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Microfluidic capture chips are useful for preparing or analyzing a wide range of different chemical, biological, and medical samples. A typical microfluidic capture chip contains features that capture certain targets (i.e. molecules, particles, cells) as they flow through the chip. However, creating optimal capture chip designs is difficult because of the inherent relationship between capture efficiency and flow resistance: as more capture features are added to the chip, the capture efficiency increases, but the additional features slow the flow of fluid through the chip. This thesis introduces the use of multi-objective optimization to generate capture chip designs that balance the trade-off between maximizing target capture efficiency and minimizing resistance to fluid flow. Design automation for this important class of microfluidic chips has not been attempted previously. Our approach automatically produces a Pareto Front of non-dominated chip designs in a reasonable amount of time, and most of these designs have comparable capture efficiency to hand-designed chips with far lower flow resistance. By choosing from the chip designs on the Pareto Front, a user can obtain high capture efficiency without exceeding the flow resistance constraints of their application.

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link. In large-scale multiobjective optimization, too many decision variables hinder the convergence search of evolutionary algorithms. Reducing the search range of the decision space will significantly alleviate this puzzle. With this in mind, this paper proposes a fuzzy decision variables framework for largescale multiobjective optimization. The framework divides the entire evolutionary process into two main stages: fuzzy evolution and precise evolution. In fuzzy evolution, we blur the decision variables of the original solution to reduce the search range of the evolutionary algorithm in the decision space so that the evolutionary population can quickly converge. The degree of fuzzification gradually decreases with the evolutionary process. Once the population approximately converges, the framework will turn to precise evolution. In precise evolution, the actual decision variables of the solution are directly optimized to increase the diversity of the population so as to be closer to the true Pareto optimal front. Finally, this paper embeds some representative algorithms into the proposed framework and verifies the framework’s effectiveness through comparative experiments on various large-scale multiobjective problems with 500 to 5000 decision variables. Experimental results show that in large-scale multiobjective optimization, the framework proposed in this paper can significantly improve the performance and computational efficiency of multiobjective optimization algorithms.

With consideration of false data injection (FDI) on the demand side, it brings a great challenge for the optimal defensive strategy with the security issue, voltage stability, power flow, and economic cost indexes. This article proposes a Takagi-Sugeuo-Kang (TSK) fuzzy system-based reinforcement learning approach for the resilient optimal defensive strategy of interconnected microgrids. Due to FDI uncertainty of the system load, TSK-based deep deterministic policy gradient (DDPG) is proposed to learn the actor network and the critic network, where multiple indexes' assessment occurs in the critic network, and the security switching control strategy is made in the actor network. Alternating direction method of multipliers (ADMM) method is improved for policy gradient with online coordination between the actor network and the critic network learning, and its convergence and optimality are proved properly. On the basis of security switching control strategy, the penalty-based boundary intersection (PBI)-based multiobjective optimization method is utilized to solve economic cost and emission issues simultaneously with considering voltage stability and rate-of-change of frequency (RoCoF) limits. According to simulation results, it reveals that the proposed resilient optimal defensive strategy can be a viable and promising alternative for tackling uncertain attack problems on interconnected microgrids.

The job-shop scheduling problem (JSSP) is a challenging scheduling and optimization problem in the industry and engineering, which relates to the work efficiency and operational costs of factories. The completion time of all jobs is the most commonly considered optimization objective in the existing work. However, factories focus on both time and cost objectives, including completion time, total tardiness, advance time, production cost, and machine loss. Therefore, this article first time proposes a many-objective JSSP that considers all these five objectives to make the model more practical to reflect the various demands of factories. To optimize these five objectives simultaneously, a novel multiple populations for multiple objectives (MPMO) framework-based genetic algorithm (GA) approach, called MPMOGA, is proposed. First, MPMOGA employs five populations to optimize the five objectives, respectively. Second, to avoid each population only focusing on its corresponding single objective, an archive sharing technique (AST) is proposed to store the elite solutions collected from the five populations so that the populations can obtain optimization information about the other objectives from the archive. This way, MPMOGA can approximate different parts of the entire Pareto front (PF). Third, an archive update strategy (AUS) is proposed to further improve the quality of the solutions in the archive. The test instances in the widely used test sets are adopted to evaluate the performance of MPMOGA. The experimental results show that MPMOGA outperforms the compared state-of-the-art algorithms on most of the test instances.

In dealing with the expensive multiobjective optimization problem, some algorithms convert it into a number of single-objective subproblems for optimization. At each iteration, these algorithms conduct surrogate-assisted optimization on one or multiple subproblems. However, these subproblems may be unnecessary or resolved. Operating on such subproblems can cause server inefficiencies, especially in the case of expensive optimization. To overcome this shortcoming, we propose an adaptive subproblem selection (ASS) strategy to identify the most promising subproblems for further modeling. To better leverage the cross information between the subproblems, we use the collaborative multioutput Gaussian process surrogate to model them jointly. Moreover, the commonly used acquisition functions (also known as infill criteria) are investigated in this article. Our analysis reveals that these acquisition functions may cause severe imbalances between exploitation and exploration in multiobjective optimization scenarios. Consequently, we develop a new acquisition function, namely, adaptive lower confidence bound (ALCB), to cope with it. The experimental results on three different sets of benchmark problems indicate that our proposed algorithm is competitive. Beyond that, we also quantitatively validate the effectiveness of the ASS strategy, the CoMOGP model, and the ALCB acquisition function.

Constrained multiobjective optimization problems widely exist in real-world applications. To handle them, the balance between constraints and objectives is crucial, but remains challenging due to non-negligible impacts of problem types. In our context, the problem types refer particularly to those determined by the relationship between the constrained Pareto-optimal front (PF) and the unconstrained PF. Unfortunately, there has been little awareness on how to achieve this balance when faced with different types of problems. In this article, we propose a new constraint handling technique (CHT) by taking into account potential problem types. Specifically, inspired by the prior work, problems are classified into three primary types: 1) I; 2) II; and 3) III, with the constrained PF being made up of the entire, part and none of the unconstrained counterpart, respectively. Clearly, any problem must be one of the three types. For each possible type, there exists a tailored mechanism being used to handle the relationships between constraints and objectives (i.e., constraint priority, objective priority, or the switch between them). It is worth mentioning that exact problem types are not required because we just consider their possibilities in the new CHT. Conceptually, we show that the new CHT can make a tradeoff among different types of problems. This argument is confirmed by experimental studies performed on 38 benchmark problems, whose types are known, and a real-world problem (with unknown types) in search-based software engineering. Results demonstrate that within both decomposition-based and nondecomposition-based frameworks, the new CHT can indeed achieve a good tradeoff among different problem types, being better than several state-of-the-art CHTs.

Surrogate-assisted multi-objective evolutionary algorithms have advanced the field of computationally expensive optimization, but their progress is often restricted to low-dimensional problems. This manuscript presents a multiple classifiers-assisted evolutionary algorithm based on decomposition, which is adapted for high-dimensional expensive problems in terms of the following two insights. Compared to approximation-based surrogates, the accuracy of classification-based surrogates is robust for few high-dimensional training samples. Further, multiple local classifiers can hedge the risk of over-fitting issues. Accordingly, the proposed algorithm builds multiple classifiers with support vector machines on a decomposition-based multi-objective algorithm, wherein each local classifier is trained for a corresponding scalarization function. Experimental results statistically confirm that the proposed algorithm is competitive to the state-of-the-art algorithms and computationally efficient as well.

Modern transportation is associated with considerable challenges related to safety, mobility, the environment and space limitations. Vehicular networks are widely considered to be a promising approach for improving satisfaction and convenience in transportation. However, with the exploding popularity among vehicle users and the growing diverse demands of different services, ensuring the efficient use of resources and meeting the emerging needs remain challenging. In this paper, we focus on resource allocation in vehicular cloud computing (VCC) and fill the gaps in the previous research by optimizing resource allocation from both the provider's and users' perspectives. We model this problem as a multi-objective optimization with constraints that aims to maximize the acceptance rate and minimize the provider's cloud cost. To solve such an NP-hard problem, we improve the nondominated sorting genetic algorithm II (NSGA-II) by modifying the initial population according to the matching factor, dynamic crossover probability and mutation probability to promote excellent individuals and increase population diversity. The simulation results show that our proposed method achieves enhanced performance compared to the previous methods.

In state-of-the-art, it has proven that multi-view ensemble learning performs better than classical machine learning algorithms, with the optimized setting of views (subsets of features) usually. Obtaining the appropriate number of views for a given dataset is a complex problem in multi-view ensemble learning (MEL). The finding of the total number of possible views is an NP-hard problem, i.e., equivalent to Bell number. Moreover, the complexity of multi-view learning increases over a higher number of views of the dataset. Therefore, it is highly required to consider a smaller number of views with higher accuracy for optimal performance of MEL. In this work, MEL using Multi-Objective Particle Swarm Optimization (MEL-MOPSO) method has been proposed. The two objectives (number of views of the data and classification accuracy of MEL) have considered where the trade-off between objectives has been performed while searching for an optimal solution using Particle Swarm Optimization (PSO) in the process of multiobjective optimization. The experiments have been done over sixteen high-dimensional datasets using four state-of-art view construction methods. The individual views of the dataset has been utilized to learn through a support vector machine algorithm. The quantitative and non-parametric statistical analyses show that the proposed method has performed effectively and efficiently.

Considering the influence of iron core saturation and complex boundary conditions, a novel no-load magnetic field analytical method and system multi-objective optimization model for interior permanent magnet synchronous motor (IPMSM) are proposed. Firstly, an analytical method based on magnetic potential permeance method is proposed. The complex cogging effect and equivalent air gap permeability function are fully considered in this method. Furthermore, on the basis of Taguchi optimization design based on Fuzzy theory, an improved optimization model considering multi-variable interaction is proposed. Among them, in order to comprehensively consider the performance of electromagnetic, vibration, and temperature rise, five optimization objectives including torque, pulsation, cogging torque, loss, and flux density have been optimized. The sensitivity of design variables and the interaction between variables are not ignored. Finally, a 6-pole 36-slot IPMSM is manufactured for prototype experiments. A large number of prototype experiments, finite element, and computational fluid dynamics simulation analysis including no-load magnetic field, back electromotive force, temperature rise, electromagnetic torque, and so on are carried out. The accuracy and rationality of the proposed no-load magnetic field analysis method and global optimization model have been well verified.

Remote sensing image data clustering is a tough task, which involves classifying the image without any prior information. Remote sensing image clustering, in essence, belongs to a complex optimization problem, due to the high dimensionality and complexity of remote sensing imagery. Therefore, it can be easily affected by the initial values and trapped in locally optimal solutions. Meanwhile, remote sensing images contain complex and diverse spatial-spectral information, which makes them difficult to model with only a single objective function. Although evolutionary multiobjective optimization methods have been presented for the clustering task, the tradeoff between the global and local search abilities is not well adjusted in the evolutionary process. In this article, in order to address these problems, a multiobjective sine cosine algorithm for remote sensing image data spatial-spectral clustering (MOSCA_SSC) is proposed. In the proposed method, the clustering task is converted into a multiobjective optimization problem, and the Xie-Beni (XB) index and Jeffries-Matusita (Jm) distance combined with the spatial information term (SI_Jm measure) are utilized as the objective functions. In addition, for the first time, the sine cosine algorithm (SCA), which can effectively adjust the local and global search capabilities, is introduced into the framework of multiobjective clustering for continuous optimization. Furthermore, the destination solution in the SCA is automatically selected and updated from the current Pareto front through employing the knee-point-based selection approach. The benefits of the proposed method were demonstrated by clustering experiments with ten UCI datasets and four real remote sensing image datasets.

With the widespread application of wireless communication technology and continuous improvements to Internet of Things (IoT) technology, fog computing architecture composed of edge, fog, and cloud layers have become a research hotspot. This architecture uses Fog Nodes (FNs) close to users to implement certain cloud functions while compensating for cloud disadvantages. However, because of the limited computing and storage capabilities of a single FN, it is necessary to offload tasks to multiple cooperating FNs for task completion. To effectively and quickly realize task offloading, we use network calculus theory to establish an overall performance model for task offloading in a fog computing environment and propose a Globally Optimal Multi-objective Optimization algorithm for Task Offloading (GOMOTO) based on the performance model. The results show that the proposed model and algorithm can effectively reduce the total delay and total energy consumption of the system and improve the network Quality of Service (QoS).

Due to the increasing demand for high-speed motors with high stability, bearingless motors have attracted much attention. Bearingless permanent magnet synchronous motors (BPMSMs) are a kind of motor, which uses suspension force to eliminate the motor bearings. This article proposes a five-phase BPMSM with 10 slots and 8 poles. Based on the principle of suspension force of BPMSM, an analytical expression of the suspension force is derived for the proposed BPMSM. To improve the suspension stability and torque, an optimization method consisting of a response surface model and a multiobjective optimization algorithm is employed. Not only the geometric parameters but also the winding distribution are considered in the optimization process. Finally, the effectiveness and superiority of the optimal design are verified by experiment.

Constrained multiobjective optimization problems (CMOPs) involve both conflicting objective functions and various constraints. Due to the presence of constraints, CMOPs' Pareto-optimal solutions are very likely lying on constraint boundaries. The experience from the constrained single-objective optimization has shown that to quickly obtain such an optimal solution, the search should surround the boundary of the feasible region from both the feasible and infeasible sides. In this article, we extend this idea to cope with CMOPs and, accordingly, we propose a novel constrained multiobjective evolutionary algorithm with bidirectional coevolution, called BiCo. BiCo maintains two populations, that is: 1) the main population and 2) the archive population. To update the main population, the constraint-domination principle is equipped with an NSGA-II variant to move the population into the feasible region and then to guide the population toward the Pareto front (PF) from the feasible side of the search space. While for updating the archive population, a nondominated sorting procedure and an angle-based selection scheme are conducted in sequence to drive the population toward the PF within the infeasible region while maintaining good diversity. As a result, BiCo can get close to the PF from two complementary directions. In addition, to coordinate the interaction between the main and archive populations, in BiCo, a restricted mating selection mechanism is developed to choose appropriate mating parents. Comprehensive experiments have been conducted on three sets of CMOP benchmark functions and six real-world CMOPs. The experimental results suggest that BiCo can obtain quite competitive performance in comparison to eight state-of-the-art-constrained multiobjective evolutionary optimizers.

Multi-modality is commonly seen in real-world multi-objective optimization problems. In such optimization problems, namely, multi-modal multi-objective optimization problems (MMOPs), multiple decision vectors can be projected to the same solution in the objective space (i.e., there are multiple implementations corresponding to that solution). Therefore, the diversity in the decision space is very important for the decision maker when tackling MMOPs. Subset selection methods have been widely used in the field of evolutionary multi-objective optimization for selecting well-distributed solutions (in the objective space) to be presented to the decision maker. However, since most subset selection methods do not consider the diversity of solutions in the decision space, they are not suitable for MMOPs. In this paper, we aim to clearly demonstrate the usefulness of subset selection for multi-modal multi-objective optimization. We propose a novel subset selection framework that can be easily integrated into existing multi-modal multi-objective optimization algorithms. By selecting a pre-specified number of solutions with good diversity in both the objective and decision spaces from all the examined solutions, the proposed framework significantly improves the performance of state-of-the-art multi-modal multi-objective optimization algorithms on various test problems.

Sparse multi-objective optimization problems have become increasingly important in many applications in recent years, e.g., the search for lightweight deep neural networks and high-dimensional feature selection. However, little attention has been paid to sparse large-scale multi-objective optimization problems, whose Pareto optimal sets are sparse, i.e., with many decision variables equal to zero. To address this issue, this paper proposes an enhanced competitive swarm optimization algorithm assisted by a strongly convex sparse operator. A tri-competition mechanism is introduced into competitive swarm optimization, aiming to strike a better balance between exploration and exploitation. In addition, the strongly convex sparse operator is embedded in the position updating of the particles to generate sparse solutions. Our simulation results show that the proposed algorithm outperforms the state-of-the-art methods on both sparse test problems and application examples.

The design of fuzzy neural network (FNN) has long been a challenging problem since most methods rely on approximation error to train FNN, which may easily occur overfitting phenomenon to degrade the generalization performance. To improve the generalization performance, a fuzzy neural network with multi-objective optimization algorithm (MOO-FNN) is proposed in this paper. First, the multi-level learning objectives are designed around the generalization performance to guide the training process of FNN. Then, the method utilizes the approximation error, the structure complexity, and the output smoothness indicators instead of a single indicator to improve the evaluation accuracy of generalization performance. Second, a MOO algorithm with continuous-discrete variables is developed to optimize FNN. Then, MOO is able to use a novel particle update method to adjust both the structure and parameters rather than adjust them separately, thereby achieving suitable generalization performance of FNN. Third, the convergence of MOO-FNN is analyzed in detail to guarantee its successful applications. Finally, the experimental studies of MOO-FNN have been performed on model identification of nonlinear systems to verify the effectiveness. The results illustrate that MOO-FNN has a significant improvement over some state-of-the-art algorithms.

The timetable of a metro system is essential for trains running safely and efficiently. For the design of a timetable, the potential power interruptions of energy supplies from the substations to the trains should be borne in mind. In case potential power interruptions occur, the backup running plan should be completed responsively to accommodate the passenger and energy demands In this study, we propose an energy supplementation strategy utilizing regenerative energy from decelerating trains in the event of power interruptions and develop a tri-objective optimization model incorporating passenger travel time, potential power interruption, and energy consumption. Particularly, for calculating regenerative energy utilization, we suggest a many-to-many energy allocation mechanism between decelerating and accelerating trains based on the real-time energy demands and supplies. A heuristic algorithm is developed to obtain a regular and cyclic timetable for minimizing passenger travel time, the potential power interruptions, and energy consumption. The suggested model and algorithm are tested based on the smart-card data collected from a bidirectional metro line in Beijing (China). The results show that the suggested approach significantly improves energy efficiency, reduces passenger waiting time, and decreases power interruption risks, compared with the currently used scheduling method.

Additive manufacturing (AM) suggests promising manufacturing technologies, which complement traditional manufacturing in multiple areas, such as biomedical, aerospace, defense, and automotive industries. This paper addresses the production planning problem in multi-machine AM systems. We consider all relevant physical and technological parameters of the machines and the produced parts, for using direct metal laser sintering (DMLS) technology. In DMLS technology, each machine produces jobs, where each job consists of several parts arranged horizontally on the build tray. Starting a new job requires a setup operation. We address the simultaneous assignment of parts to jobs and jobs to the machines, while considering the cost and makespan objectives. A unified mixed-integer linear-programming (MILP) formulation that can minimize the above objectives separately and simultaneously is suggested, along with analytical bounds and valid inequalities. Experimentation demonstrates the effectiveness of the proposed formulation with single objectives versus similar formulations from the literature. An efficient frontier approach is applied to the multi-objective problem while generating a diverse set of exact non-dominated solutions. The trade-off between the objectives is analyzed via experimentation. Results show that when identical machines are used, the trade-off is relatively small, and hence the decision-maker can use any of the single objectives. However, when non-identical machines are used, it is important to consider both objectives simultaneously. Moreover, the trade-off increases with the number of machines and heterogeneity of the system, with respect to the size and settings of the machines.

How to evaluate Pareto front approximations generated by multi/many-objective optimizers is a critical issue in the field of multiobjective optimization. Currently, there exist two types of comprehensive quality indicators (i.e., volume-based and distance-based indicators). Distance-based indicators, such as Inverted Generational Distance (IGD), are usually computed by summing up the distance of each reference point to its nearest solution. Their high computational efficiency leads to their prevalence in many-objective optimization. However, in the existing distance-based indicators, the distributions of the solution sets are usually neglected, leading to their lacks of ability to well distinguish between different solution sets. This phenomenon may become even more severe in high-dimensional space. To address such an issue, a kernel-based indicator (KBI) is proposed as a comprehensive indicator. Different from other distance-based indicators, a kernel-based maximum mean discrepancy is adopted in KBI for directly measuring the difference that can characterize the convergence, spread and uniformity of two sets, i.e., the solution set and reference set, by embedding them in Reproducing Kernel Hilbert Space (RKHS). As a result, KBI not only reflects the distance between the solution set and the reference set, but also can reflect the distribution of the solution set itself. In addition, to maintain the desirable weak Pareto compliance property of KBI, a nondominated set reconstruction approach is also proposed to shift the original solution set. The detailed theoretical and experimental analysis of KBI is provided in this paper. The properties of KBI have also been analyzed by the optimal μ-distribution.

This work is geared toward a real-world manufacturing planning (MP) task, whose two objectives are to maximize the order fulfillment rate and minimize the total cost. More important, the requirements and constraints in real manufacturing make the MP task very challenging in several aspects. For example, the MP needs to cover many production components of multiple plants over a 30-day horizon, which means that it involves a large number of decision variables. Furthermore, the MP task's two objectives have extremely different magnitudes, and some constraints are difficult to handle. Facing these uncompromising practical requirements, we introduce an interactive multiobjective optimization-based MP system in this article. It can help the decision maker reach a satisfactory tradeoff between the two objectives without consuming massive calculations. In the MP system, the submitted MP task is modeled as a multiobjective integer programming (MOIP) problem. Then, the MOIP problem is addressed via a two-stage multiobjective optimization algorithm (TSMOA). To alleviate the heavy calculation burden, TSMOA transforms the optimization of the MOIP problem into the optimization of a series of single-objective problems (SOPs). Meanwhile, a new SOP solving strategy is used in the MP system to further reduce the computational cost. It utilizes two sequential easier SOPs as the approximator of the original complex SOP for optimization. As part of the MP system, TSMOA and the SOP solving strategy are demonstrated to be efficient in real-world MP applications. In addition, the effectiveness of TSMOA is also validated on benchmark problems. The results indicate that TSMOA as well as the MP system are promising.

Despite the growing interest on many-objective evolutionary algorithms, studies on combinatorial problems are still rare. In this study, we choose many-objective knapsack problem (MaOKP) as the benchmark and target the challenges imposed by many-objectives in discrete search spaces by investigating several reference set handling approaches and combining several prominent evolutionary strategies in an innovative fashion. Our proposed algorithm uses elitist nondominated sorting and reference set based sorting, however reference points are mapped onto a fixed hyperplane obtained at the beginning of the algorithm. All evolutionary mechanisms are designed in a way to complement the reference set based sorting. Reference point guided path relinking is proposed as the recombination scheme for this purpose. Repair and local improvement procedures are also guided by reference points. Moreover, the reference set co-evolves simultaneously with the solution set, using both cooperative and competitive interactions to balance diversity and convergence, and adapts to the topology of the Pareto front in a self-adaptive parametric way. Numerical experiments display the success of the proposed algorithm compared to state-of-art approaches and yield the best results for MaOKP. The findings are inspiring and encouraging for the use of co-evolutionary reference set based techniques for combinatorial optimization.

Multitasking optimization can achieve better performance than traditional single-tasking optimization by leveraging knowledge transfer between tasks. However, the current multitasking optimization algorithms suffer from some deficiencies. Particularly, on high similar problems, the existing algorithms might fail to take full advantage of knowledge transfer to accelerate the convergence of the search, or easily get trapped in the local optima. Whereas, on low similar problems, they tend to suffer from negative transfer, resulting in performance degradation. To solve these issues, this article proposes an evolutionary multitasking optimization algorithm for multiobjective/many-objective optimization with two-stage adaptive knowledge transfer based on population distribution. The resultant algorithm named EMT-PD can improve the convergence performance of the target optimization tasks based on the knowledge extracted from the probability model that reflects the search trend of the whole population. At the first stage of knowledge transfer, an adaptive weight is used to adjust the search step size of each individual, which can reduce the impact of negative transfer. At the second stage of knowledge transfer, the search range of each individual is further adjusted dynamically, which can improve the population diversity and be beneficial for jumping out of the local optima. Experimental results on multitasking multiobjective optimization test suites show that EMT-PD is superior to other state-of-the-art evolutionary multitasking/single-tasking algorithms. To further investigate the effectiveness of EMT-PD on many-objective optimization problems, a multitasking many-objective optimization test suite is also designed in this article. The experimental results on the new test suite also demonstrate the competitiveness of EMT-PD.

Minimization of negative environmental impact of transport cannot be pursued through mobility limiting, but rather through efficient utilization of natural resources. Some of the ways to reduce harmful pollution and noise include increasing the use of electric energy for transportation and developing electromobility. However, municipalities face difficult decisions connected with the siting of charging stations, for example, budget limitations are an important factor. The presented method allows for selecting a subset of existing parking lots where the charging devices will be sited. As the inputs, only easily accessible data is required. Applying a genetic algorithm combined with fuzzy logic and the Pareto front analysis, one could establish a set of optimal solutions for multiple pre-defined restrictive and partially contradictory criteria. The method has been discussed using a real example of a medium-sized city in southern Poland. Its results have also made it possible to verify whether a budget required for the planned investment is substantiated.

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link. This paper proposes an adaptive localized decision variable analysis approach under the decomposition-based framework to solve the large scale multi-objective and many objective optimization problems. Its main idea is to incorporate the guidance of reference vectors into the control variable analysis and optimize the decision variables using an adaptive strategy. Especially, in the control variable analysis, for each search direction, the convergence relevance degree of each decision variable is measured by a projection-based detection method. In the decision variable optimization, the grouped decision variables are optimized with an adaptive scalarization strategy, which is able to adaptively balance the convergence and diversity of the solutions in the objective space. The proposed algorithm is evaluated with a suite of test problems with 2-10 objectives and 200-1000 variables. Experimental results validate the effectiveness and efficiency of the proposed algorithm on the large scale multiobjective and many-objective optimization problems.

The current critical global concerns regarding fossil fuel exhaustion and environmental pollution have been driving advancements in transportation electrification and related battery technologies. In turn, the resultant growing popularity of electric vehicles (EVs) calls for the development of a well-designed charging infrastructure. However, an inappropriate placement of charging stations might hamper smooth operation of the power grid and be inconvenient to EV drivers. Thus, the present work proposes a novel two-stage planning model for charging station placement. The candidate locations for the placement of charging stations are first determined by fuzzy inference considering distance, road traffic, and grid stability. The randomness in road traffic is modelled by applying a Bayesian network (BN). Then, the charging station placement problem is represented in a multi-objective framework with cost, voltage stability reliability power loss (VRP) index, accessibility index, and waiting time as objective functions. A hybrid algorithm combining chicken swarm optimization and the teaching-learning-based optimization (CSO TLBO) algorithm is used to obtain the Pareto front. Further, fuzzy decision making is used to compare the Pareto optimal solutions. The proposed planning model is validated on a superimposed IEEE 33-bus and 25-node test network and on a practical network in Tianjin, China. Simulation results validate the efficacy of the proposed model.

With the increasing penetration of renewable energy (RE), the operation of distribution network is threatened and some issues may appear, i.e., large voltage deviation, deterioration of statistic voltage stability, high power loss, etc. In turn, RE accommodation would be significantly impacted. Therefore, we propose a many-objective distribution network reconfiguration (MDNR) model, with the consideration of RE curtailment, voltage deviation, power loss, statistic voltage stability, and generation cost. This aims to assess the trade-off among these objectives for better operations of distribution networks. As this proposed model is a non-convex, non-linear, many-objective optimization problem, it is difficult to be solved. We further propose a deep reinforcement learning (DRL) assisted multi-objective bacterial foraging optimization (DRLMBFO) algorithm. This algorithm combines the advantages of DRL and MBFO, and is targeted to find the Pareto front of proposed MDNR model with better searching efficiency. Finally, case study based on a modified IEEE 33-bus distribution system verifies the effectiveness of MDNR model and outperformance of DRL-MBFO.

This work investigates the energy efficiency (EE) and the spectral efficiency (SE) performance of multi-hop full duplex cognitive relay networks (MH-FDCRNs) operating in the spectrum sharing mode, under the influence of interference from the primary source. We formulate three distinct optimization problems for finding the optimal power allocation for the secondary nodes in MH-FDCRN: (i) EE optimization with minimum SE requirement, (ii) SE optimization with minimum EE requirement, and (iii) EE-SE trade-off optimization. The impact of residual self-interference (RSI) arising due to full duplex operation at the relay nodes and the inter relay interference (IRI) arising due to frequency re-use are considered. For the EE/SE optimization problems, we transform the original non-convex optimization problems to their convex forms by expressing the numerator of the objective function as the difference of concave functions, and by using parametric transformation. For the EE-SE trade-off optimization problem, we first transform the original multi objective optimization problem into a single objective form; and then into its convex form by introducing an auxiliary variable. Computationally efficient algorithms are proposed to solve the considered problems. With the help of numerical results, the best trade-off among EE and SE can be achieved by proper selection of priority factor

This article proposes a new three-stage stochastic framework for dealing with predictable two-phase natural disasters in distribution systems. This framework is a multiobjective optimization, in which the amount of curtailed energy, the number of switching actions, and the vulnerability of operational components are selected as the main criteria for decision-making process. The optimization problem is formulated in the form of a stochastic mixed-integer linear programming (MILP) problem. In this article, a windstorm event followed by flooding is analyzed as a two-phase natural disaster. In this regard, the uncertainties associated with gust-wind speed, floodwater depths, and load demands are taken into account by the proposed framework. The initial configurations of islands are formed just ahead of the storm event (first stage), and their borders are changed in the second stage, which is associated with the storm event and its aftermath. The final configurations of islands are determined by the third stage once the uncertainties of floodwater depths are revealed. In the proposed framework, the emergency generators (EGs) are assumed to be prone to flooding, and a novel approach is proposed for quantifying the flood-related failure probability of EGs. Likewise, overhead distribution structures are recognized as vulnerable components to storms. The proposed framework is implemented on a test system, and its effectiveness is investigated and verified through seven case studies.

In special aluminum alloy production, smelting for aluminum ingots is the first process that affects production efficiency and product quality in subsequent processes directly. There exists two problems that charging plans cannot be made efficiently and furnace-grouping results are not optimal in the smelting process due to product variety and difference of batch size. To solve them, a furnace-grouping optimization model is established. The furnace-grouping problem is formulated with two objectives of minimizing the number of charging plans and the percentage of scrap metal with some constraints such as capacity of melting furnace and ingot-grouping rules in this model. According to the feature of this model, real number coding rule is employed that takes the percentage of order allocation as decision variable. A specialized multi-objective approach combining multi-swarm cooperative artificial bee colony is proposed to solve this optimization model. Decomposition strategy and multi-swarm strategy with information learning is employed to improve optimizing ability of the algorithm. The simulation experiment is designed on the basis of the truthful data of special aluminum alloy production. The numerical results demonstrate that this optimization model meets the requirements of manufacturing enterprises and the proposed algorithm is a powerful search and optimization technique for the furnace-grouping problem of special aluminum ingots.

The noise reduction of air-conditioning systems has gradually become an urgent problem linked to the requirement of driving comfort, and the muffler is a commonly used noise reduction equipment for air-conditioning pipelines. In this study, the transmission loss of a prototype muffler is co-simulated at different speeds. To optimize the muffler, a new method that combines orthogonal and detailed optimization was proposed. In orthogonal optimization, a multi-objective orthogonal test was used to analyze the effect of four structural parameters (shoulder height, cavity length, cavity diameter, and intubation length) on the average transmission loss, transmission loss at 1120 Hz, and frequency bandwidth below 4 dB. The influence of different factors on the transmission loss was studied at different speeds, and it was found that the length of intubation had a significant impact on the transmission loss. In a detailed optimization, the method is characterized by rapidity in the design of the air-conditioning system of a vehicle, and the final optimization model is determined. The results showed that the optimized structure was better than the original structure. The maximum reduction in the average noise can reach 11.99 dB, and the maximum noise reduction at 1120 Hz can reach 8.58 dB.

Towards 6G networks, such as virtual reality (VR) applications, Industry 4.0 and automated driving, demand mobile edge computing (MEC) techniques to offload computing tasks to nearby servers, which however causes fierce competition with traditional communication services. On the other hand, by introducing millimeter wave (mmWave) communication, it can significantly improve the offloading capability of MEC, so that enabling low latency and high throughput. For this sake, this paper investigates the resource management for the offload transmission of mmWave MEC system, when considering the data transmission demands from both communication-oriented users (CM-UEs) and computing-oriented users (CP-UEs). In particular, the joint consideration of user pairing, beamwidth allocation and power allocation is formulated as a multi-objective problem (MOP), which includes minimizing the offloading delay of CP-UEs and maximizing the transmission rate of CM-UEs. By using -constraint approach, the MOP is converted into a single-objective optimization problem (SOP) without losing Pareto optimality, and then the three-stage iterative resource allocation algorithm is proposed. Our simulation results show that, the gap between Pareto front generated by three-stage iterative resource allocation algorithm and the real Pareto front less than 0.16%. Futher, the proposed algorithm with much lower complexity can achieve the performance similar to the benchmark scheme of NSGA-2, while significantly outperforms the other traditional schemes.

With the extensive application of active magnetic bearings (AMB), the robust multi-objective optimization of the structure seems to be a priority. However, it is a challenge due to the high dimension and huge computational cost of finite element analysis (FEA). In this paper, a robust multi-objective optimization method is proposed to pursue good performance for a 3-pole AMB. To increase the efficiency of the optimization process, the Pearson correlation coefficient is applied to analyze the correlation between variables and objectives. The parameters are divided into three layers, and a 3-level multi-objective optimization structure is established. Meanwhile, Kriging model is employed to improve the optimization efficiency. The selection of the final solution in Pareto curves is always an issue. The proposed optimization structure can only ensure the performance of the AMB, rather than robustness. Thus, a robust solution selection method is proposed based on the climbing algorithm. The robustness can be easily shown in the Pareto curve obtained through the optimization structure. The final solution is selected with good robustness in terms of suspension force and force ripple. The experimental results based on a prototype are provided to verify the effectiveness of the proposed optimization method.

In this paper, we extend the concept of quasidifferential to a new notion called semi-quasidifferential. This generalization is motivated by the convexificator notion. Some important properties of semi-quasidifferentials are established. The relationship between semi-quasidifferentials and the Clarke subdifferential is studied, and a mean value theorem in terms of semi-quasidifferentials is proved. It is shown that this notion is helpful to investigate nonsmooth optimization problems even when the objective and/or constraint functions are discontinuous. Considering a multiobjective optimization problem, a characterization of some cones related to the feasible set is provided. They are used for deriving necessary and sufficient optimality conditions. We close the paper by obtaining optimality conditions in multiobjective optimization in terms of semi-quasidifferentials. Some outcomes of the current work generalize the related results existing in the literature.

During the last two decades, the notion of multiobjective optimization (MOO) has been successfully adopted to solve the nonconvex constrained optimization problems (COPs) in their most general forms. However, such works mainly utilized the Pareto dominance-based MOO framework while the other successful MOO frameworks, such as the reference vector (RV) and the decomposition-based ones, have not drawn sufficient attention from the COP researchers. In this article, we utilize the concepts of the RV-based MOO to design a ranking strategy for the solutions of a COP. We first transform the COP into a biobjective optimization problem (BOP) and then solve it by using the covariance matrix adaptation evolution strategy (CMA-ES), which is arguably one of the most competitive evolutionary algorithms of current interest. We propose an RV-based ranking strategy to calculate the mean and update the covariance matrix in CMA-ES. Besides, the RV is explicitly tuned during the optimization process based on the characteristics of COPs in a RV-based MOO framework. We also propose a repair mechanism for the infeasible solutions and a restart strategy to facilitate the population to escape from the infeasible region. We test the proposal extensively on two well-known benchmark suites comprised of 36 and 112 test problems (at different scales) from the IEEE CEC (Congress on Evolutionary Computation) 2010 and 2017 competitions along with a real-world problem related to power flow. Our experimental results suggest that the proposed algorithm can meet or beat several other state-of-the-art constrained optimizers in terms of the performance on a wide variety of problems.

We propose a biobjective robust simulation-based optimization (BORSO) method to solve unconstrained problems involving implementation errors and parameter perturbations. We adopt the notion that a solution is robust efficient (RE) if the region that dominates its worst-case realizations of the biobjectives under uncertainty does not contain (all) the worst-case realizations of the biobjectives of any other solution under uncertainty. Our algorithm aims to efficiently find a set of RE solutions through a series of function evaluations or simulations. First, we design surrogate-model guided search mechanisms for the worst-case neighbors of the current iterate. Subsequently, we determine the iteration distance along an effective local move direction, which excludes the worst-case neighbors from the neighborhood of the new iterate. Depending on the practical need for solution diversity, multiple initial solutions can be specified in our algorithm, and the final iterates of these solutions generate a set of RE solutions. The test results of a synthetic biobjective nonconvex optimization problem show the effectiveness of the BORSO method and its superior performance against a sampling-based robust multiobjective optimization solver. Furthermore, when the proposed algorithm is applied to a real-world biobjective traffic signal timing problem, satisfactory solutions can be obtained under a limited computational budget. These results indicate that the proposed BORSO method can solve unconstrained biobjective simulation-based optimization problems under uncertainties.

Performance of multi/many-objective evolutionary algorithms (MOEAs) based on decomposition is highly impacted by the Pareto front (PF) shapes of multi/many-objective optimization problems (MOPs), as their adopted weight vectors may not properly fit the PF shapes. To avoid this mismatch, some MOEAs treat solutions as weight vectors to guide the evolutionary search, which can adapt to the target MOP's PF automatically. However, their performance is still affected by the similarity metric used to select weight vectors. To address this issue, this article proposes a fuzzy decomposition-based MOEA. First, a fuzzy prediction is designed to estimate the population's shape, which helps to exactly reflect the similarities of solutions. Then, N least similar solutions are extracted as weight vectors to obtain N constrained fuzzy subproblems ( N is the population size), and accordingly, a shared weight vector is calculated for all subproblems to provide a stable search direction. Finally, the corner solution for each of m least similar subproblems ( m is the objective number) is preserved to maintain diversity, while one solution having the best aggregated value on the shared weight vector is selected for each of the remaining subproblems to speed up convergence. When compared to several competitive MOEAs in solving a variety of test MOPs, the proposed algorithm shows some advantages at fitting their different PF shapes.

The multiplayer stochastic noncooperative tracking game (NTG) with conflicting target strategy and cooperative tracking game (CTG) with a common target strategy of the mean-field stochastic jump-diffusion (MFSJD) system with external disturbance is investigated in this study. Due to the mean (collective) behavior in the system dynamic and cost function, the designs of the NTG strategy and CTG strategy for target tracking of the MFSJD system are more difficult than the conventional stochastic system. By the proposed indirect method, the NTG and CTG strategy design problems are transformed into linear matrix inequalities (LMIs)-constrained multiobjective optimization problem (MOP) and LMIs-constrained single-objective optimization problem (SOP), respectively. The LMIs-constrained MOP could be solved effectively for all Nash equilibrium solutions of NTG at the Pareto front by the proposed LMIs-constrained multiobjective evolutionary algorithm (MOEA). Two simulation examples, including the share market allocation and network security strategies in cyber-social systems, are given to illustrate the design procedure and validate the effectiveness of the proposed LMI-constrained MOEA for all Nash equilibrium solutions of NTG strategies of the MFSJD system.

Development of microwave components is an inherently multi-objective task. This is especially pertinent to the design closure stage, i.e., final adjustment of geometry and/or material parameters carried out to improve the electrical performance of the system. The design goals are often conflicting so that the improvement of one normally leads to a degradation of others. Compact microwave passives constitute a representative case: reduction of the circuit footprint area is detrimental to electrical figures of merit (e.g., the operating bandwidth). Identification of the best available trade-off designs requires multi-objective optimization (MO). This is a computationally expensive task, especially when executed at the level of full-wave electromagnetic (EM) simulation. The computational complexity issue can be mitigated through the employment of surrogate modeling methods, yet their application is limited by a typically high nonlinearity of system responses, and the curse of dimensionality. In this paper, a novel technique for fast MO of compact microwave components is proposed, which allows for sequential rendition of the trade-off designs using triangulation of the already available Pareto front as well as rapid refinement algorithms. Our methodology is purely deterministic; in particular, it does not rely on population-based nature-inspired procedures. The three major benefits are low computational cost, possibility of handling explicit design constraints, and a capability of producing a visually uniform representation of the Pareto front. The algorithm is demonstrated using a compact branch-line coupler and a three-section impedance matching transformer. In both cases, considerable savings are obtained over the benchmark, here, the state-of-the-art surrogate-assisted MO technique.

Natural ice accretion on the lifting surface of an aircraft is detrimental to its aerodynamic performance, as it changes the effective streamlined body. The main focus of this work considers the optimization design of airfoils under atmospheric icing conditions for the Unmanned Aerial Vehicle (UAV). The ice formation process is simulated by the Eulerian approach and the three-dimensional Myers model. A three-equation turbulence model is implemented to accurately predict the stall performance of the iced airfoil. In recognition of the real atmospheric variability in the icing parameters, the medium volume diameter of supercooled water droplets is treated as an uncertainty with an assumed probability density function. A technique of polynomial chaos expansion is used to propagate the input uncertainty through the deterministic system. The numerical results show that the multipoint/multiobjective optimization strategy can efficiently improve both the ice tolerance and the cruise performance of an airfoil. The reason for the focus on robust optimization is that the ice angle of the optimized airfoil becomes less critical to the incoming flow. The optimized airfoils are applied to a UAV platform, in which the performance improvement and the relevant key flow feature are both preserved.

To prevent the population from getting stuck in local areas and then missing the constrained Pareto front fragments in dealing with constrained multi-objective optimization problems (CMOPs), it is important to guide the population to evenly explore the promising areas that are not dominated by all examined feasible solutions. To this end, we first introduce a cost value based distance into the objective space, and then use this distance and the constraints to define an indicator to evaluate the contribution of each individual to exploring the promising areas. Theoretical studies show that the proposed indicator can effectively guide population to focus on exploring the promising areas without crowding in local areas. Accordingly, we propose a new constraint handling technique (CHT) based on this indicator. To further improve the diversity of population in the promising areas, the proposed indicator-based CHT divides the promising areas into multiple subregions, and then gives priority to removing the individuals with the worst fitness values in the densest subregions. We embed the indicator-based CHT in evolutionary algorithm and propose an indicator-based constrained multi-objective algorithm for solving CMOPs. Numerical experiments on several benchmark suites show the effectiveness of the proposed algorithm. Compared with six state-of-the-art constrained evolutionary multi-objective optimization algorithms, the proposed algorithm performs better in dealing with different types of CMOPs, especially in those problems that the individuals are easy to appear in the local infeasible areas that dominate the constrained Pareto front fragments.

In this paper, a parallel-series magnetic circuit multi-permanent magnet motor is designed and optimized considering magnet characteristic variation effects, where two kinds of PMs are utilized as co-magnetic. Based on the equivalent magnetic circuit method, the detailed design method for the multi-permanent magnet motor is illustrated. And considering the various operation conditions in potential EV applications, the B-H curves of two PMs of different typical operation conditions are obtained. Then, a multi-objective optimization method is newly proposed which not only focuses on the magnet characteristics variation effect, but also considers output torque, toque ripple as well as anti-demagnetization capability under three typical operation conditions. And the performance of the initial motor and optimal motor are compared under typical operation conditions. Finally, a prototype machine is built and tested. Both theoretical analysis and experimental results verify the validity of the motor and the proposed design optimization method.

Utilities are already concerned about power quality monitoring. Several papers proposed strategies to choose the best locations to install power quality monitors, minimizing the investment cost while guaranteeing observability of power quality disturbances, mostly voltage sags. Although several papers studied this problem in power transmission systems, many problems remain unsolved for power distribution systems, such as power quality monitors allocation in unbalanced distribution systems, the impact of distributed generation in allocation methods, and allocation of power quality monitor for fault location. This paper makes contributions to all these three points. It proposes a multi-objective binary integer linear programming model for unbalanced systems, which is still suitable for power transmission systems. Furthermore, we analyze the connection/disconnection of a distributed generator, and our tests showed no need to change allocation regardless of the generator connection status. Finally, the allocation method reduced the multiple estimation problem; therefore, meter-based fault location methods could improve their performance with our allocation.