Multi-objective Evolutionary Algorithm Based On Decomposition Research Articles

Reliability of the weight vector generation method of the multi-objective evolutionary algorithm and application

The decomposition-based multi-objective evolutionary algorithm first generates a set of weight vectors in advance, and it is very important to select a set of appropriate weight vectors for the decomposition-based algorithm. A variety of weight vector generation methods have been proposed in the existing algorithms, but in most algorithms, a pre-defined weight vector generation method is still used, the pre-defined weight vector is too specialized for the simplex-like front surface, which results in poor performance on the front surface with irregularities. At the same time, most of the existing algorithms have proposed many new adaptive strategies for weight vectors, but if you generate a set of more suitable weight vectors at the beginning, and then use the update strategy, it can make the algorithm achieve a better balance between diversity and convergence. In order to select a suitable weight vector, this paper proposes a multi-stage MOEA to select a suitable weight vector. The algorithm is divided into multiple stages according to the evolution process, first of all, in the early stage of evolution, the reliability of multiple weight vector generation methods was evaluated according to the spearman correlation coefficient in statistics, choose the most suitable weight generation method; Secondly, this method can be applied to the search for high-quality solutions in the middle of evolution; Finally, a weight vector adaptive strategy is adopted in the overall evolution process. In the experiment, the proposed algorithm was analyzed in the benchmark test problem, mechanical bearing and light aircraft gear reducer. The experimental results show the effectiveness of the proposed algorithm.

A decomposition-based multi-objective evolutionary algorithm for hybrid flowshop rescheduling problem with consistent sublots

ABSTRACT Lot streaming is the most widely used technique to facilitate the overlap of successive operations. Considering the consistent sublots and machine breakdown, this study investigates the multi-objective hybrid flowshop rescheduling problem with consistent sublots (MOHFRP_CS), which aims at optimising the total completion time, starting time deviations of operations, and average adjustment of sublot sizes simultaneously. By introducing the decomposition strategy and effective migrating birds optimisation framework, this paper develops a multi-objective migrating birds optimisation algorithm based on decomposition (MMBO/D). In MMBO/D, the problem is decomposed into a series of sub-problems, and its solutions are initialised by the Glover operator and further optimised by the variable neighbourhood descent strategy. The weights assigned to the sub-problems are adapted dynamically according to a variable weight strategy, and a global update strategy is employed to update the solutions. A novel sharing and benefiting mechanism is proposed to implement coevolution among different sub-problems. Competitive mechanisms are modified by considering similar sub-problems to improve population quality. A criterion is designed to check whether a subproblem is stuck in the local optima. The comprehensive computational results demonstrate that MMBO/D outperforms other state-of-the-art multi-objective evolutionary algorithms (MOEAs) for the addressed problem.

Multi-Objective Optimal Power Flow including Wind and Solar Generation Uncertainty Using New Hybrid Evolutionary Algorithm with Efficient Constraint Handling Method

A new hybrid decomposition-based multiobjective evolutionary algorithm is proposed for optimal power flow (OPF) including wind and solar generation uncertainty. This study recommends a novel constraint-handling method, which adaptively adds the penalty function and eliminates the parameter dependency on penalty function evaluation. The summation-based sorting and improved diversified selection methods are utilized to enhance the diversity of multiobjective optimization algorithms. The OPF problem is modeled as a multiobjective optimization problem with four objectives such as minimizing (i) total fuel cost (TC) including the cost of renewable energy source (RES), (ii) total emission (TE), (iii) active power loss (APL), and (iv) voltage magnitude deviation (VMD). The impact of RESs such as wind and solar energy sources on integration is considered in optimal power flow cost analysis. The costs of RESs are considered in the OPF problem to minimize the overall cost so that the impact of intermittence and uncertainty of renewable sources is studied in terms of cost and operation wise. The uncertainty of wind and solar energy sources is described using probability distribution functions (PDFs) such as Weibull and lognormal distributions. The efficiency of the algorithm is tested on IEEE 30-, IEEE 57-, and IEEE 118-bus systems for all possible conditions of renewable sources using Monte Carlo simulations.

Green Energy Forecast-Based Bi-Objective Scheduling of Tasks Across Distributed Clouds

Current large-scale green cloud data centers (GCDCs) tend to consume a huge amount of energy and generate enormous carbon emissions. Existing studies have tried to solve this problem by either realizing prediction of green energy, or optimizing task scheduling. In contrast, this work seamlessly combines green energy prediction and task scheduling to jointly optimize revenue and energy cost of GCDCs. Specifically, this work designs a prediction method, named Savitzky-Golay and Long Short-Term Memory network (SG-LSTM), to realize noise filtering and forecast green energy. Based on such prediction, a bi-objective optimization method, named Decomposition-based Multi-objective evolutionary algorithm with Gaussian mutation and Crowding distance (DMGC), is developed to optimize the revenue and energy cost of GCDCs. Its performance is demonstrated over real-life datasets including Google cluster traces, wind speeds, solar irradiance and prices of electricity. Experimental results show that SG-LSTM outperforms its two peers, back propagation neural network and gated recurrent unit, in terms of root mean square errors and mean absolute errors. In addition, DMGC surpasses its such peers as NSGA-II, SPEA2, and MOEA/D in terms of revenue, energy cost and average execution time. Particularly, DMGC's revenue is 18%, 20% and 13.1% higher, energy cost is 16%, 19.8% and 15.2% lower, and average execution time is 60.02%, 38.47% and 24.17% lower than those of NSGA-II, SPEA2, and MOEA/D, respectively.

Developing an integrated model for planning the delivery of construction materials to post-disaster reconstruction projects

AbstractConstruction material delivery to post-disaster reconstruction projects is challenging because of the resource and time limitations that follow a large-scale disaster. There is compelling evidence that inadequate planning jeopardises the success of a large number of post-disaster reconstruction projects. Thus, the current study proposes an integrated approach to facilitate the procurement planning of construction materials following a large-scale disaster. The proposed approach clustered the location of construction projects using a differential evolution (DE)-K-prototypes, a new partitional clustering algorithm based on DE and K-prototypes, method. Then, using a permanent matrix prioritises cluster points based on route reliability-affecting factors. The model’s objectives are to minimise the total travel time, maximise the reliability of the route, and minimise the total weighted undelivered materials to projects. In the case of distribution of material through land vehicles, the possibility of breakdowns in the vehicle is considered, allowing for the determination of vehicle breakdown under various scenarios and the minimisation of undelivered materials to projects. As a result of the uncertain character of the disaster, the demands of construction projects are fuzzy, and Jimenez’s method is used to handle it. Due to the complexity of the problem, two algorithms are proposed, a multi-objective evolutionary algorithm based on decomposition (MOEA/D) and a non-dominated sorting genetic algorithm-II (NSGA-II). The results confirm that the proposed MOEA/D has a higher accuracy while NSGA-II has a shorter computational time. By providing new theoretical perspectives on disaster recovery strategies in the construction sector, this study contributes to the growing body of knowledge about disaster recovery strategies in the sector. The findings of this study can be employed to develop an integrated planning system for the delivery of construction materials to post-disaster reconstruction projects in disaster-prone countries.

A twin-archive guided decomposition based multi/many-objective evolutionary algorithm

1 Developed a decomposition based evolutionary algorithm to solve both multi and many objective optimization problems. 2 Developed an archive guided weight vector adaptation and Nadir point estimation strategy. 3 Compared with ten state-of-the-art MOEAs on IGD metric. 4 Problems with regular and irregular PFs handled efficiently. Decomposition-based Multi-Objective Evolutionary Algorithms (DMOEAs) gained popularity due to their ability to handle Multi/Many-objective Optimization Problems (MOPs/MaOPs). On the other hand, the weight vector adaptation strategy in DMOEAs is an essential ingredient for better performance, especially when dealing with MaOPs with irregular Pareto Front (PF). In general, an effective weight vector adaptation strategy faces challenges like identification of ineffective weight vectors, the proper timing and frequency of adaptation, reallocation of ineffective weight vectors and effective estimation of reference points. DMOEAs proposed in the literature try to address a subset of these issues, but fail to handle all of them simultaneously. In this paper, we propose a DMOEA namely ‘A Twin-Archive Guided Decomposition based Multi/Many-objective Evolutionary Algorithm’ (TAG-DMOEA) that basically employs two archives to update weight vectors and to estimate nadir point, separately. The better performance of TAG-DMOEA is validated over 10 representative state-of-the-art algorithms on 16 test problems with the number of objectives ranging from 2 to 10. The empirical results demonstrate the effectiveness of TAG-DMOEA on MOPs/MaOPs in both regular and irregular PFs.

Optimal prediction intervals for macroeconomic time series using chaos and evolutionary multi-objective optimization algorithms

In a first-of-its-kind study, this paper formulates the problem of estimating the prediction intervals (PIs) in a macroeconomic time series as a bi-objective optimization problem and solves it with three evolutionary algorithms namely, Non-dominated Sorting Genetic Algorithm (NSGA-II), Non-dominated Sorting Particle Swarm Optimization (NSPSO) and Multi-Objective Evolutionary Algorithm based on Decomposition (MOEA-D). We also proposed modeling the chaos present in the time series as a preprocessor, which we called stage-1. Accordingly, we proposed 2-stage models, where stage-1 is followed by obtaining the optimal point prediction using NSGA-II/NSPSO/MOEA-D and using these point predictions to obtain PIs (stage-2). We then proposed a 3-stage hybrid, which is built on the 2-stage model, wherein the 3 rd stage also invokes NSGA-II/NSPSO/MOEA-D in order to estimate the PIs from the point predictions obtained in 2 nd stage by simultaneously and explicitly optimizing (i) prediction interval coverage probability (PICP) and (ii) prediction interval average width (PIAW). The proposed models yielded better results in terms of both PICP and PIAW compared to the state-of-the-art Lower Upper Bound Estimation Method (LUBE) with Gradient Descent (GD) and LUBE with long short-term memory (LSTM) network. The 3-stage models outperformed the 2-stage models with respect to PICP but showed similar performance in PIAW at the cost of running NSGA-II/NSPSO/MOEA-D second time. Overall, MOEA-D yielded best PIs in two datasets and NSGA-II outperformed the other two in the third dataset. But, in terms of hypervolume, in 2-stage MOEA-D produced most diverse solutions in two datasets, while NSGA-II was the winner in the third dataset.

Design of droop controller in islanded microgrids using multi‐objective optimisation based on accurate small‐signal model

The inaccuracy of power sharing is a classic problem of droop control when an islanded AC microgrid suffers from high loads and line impedance differences. It degrades system performance and even destroys system stability. This paper originally presents a multi-objective optimisation droop control method to solve such a problem. And three objective functions are presented according to the characteristics of microgrids. First, a complete small-signal model of a microgrid in autonomous operation mode is established. Next, this paper derives constraint conditions for the stable microgrid. Then, this paper originally designs three objective functions for constructing a multi-objective optimisation (MOO) problem to improve control performance. The multiobjective evolutionary algorithm based on decomposition (MOEA/D) is used to obtain the Pareto optimal frontier of the MOO problem. The fuzzy affiliation function method is used to choose the best solution from the generated Pareto optimal frontier. Finally, simulations verified the validity and superiority of the presented method.

Dynamic multiobjective evolutionary algorithm with adaptive response mechanism selection strategy

In this paper, a dynamic multiobjective evolutionary algorithm (DMOEA) with an adaptive response mechanism selection strategy is proposed to address the shortcoming that a single response mechanism is suitable only for solving a certain type of dynamic multiobjective optimization problem. The proposed algorithm combines an adaptive response mechanism selection (ARMS) strategy and a multiobjective evolutionary algorithm based on decomposition (MOEA/D), and it is denoted as the MOEA/D-ARMS. Unlike the existing approaches, the ARMS strategy can adaptively select effective response mechanisms from the response mechanism pool based on the recent performance of each response mechanism. Four representative response mechanisms are selected to form the response mechanism pool. An overall evaluation strategy that assigns rewards to the response mechanism is adopted, and a probability-based method that is used to decide which response mechanism can be used to generate a new solution is employed. The proposed MOEA/D-ARMS algorithm is tested on two groups of test instances and compared with the decomposition-based and dominance-based DMOEAs. The results of the proposed MOEA/D-ARMS algorithm are superior to the compared algorithms, demonstrating its effectiveness.

Multi-Objective Evolutionary Algorithm Based on Two Reference Points Decomposition and Historical Information Prediction

Aims: The main goal of this paper is to address the issues of low-quality offspring solutions generated by traditional evolutionary operators, as well as the evolutionary algorithm's inability to solve multi-objective optimization problems (MOPs) with complicated Pareto fronts (PFs). Background: For some complicated multi-objective optimization problems, the effect of the multiobjective evolutionary algorithm based on decomposition (MOEA/D) is poor. For specific complicated problems, there is less research on how to improve the performance of the algorithm by setting and adjusting the direction vector in the decomposition-based evolutionary algorithm. Considering that in the existing algorithms, the optimal solutions are selected according to the selection strategy in the selection stage, without considering whether it could produce the better solutions in the stage of individual generation to achieve the optimization effect faster. As a result, a multi-objective evolutionary algorithm based on two reference points decomposition and historical information prediction is proposed. Objective: In order to verify the feasibility of the proposed strategy, the F-series test function with complicated PFs is used as the test function to simulate the proposed strategy. Method: Firstly, the evolutionary operator based on historical information prediction (EHIP) is used to generate better offspring solutions to improve the convergence of the algorithm; secondly, the decomposition strategy based on ideal point and nadir point is used to select solutions to solve the MOPs with complicated PFs, and the decomposition method with augmentation term is used to improve the population diversity when selecting solutions according to the nadir point. Finally, the proposed algorithm is compared to several popular algorithms by the F-series test function, and the comparison is made according to the corresponding performance metrics. Result: The performance of the algorithm is improved obviously compared with the popular algorithms after using the EHIP. When the decomposition method with augmentation term is added, the performance of the proposed algorithm is better than the algorithm with only the EHIP on the whole, but the overall performance is better than the popular algorithms. Conclusion : The experimental results show that the overall performance of the proposed algorithm is superior to the popular algorithms. The EHIP can produce better quality offspring solutions, and the decomposition strategy based on two reference points can well solve the MOPs with complicated PFs. This paper mainly demonstrates the theory without testing the practical problems. The following research mainly focuses on the application of the proposed algorithm to the practical problems such as robot path planning.

Multi-objective Iterated Local Search based on decomposition for job scheduling problems with machine deterioration effect

This work addresses an unrelated parallel machine scheduling problem in which the jobs cause deterioration of the machines. This factor decreases the performance of the machines, increasing the processing times of the jobs over time. We propose a mixed-integer nonlinear programming model for the problem that has two objectives: to minimize the maximum completion time of jobs (makespan) and to minimize the total time of delay of the jobs. In this paper, we also develop a different approach to extend Iterated Local Search (ILS) meta-heuristic to multi-objective problems. The Iterated Local Search Based on Decomposition (ILS/D) employs the decomposition strategy similar to the Multi-objective Evolutionary Algorithm Based on Decomposition (MOEA/D), in which the ILS is used as the search engine to improve the search process within the structure of the MOEA/D. We compared the ILS/D, MOEA/D and Non-dominated Sorting Genetic Algorithm II (NSGA-II) algorithms. The results show that the ILS/D outperforms the MOEA/D and NSGA-II algorithms by a significant margin. These findings show that the decomposition strategy is beneficial not only for evolutionary algorithms, but is also an efficient way to extend the ILS to multi-objective problems.

A Hybrid Multiobjective Optimization Based on Nondominated Sorting and Crowding Distance, with Applications to Wave Energy Converters

Multiobjective evolutionary algorithm based on decomposition (MOEA/D) has attracted a lot of attention since it can handle multiobjective problems (MOP) with a complicated Pareto front. The procedure involves decomposing a MOP into single subproblems, which are eventually optimized simultaneously based on the MOP neighborhood information. However, the MOEA/D strategy tends to produce a distributed optimization that is not of good quality in some problems with complex Pareto optimal front, such as problems with a long tail and sharp peak, common in real-world situations. This paper proposes an improved MOEA/D to enhance the distributed optimization quality and minimize its complexity while accelerating the optimization to get a better solution. The improved method is achieved by incorporating a Hybrid Differential Evolution/Particle Swarm Optimization algorithm and a hybrid operator based on nondominated sorting and crowding distance algorithm. This incorporation takes place in the mutation generator and initial population part of the original MOEA/D algorithm. Simulations and comparisons are carried out based on some MOP benchmark functions to verify the proposed method’s performance. The experimental results show that the proposed method achieves better performance compared to other algorithms. Furthermore, the proposed method is also applied to optimize the multiobjective wave energy converter model to maximize power per year and minimize cost per unit power.

A fuzzy constraint handling technique for decomposition-based constrained multi- and many-objective optimization

The challenge in solving constrained multi-objective optimization problems (CMOPs) is how to balance minimizing objectives and satisfying constraints, especially when the infeasible region is very large. To address this issue, this work proposes a fuzzy constraint handling technique, which uses the fuzzy set theory to accurately characterize the difference between solutions on objective function values and constraint violation degrees. On this basis, a new concept, called “fuzzy advantage”, is introduced to comprehensively quantify the degree to which one solution is better than others, allowing the infeasible solutions with promising fitness to survive. The proposed method is integrated with a decomposition-based multi-objective evolutionary algorithm to verify its effectiveness. Compared with nine state-of-the-art MOEAs on a number of test problems and a real-world optimization problem, the proposed algorithm shows high competitiveness in solving a variety of CMOPs.

Intrusion detection using multi-objective evolutionary convolutional neural network for Internet of Things in Fog computing

Our world is moving fast towards the era of the Internet of Things (IoT), which connects all kinds of devices to digital services and brings significant convenience to our lives. With the rapid increase in the number of devices connected to the IoT, there may exist more network vulnerabilities, resulting in more network attacks. Under this dynamic IoT environment, an effective intrusion detection system (IDS) is urgently needed to detect attacks with low-latency and high accuracy. A number of promising IDSs have been proposed based on deep learning (DL) techniques, but they need to do parameter tuning under different environments, which is very time-consuming. To alleviate this problem, this paper proposes a multi-objective evolutionary convolutional neural network for intrusion detection system, called MECNN, which is run on the fog nodes of Fog computing on IoT. In this approach, convolutional neural network (CNN) is used as the classifier to detect intrusions and the multi-objective evolutionary algorithm based on decomposition (MOEA/D) algorithm is modified to evolve the CNN model, which greatly simplifies the parameter tuning process of DL. To be specific, a novel encoding scheme is first proposed to transform the topological architecture of CNN into a chromosome of MOEA/D and then the two conflicting objectives, i.e., detection performance and model complexity of the CNN model, are simultaneously optimized by MOEA/D, which can obtain a number of IDSs with various detection performance and model complexities. Then, the most suitable MECNN model can be deployed in different fog nodes of Fog computing, providing low-latency and high-accuracy intrusion detection for IoT. Finally, the experimental studies are conducted on two popular datasets (AWID and CIC-IDS2107), which have validated that our MECNN model can improve detection performance and robustness to better protect the IoT when compared to other state-of-the-art IDSs.

Multi-objective parallel adjacent U-shaped assembly line balancing collaborated by robots and normal and disabled workers

This paper emphasises the parallel adjacent U-shaped assembly line balancing problem in which the collaborative work forces in the system comprise human workers and robots. Apart from normal workers, disabled workers are also hired to enable the company to enjoy corporate tax benefits from the government. Five objectives related to the system as a whole and another three interacting entities are optimised simultaneously. A mathematical model is formulated for the first time for this type of layout. Due to the NP-hard nature of the problem, a reference point based evolutionary algorithm, namely non-dominated sorting teaching-learning-based optimisation (NSTLBO III), is proposed to solve medium- and large-sized problems. The performances of NSTLBO III are benchmarked in the sense of Pareto efficiency with two well-known multi-objective evolutionary algorithms, i.e. non-dominated sorting genetic algorithm (NSGA III) and multi-objective evolutionary algorithm based on decomposition (MOEA/D). The experimental results show that NSTLBO III surpasses its contestants significantly concerning the convergence to the true Pareto front.

Randomized Decomposition Methods in Multi-objective Evolutionary Algorithm based on Decomposition for Many-objective Optimization Problems

As the number of objectives are increased in the optimization problem, the objective space is increased therefore it is not possible to use conventional methods to get answers for these problems. Therefore, some methods are proposed to solve this problem. As one of the solutions is called the decomposition. In decomposition the objectives are applied to the scalarization functions, and many sub-problems are obtained. Based on their neighborhood, the best members in the current generation of the evolutionary algorithm will be survived to the next generation. The algorithm which uses that idea is called Multi-objective Evolutionary Algorithm based on Decomposition (MOEA/D). Different typed of decomposition methods can be used with the MOEA/D algorithm. However, each of them has their own weaknesses or advantages. Therefore, to reduce the disadvantage of the decomposition methods, a hybrid approach is proposed in this research such that instead of a single decomposition method, two methods will be use randomly. The performance of the proposed hybrid method will be demonstrated on seven benchmark problems by using two metrics.

Optimal control of the multi-module vibration-driven locomotion robot

The vibration-driven robot utilizes the periodic inertia force from the oscillator to realize locomotion. Because its movement does not rely on wheels or legs, the robot's body can be designed very neatly for working in restricted circumstances such as pipeline inspection and post-disaster rescue. Because high mobility is essential in these applications, the issue of actuation design to maximize the robot's average locomotion velocity emerges. Distinct from parameter optimization at given actuation patterns, the present paper represents the actuation design as the problem of optimal control and constructs an evolutionary algorithm to solve it. First, taking advantage of the periodicity, the internal actuation is represented as the Fourier series with the unknown period, harmonic coefficients, and phase shifts. Then, the multi-objective evolutionary algorithm based on decomposition (MOEA/D) is employed to optimize the unknown multi-parameters. Numerical results show that the optimal actuation of the one-module robot with isotropic friction is consistent with existing theoretical solutions, which verifies the correctness and practicability of our general scheme. Further explorations of the multi-module robot reveal that the optimal actuation continuously degenerates from the three-phase pattern to the two-phase when the friction ratio gradually attenuates to zero. Most importantly, although the optimal actuation phase shift between adjacent robot modules has been commonly accepted as half of the actuation period, the proposed scheme finds that the average velocity indeed maintains the maximum within a certain phase margin. As can be expected, this robustness will relax the burden of sophisticated actuation tuning in practice.

A Comparison Study of Multi-Objective Bonobo Optimizers for Optimal Integration of Distributed Generation in Distribution Systems

In this paper, the three newly published Multi-Objective Bonobo Optimizer (MOBO) variants are assessed and evaluated using statistical analysis for solving the multi-objective optimization of Distributed Generation (DG) into distribution systems. The main objectives of the study are to minimize system loss and enhance voltage profile. While the first variant, MOBO1, depends on the sort and grid-index approach, the second variant, MOBO2, relies on the Non-dominated Sorting Genetic Algorithm-II (NSGA-II) algorithm technique. The last variant, MOBO3, is inspired by the Multi-objective Evolutionary Algorithm based on Decomposition (MOEA/D). The three MOBO algorithms are compared to themselves and to other algorithms solving the same optimization problem. These algorithms include the MOJAYA, Multi-Objective Artificial Ecosystem-Based Algorithm (MOAEO), Multi-Objective Gravitational Search Algorithm (MOGSA), and Multi-Objective Particle Swarm Optimization (MOPSO). The 33-bus and 85-bus radial distribution systems are used test systems for solving the optimal allocation of single- and three-DG units operating at unity power factor. In order to find the best compromise solution, the Pareto Optimal front method is adopted with the help of a fuzzy-based function. The obtained results show the effectiveness of the MOBO variants compared with other algorithms in terms of different statistical parameters and multi-objective performance metrics such as diversity, hypervolume, spacing, and set coverage. While the MOBO algorithm reduces power loss and TVD by 39.59 and 68.31% for a single DG, they are reduced to 58.13 and 88.44% for three DG units allocated to the 33-bus distribution system, respectively. On the other hand, the MOBO algorithm reduces power loss and TVD by 37.28 and 66.84% for a single DG, respectively, they are decreased to 46.35 and 82.53% for three DG units assigned to the 85-bus distribution system. Among the three MOBO variants, it is found that the MOBO1 is superior for a single-DG allocation, while the MOBO3 is the best for the allocation of three-DG units.

A multi-objective model for optimizing the redundancy allocation, component supplier selection, and reliable activities for multi-state systems

This paper presents a multi-objective availability-redundancy allocation optimization model for a hyper-system. The hyper-system consists of B systems with shared resources. The structure of the systems is series-parallel subsystems consisting of multi-failure and multi-state components. The components may be purchased from different suppliers based on their price and discounts. It is assumed that technical and organizational activities continuously affect the components' failure rates and the subsystems' working conditions before starting the system's mission horizon. The model aims to find the optimal number and the type of the subsystems' components for all systems from each supplier and the level of the technical and organizational activities. The problem is classified as an NP-hard class of problems; thus, four multi-objective meta-heuristics are adapted to solve the proposed model. These four meta-heuristics are non-dominated sorting genetic algorithm type II (NSGA-II) and type III (NSGA-III), non-dominated ranking genetic algorithm (NRGA), and multi-objective evolutionary algorithm based on decomposition (MOEA/D). The parameters of all algorithms are calibrated using response surface methodology. Moreover, a method based on a sequential combination of multi-objective evolutionary algorithms and data clustering is used on the Pareto solutions to yield a smaller and more manageable set of prospective solutions. The results showed the superiority of the NSGA-III and the MOEA/D algorithms to solve the presented model.

A structural optimization model of a biochemical detection micromixer based on RSM and MOEA/D

Microfluidic mixers are widely applied in biochemical detection experiments. In this study, based on the compact rectangular baffle structure, the structural optimization is performed from the perspectives of baffle length and angle parameters. To shorten the optimization time and reduce the cost of simulation calculation, the response surface method (RSM) is adopted. In the optimization process, different indicators of mixing effects have contradictory objectives and it is prone to generate local optimal solutions of design parameters of the baffle. Therefore, the multi-objective evolutionary algorithm based on decomposition (MOEA/D) is introduced to obtain the Pareto solution set of the optimal baffle parameters. The results of biochemical detection simulation experiments indicated that when the length of the baffle is 140μm, the degree of asymmetry of the velocity curve is the largest and the detection sensitivity is the highest. When the baffle angle is between 60∘ and 80∘, the microchannel fluid can generate obvious vortices near the baffle and reduce the pressure drop. The MOEA/D algorithm obtains a set of rectangular baffle parameters (l=140μm; θ=61.5°). The structural optimization model can improve the concentration distribution level and reduce the pressure drop and the mixed energy cost.