effects of suspension parameters. In order to analyze the effects on the dynamic indexes, which were affected by the suspension parameters, a virtual prototype model of a rail vehicle was established. The indexes of lateral ride quality and motion stability were obtained under different combinations of suspension parameters by design of experiment and simulation of virtual prototype. For constructing objective function of multi-objective optimization model for suspension parameters, the suspension parameters that have significant effects on ride quality and motion stability simultaneously were taken as the design variables, and thereafter Kriging models of lateral ride quality index, derailment coefficient, and reduction ratio of wheel load were obtained. On this basis, the multi-objective optimization model of suspension parameters was established, in which the objective function was combined with the three Kriging models. Then, the Pareto optimal solution set and concrete value of suspension parameters were sought using the NSGA-II algorithm. The dynamic simulation results indicated that both ride quality and motion stability of the rail vehicle had been improved after the multi-objective optimization of suspension parameters.