Hybrid Multi-objective Evolutionary Algorithm Research Articles

Open Energy Market Strategies in Microgrids: A Stackelberg Game Approach Based on a Hybrid Multiobjective Evolutionary Algorithm

The emergence of microsources holds promise to reduce the carbon emissions and exploit more renewables in order to meet the worldwide growing electrical energy demands. However, there exist several challenges, such as optimizing the tradeoff between the use of renewable and nonrenewable energy sources, to leverage affordable electric power while minimizing carbon emissions. Game theoretic approaches have been widely used in various scientific domains and have recently also increasingly been used in smart grids, whereby evolutionary paradigms have been widely deployed as a popular heuristic search method to solve and optimize complex real-life scientific problems. A promising approach is the development of such evolutionary algorithms and game theoretic approaches in the context of open energy markets. In this paper, we develop an analytic model of a multileader and multifollower Stackelberg game approach and propose a bi-level hybrid multiobjective evolutionary algorithm to find optimal strategies that maximize the profit of utilities, and minimize carbon emissions in an open energy market among interconnected microsources.

Stopping criteria for MAPLS-AW, a hybrid multi-objective evolutionary algorithm

Evolutionary algorithms are widely used to solve multi-objective optimization problems effectively by performing global search over the solution space to find better solutions. Hybrid evolutionary algorithms have been introduced to enhance the quality of solutions obtained. One such hybrid algorithm is memetic algorithm with preferential local search using adaptive weights (MAPLS-AW) (Bhuvana and Aravindan in Soft Comput, doi:10.1007/s00500-015-1593-9, 2015). MAPLS-AW, a variant of NSGA-II algorithm, recognizes the elite solutions of the population and preferences are given to them for local search during the evolution. This paper proposes a termination scheme derived from the features of MAPLS-AW. The objective of the proposed scheme is to detect convergence of population without compromising quality of solutions generated by MAPLS-AW. The proposed termination scheme consists of five stopping measures, among which two are newly proposed in this paper to predict the convergence of the population. Experimental study has been carried out to analyze the performance of the proposed termination scheme and to compare with existing termination schemes. Several constrained and unconstrained multi-objective benchmark test problems are used for this comparison. Additionally, a real-time application economic emission and load dispatch has also been used to check the performance of the proposed scheme. The results show that the proposed scheme identifies convergence of population much earlier than the existing stopping schemes without compromising the quality of solutions.

A multi-objective hybrid evolutionary algorithm for dynamic economic emission load dispatch

SUMMARY This paper presents a novel multi-objective evolutionary algorithm, namely chemical reaction optimization (CRO) algorithm for solving dynamic economic emission dispatch (DEED) problem of power systems. The DEED problem is a non-linear, non-convex, multi-dimensional, and highly constrained multi-objective optimization problem. It has no unique optimal solution with respect to all criteria because it involves multiple and often conflicting optimization criteria. In order to improve the convergence speed and quality of the solutions attained by CRO, it is combined with differential evolution to escape from local minima solutions. This hybrid differential evolution-based CRO (HCRO) methodology determines the feasible optimal solution of the non-linear DEED problem. To demonstrate the superiority of the proposed CRO and HCRO methods in solving non-convex, non-linear, and constrained DEED problem, the proposed frameworks are implemented on 10-unit and 30-unit test systems. It is found from the simulation results that HCRO exhibits significantly better performance in terms of solution quality and convergence speed for all the cases compared with CRO algorithm. Furthermore, the proposed HCRO algorithm is superior to most of the existing algorithms available in the literature. Copyright © 2015 John Wiley & Sons, Ltd.

A hybrid multiobjective evolutionary algorithm model based on local linear embedding

Based on the following property: under mild conditions, it can be induced from the Karush-Kuhn-Tucker condition that the Pareto set, in the decision space, of a continuous multiobjective optimisation problems (MOPs) is a piecewise continuous (m − 1) − D manifold (where m is the number of objectives), a hybrid multiobjective evolutionary algorithm model based on local linear embedding is proposed for continuous MOPs. At each generation: 1) via local linear embedding and its improved algorithms, the proposed algorithm digs out a nonlinear manifold in the decision space; 2) the new trial solutions are built through the manifold of step 1; 3) a non-dominated sorting-based selection is used for choosing solutions and produce the next generation. Systematic experiments have shown that the algorithm can find out nonlinear manifold hidden in the decision space of MOPs and guide rapid convergence of algorithm.

Design Optimization of a Centrifugal Fan with Splitter Blades

AbstractMulti-objective optimization of a centrifugal fan with additionally installed splitter blades was performed to simultaneously maximize the efficiency and pressure rise using three-dimensional Reynolds-averaged Navier-Stokes equations and hybrid multi-objective evolutionary algorithm. Two design variables defining the location of splitter, and the height ratio between inlet and outlet of impeller were selected for the optimization. In addition, the aerodynamic characteristics of the centrifugal fan were investigated with the variation of design variables in the design space. Latin hypercube sampling was used to select the training points, and response surface approximation models were constructed as surrogate models of the objective functions. With the optimization, both the efficiency and pressure rise of the centrifugal fan with splitter blades were improved considerably compared to the reference model.

A learning-guided multi-objective evolutionary algorithm for constrained portfolio optimization

Portfolio optimization involves the optimal assignment of limited capital to different available financial assets to achieve a reasonable trade-off between profit and risk objectives. In this paper, we studied the extended Markowitz's mean-variance portfolio optimization model. We considered the cardinality, quantity, pre-assignment and round lot constraints in the extended model. These four real-world constraints limit the number of assets in a portfolio, restrict the minimum and maximum proportions of assets held in the portfolio, require some specific assets to be included in the portfolio and require to invest the assets in units of a certain size respectively. An efficient learning-guided hybrid multi-objective evolutionary algorithm is proposed to solve the constrained portfolio optimization problem in the extended mean-variance framework. A learning-guided solution generation strategy is incorporated into the multi-objective optimization process to promote the efficient convergence by guiding the evolutionary search towards the promising regions of the search space. The proposed algorithm is compared against four existing state-of-the-art multi-objective evolutionary algorithms, namely Non-dominated Sorting Genetic Algorithm (NSGA-II), Strength Pareto Evolutionary Algorithm (SPEA-2), Pareto Envelope-based Selection Algorithm (PESA-II) and Pareto Archived Evolution Strategy (PAES). Computational results are reported for publicly available OR-library datasets from seven market indices involving up to 1318 assets. Experimental results on the constrained portfolio optimization problem demonstrate that the proposed algorithm significantly outperforms the four well-known multi-objective evolutionary algorithms with respect to the quality of obtained efficient frontier in the conducted experiments.

A hybrid multi-objective evolutionary algorithm for wind-turbine blade optimization

A concurrent-hybrid non-dominated sorting genetic algorithm (hybrid NSGA-II) has been developed and applied to the simultaneous optimization of the annual energy production, flapwise root-bending moment and mass of the NREL 5 MW wind-turbine blade. By hybridizing a multi-objective evolutionary algorithm (MOEA) with gradient-based local search, it is believed that the optimal set of blade designs could be achieved in lower computational cost than for a conventional MOEA. To measure the convergence between the hybrid and non-hybrid NSGA-II on a wind-turbine blade optimization problem, a computationally intensive case was performed using the non-hybrid NSGA-II. From this particular case, a three-dimensional surface representing the optimal trade-off between the annual energy production, flapwise root-bending moment and blade mass was achieved. The inclusion of local gradients in the blade optimization, however, shows no improvement in the convergence for this three-objective problem.

A multiobjective hybrid evolutionary algorithm for robust design of distribution networks

In this paper, an evolutionary multiobjective algorithm (NSGA-II) and some local search methods are employed to solve the power distribution network design problem. The design procedure takes into account three relevant aspects: monetary cost, fault cost (reliability) and robustness (ability to deal with different scenarios of load growth). The final objective is to identify topologies (conductor configuration and capacity) that are efficient with regard to cost and reliability at the same time they are robust enough for dealing with uncertainties on load prediction. Uncertainties in the load growth, energy price and interest rate are considered. Four local search methods are proposed in order to improve solution robustness and reliability, taking into account a given set of possible scenarios. The proposed algorithm achieves high-quality solutions with low computational cost, outperforming the results achieved by former works that dealt with similar problem formulations. Results for 21, 100 and 300 bus systems are presented in order to illustrate the efficiency of the proposed method.

Evolutionary multi-objective generation of recurrent neural network ensembles for time series prediction

Ensembles have been shown to provide better generalization performance than single models. However, the creation, selection and combination of individual predictors is critical to the success of an ensemble, as each individual model needs to be both accurate and diverse. In this paper we present a hybrid multi-objective evolutionary algorithm that trains and optimizes the structure of recurrent neural networks for time series prediction. We then present methods of selecting individual prediction models from the Pareto set of solutions. The first method selects all individuals below a threshold in the Pareto front and the second one is based on the training error. Individuals near the knee point of the Pareto front are also selected and the final method selects individuals based on the diversity of the individual predictors. Results on two time series data sets, Mackey-Glass and Sunspot, show that the training algorithm is competitive with other algorithms and that the final two selection methods are better than selecting all individuals below a given threshold or based on the training error.

Optimization of the Aerodynamic and Aeroacoustic Performance of an Axial-Flow Fan

A multidisciplinary optimization to simultaneously enhance the aerodynamic and aeroacoustic performance of an axial-flow fan was performed. Flow analysis through the axial-flow fan was conducted by solving three-dimensional steady and unsteady Reynolds-averaged Navier–Stokes equations with the shear-stress transport turbulence model. Starting with the results for the unsteady flow, aeroacoustic analysis was performed by solving the Ffowcs Williams–Hawkings equations. A single-objective optimization for high-efficiency design was carried out before the multi-objective optimization. The single-objective optimization was conducted using a weighted average surrogate model with five design variables defining the hub-to-tip ratio, hubcap installation distance, hubcap ratio, and angle distributions at the midspan and blade tip. The objective function (i.e., the efficiency) was evaluated at the design points, sampled by Latin hypercube sampling in the design space, to construct the surrogate model. Then, multi-objective optimization on the basis of the single-objective optimization result was performed to simultaneously improve the efficiency and reduce the sound pressure level through a hybrid multi-objective evolutionary algorithm coupled with a response surface approximation surrogate model with two design variables defining the sweep and lean angles at the blade tip. These objective functions were numerically accessed through the aerodynamic and aeroacoustic analyses. Arbitrary selected optimum designs in the Pareto-optimal solutions yielded increases in efficiency and decreases in the sound pressure level compared to the reference design.

Hybrid Multiobjective Evolutionary Algorithm for Assembly Line Balancing Problem with Stochastic Processing Time

An assembly line (AL) is a typical manufacturing process consisting of various tasks in which interchangeable parts are added to a product in a sequential manner at a station to produce a final product. Most of the work related to the ALs concentrate on the assembly line balancing (ALB) which deals with the allocation of the tasks among stations so that the precedence relations among them are not violated and a given objective function is optimized. From the view point of the real ALB systems, multiobjective ALB with stochastic processing time (S-moALB) is an important and practical topic from traditional ALB problem involving conflicting criteria such as the cycle time, variation of workload, and/or the processing cost under uncertain manufacturing environment.This paper proposes a hybrid multiobjective evolutionary algorithm (hMOEA) to deal with such S-moALB problem with stochastic processing time considering minimization of the cycle time and the processing cost, given a fixed number of stations available. The special fitness function strategy is adopted and a hybrid selection mechanism is designed to improve the convergence and distribution performance. Experimental results with various instances show that hMOEA could get the better convergence distribution performance than existing MOEAs.

Multiobjective Optimization of a Counterrotating Type Pump-Turbine Unit Operated at Turbine Mode

A multiobjective optimization for improving the turbine output and efficiency of a counterrotating type pump-turbine unit operated at turbine mode was carried out in this work. The blade geometry of both the runners was optimized using a hybrid multiobjective evolutionary algorithm coupled with a surrogate model. Three-dimensional Reynolds-averaged Navier-Stokes equations with the shear stress transport turbulence model were discretized by finite volume approximations and solved on hexahedral grids to analyze the flow in the pump-turbine unit. As major hydrodynamic performance parameters, the turbine output and efficiency were selected as objective functions with two design variables related to the hub profiles of both the runner blades. These objectives were numerically assessed at twelve design points selected by Latin hypercube sampling in the design space. Response surface approximation models for the objectives were constructed based on the objective function values at the design points. A fast nondominated sorting genetic algorithm for the local search coupled with the response surface approximation models was applied to determine the global Pareto-optimal solutions. The trade-off between the two objectives was determined and described with respect to the Pareto-optimal solutions. The results of this work showed that the turbine outputs and efficiencies of optimized pump-turbine units were simultaneously improved in comparison to the reference unit.

Two-Level Production Plan Decomposition Based on a Hybrid MOEA for Mineral Processing

This paper addresses the integrated multiobjective production planning and decomposing (P&D) problem for mineral processing. A novel multiobjective 0-1 mixed integer nonlinear programming model is presented for the simultaneous P&D problem (O-model). In order to reduce the computational cost for solving O-model, a rolling horizon-based two-level decomposition approach is proposed to separate O-model into an upper level model (H-model) and a lower level model (L-model). An interactive partition (IP) and multiobjective gradient (MO-G)-based hybrid evolutionary multiobjective (EMO) algorithm named as IG-NSGA-II/IG-SPEA2, which takes the popular NSGA-II/SPEA2 as the basic EA, is proposed to solve both H-model and L-model, where an IP technique is designed to generate the efficient feasible combinational nodes, an ideal solution technique is provided for fathoming the infeasible nodes, an improved multiobjective gradient-based operator is developed to accelerate the evolution process in each selected node, and a cut with all continuous variables is constructed to exclude the previous feasible combination if it is not desired for the decision makers (DMs). The experimental results demonstrate that the presented two-level decomposition strategy can effectively integrate both levels. Moreover, the proposed hybrid method can effectively reduce the combinatorial space so as to concentrate the computing resource on the subspace of most interest, and can generate better feasible solutions than the pure EA in the full-space under computation time limits.

Aerodynamic optimization of a transonic axial compressor with a casing groove combined with tip injection

A multiobjective optimization to enhance the stall margin and peak adiabatic efficiency of an axial compressor with a casing groove combined with injection was performed in this work. The geometry of the casing groove was optimized using a hybrid multiobjective evolutionary algorithm coupled with a surrogate model. Reynolds-averaged Navier–Stokes equations with a k– ɛ turbulence model were discretized by finite volume approximations and solved on hexahedral grids to analyze the flow in the compressor. The stall margin and peak adiabatic efficiency were selected as objective functions with three design variables related to the geometry of the casing groove. Latin hypercube sampling was applied as a design-of-experiment technique to generate 25 design points within the design space. Response surface approximation models as the surrogate models for the objectives were constructed based on the objective function values at the design points. A fast nondominated sorting genetic algorithm for the local search coupled with the surrogate models was applied to determine the global Pareto-optimal solutions. The tradeoff between the two objectives was determined and is described with respect to the Pareto-optimal solutions. The multiobjective optimization results showed that the stall margin and peak adiabatic efficiency of the axial compressor with an optimized casing groove combined with injection were simultaneously improved compared to the compressor with a smooth casing.

Simultaneous topology and sizing optimization of a water distribution network using a hybrid multiobjective evolutionary algorithm

This paper proposes a new direction for design optimization of a water distribution network (WDN). The new approach introduces an optimization process to the conceptual design stage of a WDN. The use of multiobjective evolutionary algorithms (MOEAs) for simultaneous topology and sizing design of piping networks is presented. The design problem includes both topological and sizing design variables while the objective functions are network cost and total head loss in pipes. The numerical technique, called a network repairing technique (NRT), is proposed to overcome difficulties in operating MOEAs for network topological design. The problem is then solved by using a number of established and newly developed MOEAs. Also, two new MOEAs namely multiobjective real code population-based incremental learning (RPBIL) and a hybrid algorithm of RPBIL with differential evolution (termed RPBIL–DE) are proposed to tackle the design problems. The optimum results obtained are illustrated and compared. It is shown that the proposed network repairing technique is an efficient and effective tool for topological design of WDNs. Based on the hypervolume indicator, the proposed RPBIL–DE is among the best MOEA performers.

Design Optimization of Manifold Microchannel Heat Sink Through Evolutionary Algorithm Coupled With Surrogate Model

A liquid flow manifold microchannel heat sink is optimized with the help of 3-D numerical analysis, a surrogate method, and a multiobjective evolutionary algorithm. The performance of the manifold microchannel heat sink is optimized for the overall thermal resistance and the pumping power required for driving the coolant. The design variables related to the width of the microchannel, depth of the microchannel, width of fins, length of the nozzles, and height of the nozzles, which contribute to objective functions, are identified and optimized for minimum thermal resistance and pumping power. A Latin hypercube sampling method is used to exploit the design space. The numerical solutions obtained at these design points are utilized to construct a surrogate model, i.e., response surface approximation. The Navier-Stokes and energy equations for laminar flow and conjugate heat transfer are solved using a finite-volume solver. A hybrid multi objective evolutionary algorithm coupled with a surrogate model is applied to find out global Pareto-optimal designs (PODs). Trade-off analysis is performed in view of the conflicting nature of the two objectives, which yields PODs with low thermal resistance at various pumping powers. The ratio of the microchannel width to the microchannel height and that of the nozzle height to the microchannel height are found to be more Pareto-optimal sensitive (sensitive along the Pareto-optimal front) than others. In contrast, the ratio of the fin width to the microchannel height and that of the nozzle length to the microchannel width are found to be less Pareto-optimal sensitive than other design variables. The PODs showed lower thermal resistance and pumping power than the reference designs at various mass flow rates.

Comprehensive Survey of the Hybrid Evolutionary Algorithms

Multiobjective evolutionary algorithm based on decomposition (MOEA/D) and an improved non-dominating sorting multiobjective genetic algorithm (NSGA-II) is two well known multiobjective evolutionary algorithms (MOEAs) in the field of evolutionary computation. This paper mainly reviews their hybrid versions and some other algorithms which are developed for solving multiobjective optimization problems (MOPs. The mathematical formulation of a MOP and some basic definitions for tackling MOPs, including Pareto optimality, Pareto optimal set (PS), Pareto front (PF) are provided in Section 1. Section 2 presents a brief introduction to hybrid MOEAs. The authors present literature review in subsections. Subsection 2.1 provides memetic multiobjective evolutionary algorithms. Subsection 2.2 presents the hybrid versions of well-known Pareto dominance based MOEAs. Subsection 2.4 summarizes some enhanced Versions of MOEA/D paradigm. Subsection 2.5 reviews some multimethod search approaches dealing optimization problems.

Development and application of a master-slave parallel hybrid multi-objective evolutionary algorithm for groundwater remediation design

Two primary goals of a multi-objective evolutionary algorithm (MOEA) for solving multi-objective optimization problems are to find as many nondominated solutions as possible toward the true Pareto front and to maintain diversity of Pareto-optimal solutions along the tradeoff curves. However, few MOEAs can achieve these two goals concurrently. This study presents a new hybrid MOEA, the niched Pareto tabu search combined with a genetic algorithm (NPTSGA), in which the global search ability of niched Pareto tabu search (NPTS) is improved by the diversification of candidate solutions that arose from the evolving population of nondominated sorting genetic algorithm-II (NSGA-II). The NPTSGA coupled with a flow and transport model is developed for multi-objective optimal design of groundwater remediation systems. The proposed methodology is then applied to a large field-scale groundwater remediation system for cleanup of large trichloroethylene plume at the Massachusetts Military Reservation in Cape Cod, Massachusetts. Furthermore, a master-slave (MS) parallelization scheme based on the Message Passing Interface is incorporated into the NPTSGA to implement objective function evaluations in a distributed processor environment, which can greatly improve the efficiency of the NPTSGA in finding Pareto-optimal solutions to the real-world applications. This study shows that the MS parallel NPTSGA in comparison with the original NPTS and NSGA-II can balance the tradeoff between the diversity and optimality of solutions during the search process and is an efficient and effective tool for optimizing the multi-objective design of groundwater remediation systems under complicated hydrogeologic conditions.

Dynamic Economic Emission Dispatch Using Multi-Objective Hybrid Evolutionary Algorithm

Dynamic economic emission dispatch (DEED) is an important optimization task for power plants. The problem is a highly constrained multi-objective optimization problem involving conflicting objectives with both equality and inequality constraints. This paper introduces two objective functions of DEED model: the lowest generation cost and the smallest carbon emissions with power balance constraints, unit output constraints and unit ramp rate limits. Then the paper presents a multi-objective hybrid evolutionary algorithm (MHEA) to solve the DEED model. The MHEA is a hybrid optimization algorithm based on orthogonal initialization, improved differential operation with migration strategy, parameter adaptive control, multi-objective selection strategy and analytic hierarchy process based fuzzy technique (AFT). Numerical results of one test system demonstrate the capabilities of the proposed approach. Compared with other classical methods, the proposed approach gets better result.

A Hybrid Multiobjective Evolutionary Algorithm for Multiobjective Optimization Problems

Recently, the hybridization between evolutionary algorithms and other metaheuristics has shown very good performances in many kinds of multiobjective optimization problems (MOPs), and thus has attracted considerable attentions from both academic and industrial communities. In this paper, we propose a novel hybrid multiobjective evolutionary algorithm (HMOEA) for real-valued MOPs by incorporating the concepts of personal best and global best in particle swarm optimization and multiple crossover operators to update the population. One major feature of the HMOEA is that each solution in the population maintains a nondominated archive of personal best and the update of each solution is in fact the exploration of the region between a selected personal best and a selected global best from the external archive. Before the exploration, a selfadaptive selection mechanism is developed to determine an appropriate crossover operator from several candidates so as to improve the robustness of the HMOEA for different instances of MOPs. Besides the selection of global best from the external archive, the quality of the external archive is also considered in the HMOEA through a propagating mechanism. Computational study on the biobjective and three-objective benchmark problems shows that the HMOEA is competitive or superior to previous multiobjective algorithms in the literature.