Multi-objective Hybrid Differential Evolution Research Articles

A grid‐based searching algorithm for observer‐based multiobjective control of T–S fuzzy stochastic jump‐diffusion systems

Most studies on a multiobjective optimal control problem (MOCP) with nonlinear stochastic jump-diffusion system (NSJDS) constraints assume the state vector is available, but in practice, this is not necessarily the case. The observer-based MOCP is worthy of further research. Furthermore, the hybrid multiobjective differential evolution algorithm (HMODEA) is usually employed to help solve MOCPs with dynamical system constraints, and such problems often have a higher computational burden. To address these two issues, a grid-based front-squeezing searching algorithm (GBFSA) is proposed to solve the observer-based MOCP with NSJDS. Takagi-Sugeno (T-S) fuzzy model is used to approximate the NSJDS and convert the problem into an MOCP with linear matrix inequality (LMI) constraints. Then, the GBFSA efficiently searches for the Pareto front by merging the LMIs and the squeezing theorem. To automatically select a preferred Pareto controller, the minimum Manhattan distance (MMD) approch is applied. Mathematical proofs are given to show that the obtained Pareto optimal controller can concurrently stabilize the associated NSJDS and achieve the desired performance indices. In addition, computational complexity and convergence analysis are also provided.

Dynamic economic emission dispatch using whale optimization algorithm for multi-objective function

Introduction. Dynamic Economic Emission Dispatch is the extended version of the traditional economic emission dispatch problem in which ramp rate is taken into account for the limit of generators in a power network. Purpose. Dynamic Economic Emission Dispatch considered the treats of economy and emissions as competitive targets for optimal dispatch problems, and to reach a solution it requires some conflict resolution. Novelty. The decision-making method to solve the Dynamic Economic Emission Dispatch problem has a goal for each objective function, for this purpose, the multi-objective problem is transformed into single goal optimization by using the weighted sum method and then control/solve by Whale Optimization Algorithm. Methodology. This paper presents a newly developed metaheuristic technique based on Whale Optimization Algorithm to solve the Dynamic Economic Emission Dispatch problem. The main inspiration for this optimization technique is the fact that metaheuristic algorithms are becoming popular day by day because of their simplicity, no gradient information requirement, easily bypass local optima, and can be used for a variety of other problems. This algorithm includes all possible factors that will yield the minimum cost and emissions of a Dynamic Economic Emission Dispatch problem for the efficient operation of generators in a power network. The proposed approach performs well to perform in diverse problem and converge the solution to near best optimal solution. Results. The proposed strategy is validated by simulating on MATLAB® for 5 IEEE standard test system. Numerical results show the capabilities of the proposed algorithm to establish an optimal solution of the Dynamic Economic Emission Dispatch problem in a several runs. The proposed algorithm shows good performance over the recently proposed algorithms such as Multi-Objective Neural Network trained with Differential Evolution, Particle swarm optimization, evolutionary programming, simulated annealing, Pattern search, multi-objective differential evolution, and multi-objective hybrid differential evolution with simulated annealing technique.

Hybridized multi-objective optimization approach (HMODE) for lysine fed-batch fermentation process

A new hybrid multi-objective differential evolution (MODE) algorithm is proposed that combines the MODE algorithm for the global space search with a dynamical local search (DLS) method for the local space search. HMODE-DLS algorithm was validated using the tri-objective DTLZ7 test problem and the results were compared with MODE algorithm with respect to four performance metrics. In addition to HMODE-DLS, another three algorithms were used to solve two multi-objective optimization cases in an industrial lysine bioreactor at different feeding conditions. Case 1 considers maximizing lysine’s productivity and yield. While case 2 studies the maximization of productivity along with minimization of total operating time. In all cases, theoretical and industrial, HMODE-DLS showed a better performance with a better quality Pareto set of solutions. The Pareto front of case 1 found by HMODE-DLS was compared with a recent study trade-off, and the current non-dominated solutions values were found to be improved. This indicates that the lysine production process is enhanced. For case 2, the switching time from fed-batch to batch was found to be the key decision variable. Generally, these findings indicate the effectiveness of HMODE-DLS for the studied cases and its potential in solving real world complex problems.

Hybridization Approach Towards Improving the Performance of Evolutionary Algorithm

Multi-objective differential evolution (MODE) algorithm has been widely used in solving multi-objective optimization problems. In this paper, a hybridization technique is proposed to improve the performance of MODE algorithm in terms of speed and convergence. The proposed hybrid MODE-dynamic-random local search (HMODE-DLS) algorithm combines MODE and dynamic-random local search (DLS) algorithm. To evaluate the proposed algorithm and validate its performance, benchmark test problems (both constrained and non-constrained) are considered to be solved using MODE and the proposed HMODE-DLS algorithms. To compare between the two algorithms, five performance metrices are calculated, which are convergence, spread, generational distance, spacing and hypervolume ratio. Mean and standard deviation values for the performance metrics are reported, and the best in each category is highlighted. The Conv metric results of the new hybrid MODE are compared with other reported ones. Additionally, the effect of local search probability is studied for selected problems. In general, HMODE-DLS performance outshines, in terms of convergence and robustness, compared with other tested algorithms. HMODE-DLS is, generally, faster, and its results are of improved quality compared to MODE algorithm.

Multi-objective Hybrid DE Algorithm for Solving VRPTW

For the characteristics of the Vehicle Routing Problem with Time Windows(VRPTW) ô€€€a multi-objective hybrid Differential Evolution algorithm for VRPTW is proposed. Firstly, through a linearly varying parameter controls the probability of choice of DE/rand/1 mutation strategy and DE/best/1 mutation strategy. Secondly, a crossover operation based on merge sort is designed. Finally, selection operations employ Pareto-dominated concepts and ring rules to rank individuals and output non-dominated solutions. The experimental results compared with single strategy DE algorithm and ABC algorithms show that the proposed algorithm is effective in solving the VRPTW.

Dual-Objective Scheduling of Rescue Vehicles to Distinguish Forest Fires via Differential Evolution and Particle Swarm Optimization Combined Algorithm

It is complex and difficult to perform the emergency scheduling of forest fires in order to reduce the operational cost and improve the efficiency of extinguishing fire services. A new research issue arises when: 1) decision-makers want to minimize the number of rescue vehicles (or fire-fighting ones) while minimizing the extinguishing time; and 2) decision-makers prefer to complete this task given limited vehicle resources. To do so, this paper presents a novel multiobjective scheduling model to handle forest fires subject to limited rescue vehicle (fire engine) constraints, in which a fire-spread speed model is introduced into this problem to better describe practical forestry fire. Moreover, a Multiobjective Hybrid Differential-Evolution Particle-Swarm-Optimization (MHDP) algorithm is proposed to create a set of Pareto solutions for this problem. This approach is applied to a real-world emergency scheduling problem of the forest fire in Mt. Daxing'anling, China. Its effectiveness is verified by comparing it with a genetic algorithm and particle swarm optimization algorithm. Experimental results show that the proposed approach is able to quickly produce satisfactory Pareto solutions.

Multi-elite guide hybrid differential evolution with simulated annealing technique for dynamic economic emission dispatch

This paper proposes an improved multi-objective differential evolutionary algorithm named multi-objective hybrid differential evolution with simulated annealing technique (MOHDE-SAT) to solve dynamic economic emission dispatch (DEED) problem. The proposed MOHDE-SAT integrates the orthogonal initialization method into the differential evolution, which enlarges the population diversity at the beginning of population evolution. In addition, modified mutation operator and archive retention mechanisms are used to control convergence rate, and simulated annealing technique and entropy diversity method are utilized to adaptively monitor the population diversity as the evolution proceeds, which can properly avoid the premature convergence problem. Furthermore, the MOHDE-SAT is applied on the thermal system with a heuristic constraint handling method, and obtains more desirable results in comparison to those alternatives established recently. The obtained results also reveal that the proposed MOHDE-SAT can provide a viable way for solving DEED problems.

Multiobjective controller design by solving a multiobjective matrix inequality problem

In this study, linear matrix inequality (LMI) approaches and multiobjective (MO) evolutionary algorithms are integrated to design controllers. An MO matrix inequality problem (MOMIP) is first defined. A hybrid MO differential evolution (HMODE) algorithm is then developed to solve the MOMIP. The hybrid algorithm combines deterministic and stochastic searching schemes. In the solving process, the deterministic part aims to exploit the structures of matrix inequalities, and the stochastic part is used to fully explore the decision variable space. Simulation results show that the HMODE algorithm can produce an approximated Pareto front (APF) and Pareto-efficient controllers that stabilise the associated controlled system. In contrast with single-objective designs using LMI approaches, the proposed MO methodology can clearly illustrate how the objectives involved affect each other, that is, a broad perspective on optimality is provided. This facilitates the selecting process for a representative design, and particularly the design that corresponds to a non-dominated vector lying in the knee region of the APF. In addition, controller gains can be readily modified to incorporate the preference or need of a system designer.

A Hybrid Multiobjective Differential Evolution Algorithm and Its Application to the Optimization of Grinding and Classification

The grinding-classification is the prerequisite process for full recovery of the nonrenewable minerals with both production quality and quantity objectives concerned. Its natural formulation is a constrained multiobjective optimization problem of complex expression since the process is composed of one grinding machine and two classification machines. In this paper, a hybrid differential evolution (DE) algorithm with multi-population is proposed. Some infeasible solutions with better performance are allowed to be saved, and they participate randomly in the evolution. In order to exploit the meaningful infeasible solutions, a functionally partitioned multi-population mechanism is designed to find an optimal solution from all possible directions. Meanwhile, a simplex method for local search is inserted into the evolution process to enhance the searching strategy in the optimization process. Simulation results from the test of some benchmark problems indicate that the proposed algorithm tends to converge quickly and effectively to the Pareto frontier with better distribution. Finally, the proposed algorithm is applied to solve a multiobjective optimization model of a grinding and classification process. Based on the technique for order performance by similarity to ideal solution (TOPSIS), the satisfactory solution is obtained by using a decision-making method for multiple attributes.

Culture belief based multi-objective hybrid differential evolutionary algorithm in short term hydrothermal scheduling

A culture belief based multi-objective hybrid differential evolution (CB-MOHDE) is presented to solve short term hydrothermal optimal scheduling with economic emission (SHOSEE) problem. This problem is formulated for compromising thermal cost and emission issue while considering its complicated non-linear constraints with non-smooth and non-convex characteristics. The proposed algorithm integrates a modified multi-objective differential evolutionary algorithm into the computation model of culture algorithm (CA) as well as some communication protocols between population space and belief space, three knowledge structures in belief space are redefined according to these problem-solving characteristics, and in the differential evolution a chaotic factor is embedded into mutation operator for avoiding the premature convergence by enlarging the search scale when the search trajectory reaches local optima. Furthermore, a new heuristic constraint-handling technique is utilized to handle those complex equality and inequality constraints of SHOSEE problem. After the application on hydrothermal scheduling system, the efficiency and stability of the proposed CB-MOHDE is verified by its more desirable results in comparison to other method established recently, and the simulation results also reveal that CB-MOHDE can be a promising alternative for solving SHOSEE.

Multi-objective optimal strategy for generating and bidding in the power market

Based on the coordinated interaction between units output and electricity market prices, the benefit/risk/emission comprehensive generation optimization model with objectives of maximal profit and minimal bidding risk and emissions is established. A hybrid multi-objective differential evolution optimization algorithm, which successfully integrates Pareto non-dominated sorting with differential evolution algorithm and improves individual crowding distance mechanism and mutation strategy to avoid premature and unevenly search, is designed to achieve Pareto optimal set of this model. Moreover, fuzzy set theory and entropy weighting method are employed to extract one of the Pareto optimal solutions as the general best solution. Several optimization runs have been carried out on different cases of generation bidding and scheduling. The results confirm the potential and effectiveness of the proposed approach in solving the multi-objective optimization problem of generation bidding and scheduling. In addition, the comparison with the classical optimization algorithms demonstrates the superiorities of the proposed algorithm such as integrality of Pareto front, well-distributed Pareto-optimal solutions, high search speed.

A hybrid multiobjective differential evolution method for electromagnetic device optimization

PurposeThe purpose of this paper is to show that the performance of differential evolution (DE) can be substantially improved by a combination of techniques. These enhancements are applicable to both single and multiobjective problems. Their combined use allows the optimization of complex 3D electromagnetic devices.Design/methodology/approachDE is improved by a combination of techniques which are applied in a cascade way and their single and combined effect is tested on well‐known benchmarks and domain‐specific applications.FindingsIt is shown that the combined use of enhancement techniques provides substantial improvements in the speed of convergence for both single and multiobjective problems.Research limitations/implicationsThe increased speed of convergence may come at the price of a somewhat decreased robustness. However, such behavior is justified by the CPU time constraints under which the optimization has to be performed.Practical implicationsThe proposed approach appears to be an efficient general purpose stochastic optimizer for electromagnetic design problems.Originality/valueThis paper explorers the combined use of many of the most recent and successful algorithmic improvements to DE and applies them to both single and multiobjective problems.

Adaptive multi-objective hybrid differential evolution algorithm in union transport scheduling

The traditional single-objective algorithm can only get one solution, but the multi-objective algorithm can get a solution set after every run. The algorithm (DEASA) improved the differential evolution strategy, designed reconstruction, adjusted parameter adaptively, adopted arena's principle to build non-dominating set rules, and added simulated annealing strategies into the differential evolution algorithm which enhanced the ability to further improve the performance of the algorithm and reduced the time complexity to avoid falling into local optimum. The experiments show that this algorithm can effectively solve the union transport problem.

Hybrid multi-objective differential evolution (H-MODE) for optimisation of polyethylene terephthalate (PET) reactor

Multi-objective evolutionary algorithms (MOEAs) are used to solve the optimisation problems with more than one objective to be optimised simultaneously having conflict among each other. Due to the limitations of traditional deterministic algorithms to handle complex and nonlinear search space, several EAs are developed in the recent past. The multi-objective differential evolution (MODE) algorithm is already tested and found to be a reliable algorithm due to their ability to handle non-linear problems efficiently. Though MODE is accurate in terms of converging to the global Pareto front, traditional method has their advantage in terms of speed. We combined these two algorithms and developed hybrid strategy of MODE thus, achieving both accuracy and speed. Hybrid MODE (H-MODE) algorithm is applied on multi-objective optimisation of industrial wiped film polyethylene terephthalate reactor. The results of the present study are compared with those obtained using MODE algorithm. Smooth and well diverse Pareto optimal front is observed with a much faster speed using H-MODE.

Optimization of Adiabatic Styrene Reactor: A Hybrid Multiobjective Differential Evolution (H-MODE) Approach

In this study, a hybrid strategy of multiobjective differential evolution (hybrid-MODE) algorithm is proposed that consists of an evolutionary algorithm for global search and a deterministic algorithm for local search. To begin, the proposed algorithm is tested for its performance using a benchmark test function (KUR) as case study 1 with the nondominated sorting genetic algorithm-II (NSGA-II) (both binary- and real-coded versions), strength Pareto evolutionary algorithm (SPEA), Pareto archived evolutionary strategy (PAES), multiobjective differential evolution (MODE), and an improved strategy of MODE algorithms. Subsequently, the multiobjective optimization of an industrial adiabatic styrene reactor is carried out as case study 2, employing a prevalidated model using the hybrid-MODE algorithm and an improved strategy of MODE. Four cases (three sets of two-objective optimization, cases 1−3, and one set of three-objective optimization, case 4) are considered consisting of simultaneous maximization of styrene productivity, selectivity, and yield with four decision variables and two constraints. The proposed algorithm converges to a better set of nondominated solutions (possibly a Pareto front) as compared to the nondominated solutions obtained using NSGA and an improved strategy of MODE algorithms. The limitations of previous studies are reported in terms of key decision variables. The hybrid strategy of MODE is found to converge to the true Pareto front more rapidly (in fewer function evaluations), resulting in a well-diversified Pareto front as compared to the stand-alone evolutionary approach.

A novel multi-objective particle swarm optimization algorithm for no-wait flow shop scheduling problems

The current paper presents a novel multi-objective particle swarm optimization (MOPSO) algorithm for solving no-wait flow shop scheduling problems with makespan and maximum tardiness criteria. First, in the algorithm, particles are represented as job permutations and updated directly in the discrete domain. Second, the concept of Pareto dominance is applied to compare different solutions of multi-objective optimization, and a set is employed to hold and to update the obtained non-dominated solutions, where a randomly selected non-dominated solution is assigned as the global best particle to maintain the diversity of the searching direction and to speed up the convergence process to the Pareto front. Third, a new multi-objective heuristic, named the PWQ (Pan—Wang—Qian) heuristic, is proposed to produce a population of initial particles with relatively good performances. Fourth, a simple but effective multi-objective local search algorithm is developed to embed in the MOPSO algorithm for stressing the balance between global exploration and local exploitation. In addition, two speed-up methods are devised to evaluate a job permutation and its insert neighbourhood respectively. Computational simulation results based on the well-known benchmarks and statistical performance comparisons are provided. It is shown that the proposed algorithm is superior to a recently published multi-objective hybrid differential evolution (MHDE) algorithm in terms of searching quality, diversity level, robustness, and efficiency.