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This paper addresses the trajectory tracking problem for a class of uncertain manipulator systems under the effect of external disturbances. The main challenges lie in the input constraints and the lack of measurements of joint velocities. An extend‐state‐observer is utilized to estimate the velocity signals; then, a neural‐network‐based adaptive controller is proposed to solve the problem, where a term based on the nominal model is included to enhance the tracking ability, and the effect of uncertainties and disturbances are compensated by a neural‐network term. Compared with the existing methods, the main distinctive features of the presented approach are: (i) The control law is guaranteed to be bounded by design, instead of directly bounded by a saturation function. (ii) The trade‐off between the performance and robustness of the presented controller can be easily tuned by a parameter that depends on the size of model uncertainties and external disturbances. By virtue of the Lyapunov theorem, the convergence properties of the proposed controller are rigorously proved. The performance of the controller is validated via both simulations and experiments conducted on a two‐degree‐of‐freedom robot manipulator. [ABSTRACT FROM AUTHOR]

Evolutionary algorithms (EAs) have shown their competitiveness in solving the problem of feature selection. However, limited by their encoding scheme, most of them face the challenge of "curse of dimensionality". To address the issue, in this paper, an objective space constraint-based evolutionary algorithm, named OSC-EA, is proposed for high-dimensional feature selection (HDFS). Although the decision space of EAs for HDFS is very huge, its objective space is the same as that of the low-dimensional feature selection. Based on this fact, in the proposed OSC-EA, the HDFS is firstly modeled as a constrained problem, where a constraint of the objective space is introduced and used to partition the whole objective space into the "feasible region" and the "infeasible region". To handle the constrained problem, a two-stage $\varepsilon$ɛ constraint-based evolutionary scheme is designed. In the first stage, the value of $\varepsilon$ɛ is set to be very small, which ensures that the search concentrates on the "feasible region", and the latent high-quality feature subsets can be found quickly. Then, in the second stage, the value of $\varepsilon$ɛ increases gradually, so that more solutions in the "infeasible region" are considered. Until the end of the scheme, $\varepsilon \rightarrow \infty$ɛ→∞; all the solutions in the objective space are considered. By using the search in the second stage, the quality of the obtained feature subsets is further improved. The empirical results on different high-dimensional datasets demonstrate the effectiveness and efficiency of the proposed OSC-EA. [ABSTRACT FROM AUTHOR]

In recent years, renewable energy has seen widespread application. However, due to its intermittent nature, there is a need to develop energy management systems for its scheduling and control. This paper introduces a multi-stage constraint-handling multi-objective optimization method tailored for resilient microgrid energy management. The microgrid encompasses diesel generators, energy storage systems, renewable energy sources, and various load types. The intelligent management of generators, batteries, switchable loads, and controllable loads ensures a reliable power supply for the critical loads. Beyond operational costs, our model also considers grid dependency as a key objective, making it particularly suited for energy management in extreme environments such as islands, border regions, and military bases. Managing complex controls of generators, batteries, switchable loads, and controllable loads presents challenging constraints that the management strategy must meet. To tackle this challenge, we propose an multi-objective optimization algorithm with multi-stage constraint-handling strategy to handle the high-dimensional complex constraints of the resilient energy management problem. Our proposed approach demonstrates superior performance compared to nine leading constrained multi-objective optimization algorithms across various test scenarios. Furthermore, the benefits of our method become increasingly evident as the complexity of the problem increases. Compared to the classical NSGA-II, the proposed NSGA-II-MC method achieved a 49.7% improvement in the Hypervolume metric on large-scale problems. [ABSTRACT FROM AUTHOR]

A PDE‐constrained model predictive control (MPC) algorithm for open‐channel systems based on the Saint‐Vevant(S‐V) equations is investigated in this paper. The S‐V equations, which precisely model the dynamics of open‐channel systems, are quasi‐linear hyperbolic partial differential equations (PDEs) without analytical solutions. Directly applying the S‐V equations to an MPC controller design becomes sophisticated. In this work, the calculus of variation is used to obtain the adjoint equations and the adjoint analysis method is utilized to deduce the gradients of the MPC optimization problem. Particularly, the physical constraints involving both the state and control variables are also considered. A gradient‐based optimization algorithm in combination with the numerical computation of Preissmann implicit scheme is proposed to solve the constrained MPC optimization problem. The control performances of the developed PDE‐constrained MPC algorithm with respect to the controlled water levels and gate openings are compared with those of the MPC controller designed for the linearized model. All the simulation tests are carried out on an aqueduct reach in Yehe Irrigation District in Hebei Province, China. The results show that the proposed PDE‐constrained MPC algorithm is a promising method in dealing with the constraints in terms of hyperbolic PDEs, control variables and state variables simultaneously. [ABSTRACT FROM AUTHOR]

This paper studies the problem of scheduling machines in the photolithography area of a semiconductor manufacturing facility. The scheduling problem is characterized as an unrelated parallel machine scheduling problem with machine eligibilities, sequence- and machine-dependent setup times, auxiliary resources and transfer times for the auxiliary resources. Each job requires two auxiliary resources: a reticle and a pod. Reticles are handled in pods and a pod contains multiple reticles. Both reticles and pods are used on multiple machines and a transfer time is required if transferred from one machine to another. A novel constraint programming (CP) approach is proposed and is benchmarked against a mixed-integer programming (MIP) method. The results of the study, consisting of a real-world case study at a global semiconductor manufacturer, demonstrate that the CP approach significantly outperforms the MIP method and produces high-quality solutions for multiple real-world instances, although optimality cannot be guaranteed. [ABSTRACT FROM AUTHOR]

The large-scale multi-objective optimization problem exist widely in reality while they have complex constraints. The simultaneous effect of the large-scale decision variables and the complexity of constraints makes the traditional multi-objective evolutionary algorithm face great challenges. For the large-scale of decision variables, some reference vector-guided, competitive group optimization-based and pairwise child generation-based algorithms have improved the search efficiency of constrained LSMOPs. However, these algorithms encounter difficulties in handling large-scale decision variables and complex constraints at the same time. In this paper, a reference vector-guided with dominance co-evolutionary multi-objective algorithm is proposed to solve constrained large-scale multi-objective problems. First, a reference vector is employed to guide several sub-populations with a fixed number of neighborhood solutions. Then, a new environmental selection is constructed using the angle penalty distance with dominance relationship. This new environmental selection strategy greatly enhances selection pressure. At the same time, a co-evolutionary constraint handling technology is applied to efficiently span the infeasible region. The proposed algorithm is evaluated on constrained large-scale multi-objective problems with 100, 500 and 1000 decision variables. In addition, the impact of each component of the proposed algorithm is examined for the overall performance of the algorithm and tested in a practical application in microgrids. The experimental results demonstrate the effectiveness of the algorithm in constrained large-scale multi-objective optimization. [ABSTRACT FROM AUTHOR]

In this paper, a hybrid gradient simulated annealing algorithm is guided to solve the constrained optimization problem. In trying to solve constrained optimization problems using deterministic, stochastic optimization methods or hybridization between them, penalty function methods are the most popular approach due to their simplicity and ease of implementation. There are many approaches to handling the existence of the constraints in the constrained problem. The simulated-annealing algorithm (SA) is one of the most successful meta-heuristic strategies. On the other hand, the gradient method is the most inexpensive method among the deterministic methods. In previous literature, the hybrid gradient simulated annealing algorithm (GLMSA) has demonstrated efficiency and effectiveness to solve unconstrained optimization problems. In this paper, therefore, the GLMSA algorithm is generalized to solve the constrained optimization problems. Hence, a new approach penalty function is proposed to handle the existence of the constraints. The proposed approach penalty function is used to guide the hybrid gradient simulated annealing algorithm (GLMSA) to obtain a new algorithm (GHMSA) that finds the constrained optimization problem. The performance of the proposed algorithm is tested on several benchmark optimization test problems and some well-known engineering design problems with varying dimensions. Comprehensive comparisons against other methods in the literature are also presented. The results indicate that the proposed method is promising and competitive. The comparison results between the GHMSA and the other four state-Meta-heuristic algorithms indicate that the proposed GHMSA algorithm is competitive with, and in some cases superior to, other existing algorithms in terms of the quality, efficiency, convergence rate, and robustness of the final result. [ABSTRACT FROM AUTHOR]

Optimal reactive power dispatch plays a key role in the safe operation of electric power systems. It consists of the optimal management of the reactive power sources within the system, usually with the aim of reducing system power losses. This paper presents both a new model and a solution approach for the multi-period version of the optimal reactive power dispatch. The main feature of a multi-period approach lies on the incorporation of inter-temporal constraints that allow the number of switching operations in transformer taps and capacitor banks to be limited in order to preserve their lifetime and avoid maintenance cost overruns. The main contribution of the paper is the constraint handling approach which consists of a multiplication of sub-functions which act as penalization and allow simultaneous consideration of both the feasibility and optimality of a given candidate solution. The multi-period optimal reactive power dispatch is an inherently nonconvex and nonlinear problem; therefore, it was solved using the metaheuristic mean-variance mapping optimization algorithm. The IEEE 30-bus and IEEE 57-bus test systems were used to validate the model and solution approach. The results allow concluding that the proposed model guarantees an adequate reactive power management that meets the objective of minimizing power losses and keeping the transformer taps and capacitor bank movements within limits that allow guaranteeing their useful life. [ABSTRACT FROM AUTHOR]

It is generally accepted that the essential goal of many-objective optimization is the balance between convergence and diversity. For constrained many-objective optimization problems (CMaOPs), the feasibility of solutions should be considered as well. Then the real challenge of constrained many-objective optimization can be generalized to the balance among convergence, diversity, and feasibility. In this paper, a tri-goal evolution framework is proposed for CMaOPs. The proposed framework carefully designs two indicators for convergence and diversity, respectively, and converts the constraints into the third indicator for feasibility. Since the essential goal of constrained many-objective optimization is to balance convergence, diversity, and feasibility, the philosophy of the proposed framework matches the essential goal of constrained many-objective optimization well. Thus, it is natural to use the proposed framework to deal with CMaOPs. Further, the proposed framework is conceptually simple and easy to instantiate for constrained many-objective optimization. A variety of balance schemes and ranking methods can be used to achieve the balance among convergence, diversity and feasibility. Three typical instantiations of the proposed framework are then designed. Experimental results on a constrained many-objective optimization test suite show that the proposed framework is highly competitive with existing state-of-the-art constrained many-objective evolutionary algorithms for CMaOPs. [ABSTRACT FROM AUTHOR]

When solving constrained multi-objective optimization problems (CMOPs), multiple conflicting objectives and multiple constraints need to be considered simultaneously, which are challenging to handle. Although some recent constrained multi-objective evolutionary algorithms (CMOEAs) have been developed to solve CMOPs and have worked well on most CMOPs. However, for CMOPs with small feasible regions and complex constraints, the performance of most algorithms needs to be further improved, especially when the feasible region is composed of multiple disjoint parts or the search space is narrow. To address this issue, an efficient global diversity CMOEA (EGDCMO) is proposed in this paper to solve CMOPs, where a certain number of infeasible solutions with well-distributed feature are maintained in the evolutionary process. To this end, a set of weight vectors are used to specify several subregions in the objective space, and infeasible solutions are selected from each subregion. Furthermore, a new fitness function is used in this proposed algorithm to evaluate infeasible solutions, which can balance the importance of constraints and objectives. In addition, the infeasible solutions are ranked higher than the feasible solutions to focus on the search in the undeveloped areas for better diversity. After the comparison tests on three benchmark cases and an actual engineering application, EGDCMO has more impressive performance compared with other constrained evolutionary multi-objective algorithms. [ABSTRACT FROM AUTHOR]

Evolutionary algorithms (EAs) are widely used for a variety of optimization problems, most of them with the presence of constraints. As move operators are usually blind to the constraints, (i.e. when operating upon feasible individuals they do not necessarily generate feasible offspring) standard EAs must be equipped with a constraint handling technique. This paper focuses on exactly satisfying the linear equality constraints present in continuous optimization problems that may also include additional non-linear equality and inequality constraints. The proposed method, named DELEqC-III, is an extension of two other previously developed methods. In this work, the original constrained problem (in R n ) is transformed into a lower-dimensional ( R n - m ) unconstrained optimization problem, where n is the number of variables and m is the number of linear equality constraints. DELEqC-III performs the search in the null space associated with the linear equality constraints allowing the method to exactly satisfy such constraints. In order to show the efficiency of the method, scalable test-problems are used to analyze the performance of the new proposal. [ABSTRACT FROM AUTHOR]

The Optimal Power Flow (OPF) is a primary tool in planning and installing power systems. It attempts to minimize the operating costs associated with generating and transmitting electrical power by modifying control parameters to satisfy environmental, economic, and operational constraints. Implementing an efficient and robust optimization algorithm for the above‐said problem is critical to achieving such a typical objective. Therefore, this paper introduces and evaluates new variants of the Successive History‐based Adaptive Differential Evolutionary (SHADE) algorithm called ESHADE, SHADE‐SFS, and SHADE‐SAP to solve the OPF problems with equality and inequality constraints. Generally, the static penalty approach is widely used for eliminating infeasible solutions discovered during the search phase when searching for feasible solutions. This approach requires the accurate selection of penalty coefficients, accomplished through the trial‐and‐error method. The proposed ESHADE algorithm is formulated using Self‐Adaptive Penalty (SAP) and Superiority of Feasible Solution (SFS) mechanisms to obtain feasible solutions for OPF problems. Two IEEE bus systems are used to demonstrate the effectiveness of the proposed algorithm in handling OPF problems. The fuel cost and active power loss obtained by the proposed algorithm are better than other state‐of‐the‐art algorithms. The results reveal that the proposed framework offers significant advantages over other algorithms. [ABSTRACT FROM AUTHOR]

When the meta-heuristic algorithm solves the joint resource allocation problem of multi-beam satellites, the computational complexity increases and the algorithm is difficult to converge due to the time delay constraint and capacity constraint. This paper introduced a penalty mechanism in the objective function, and added a penalty value to the objective function of the invalid solution, so that the optimized solution adaptively satisfied these two constraints. Based on this, this paper proposed a joint resource allocation algorithm based on quantum-behaved particle swarm optimization. Simulation results show that the introduction of the penalty strategy solves the problem of difficulty in handling the delay constraint and capacity constraint when applying the meta-heuristic algorithm. The quantum-behaved particle swarm optimization algorithm with penalty mechanism outperforms the existing joint allocation algorithm in terms of allocation fairness index and total system capacity. [ABSTRACT FROM AUTHOR]

Recently, the Hypervolume Newton Method (HVN) has been proposed as a fast and precise indicator-based method for solving unconstrained bi-objective optimization problems with objective functions. The HVN is defined on the space of (vectorized) fixed cardinality sets of decision space vectors for a given multi-objective optimization problem (MOP) and seeks to maximize the hypervolume indicator adopting the Newton–Raphson method for deterministic numerical optimization. To extend its scope to non-convex optimization problems, the HVN method was hybridized with a multi-objective evolutionary algorithm (MOEA), which resulted in a competitive solver for continuous unconstrained bi-objective optimization problems. In this paper, we extend the HVN to constrained MOPs with in principle any number of objectives. Similar to the original variant, the first- and second-order derivatives of the involved functions have to be given either analytically or numerically. We demonstrate the applicability of the extended HVN on a set of challenging benchmark problems and show that the new method can be readily applied to solve equality constraints with high precision and to some extent also inequalities. We finally use HVN as a local search engine within an MOEA and show the benefit of this hybrid method on several benchmark problems. [ABSTRACT FROM AUTHOR]

A universally applicable hybrid modelling method is proposed for nonlinear industrial processes that combine the a priori process knowledge with a data‐driven model. This method constructs a unified framework for the modelling process by integrating a data‐driven modelling technique, sampling detection technique, constraint optimization problem, and an evolutionary algorithm. In the modelling process, a swarm intelligence algorithm is used to optimize the model parameters under the circumstances of satisfying the constraints of a priori knowledge. By adding the constraints of process a priori knowledge, more information can be obtained about the actual process and the over‐fitting problem can be avoided to some extent, especially when modelling a system with a small quantity of samples. In order to show the effectiveness of the method proposed in this paper, two general data‐driven models, the polynomial regression model and radial basis function network model, are used as case studies. Moreover, a function simulation experiment is designed to test effectiveness, and applied to estimate average particle size of ZrO2‐TiO2 composite colloidal sols. [ABSTRACT FROM AUTHOR]

Predictive functional control (PFC) is a straightforward and cheap model‐based technique for systematic control of well‐damped open‐loop processes. Nevertheless, its oversimplified design characteristics are often the cause of diminished efficacy in more challenging applications; processes involving lightly damped and/or unstable dynamics have been particularly difficult to control with PFC. This paper presents a more sustainable solution for such applications by integrating the concept of prestabilization within the predictive functional control formulation. This is essentially a two‐stage synthesis wherein the undesirable open‐loop dynamics are first compensated, using a well‐understood classical approach such as proportional integral derivative (PID), before implementing predictive control in a cascade structure. The proposal, although comes with significant implications for tuning and constraint handling, is, nonetheless, straightforward and provides improved closed‐loop control in the presence of external perturbations compared to the standard PFC and the PID algorithms, as demonstrated with two industrial case studies. [ABSTRACT FROM AUTHOR]

When solving constrained multiobjective optimization problems, an important issue is how to balance convergence, diversity, and feasibility simultaneously. To address this issue, this paper proposes a parameter-free constraint handling technique, a two-archive evolutionary algorithm, for constrained multiobjective optimization. It maintains two collaborative archives simultaneously: one, denoted as the convergence-oriented archive (CA), is the driving force to push the population toward the Pareto front; the other one, denoted as the diversity-oriented archive (DA), mainly tends to maintain the population diversity. In particular, to complement the behavior of the CA and provide as much diversified information as possible, the DA aims at exploring areas under-exploited by the CA including the infeasible regions. To leverage the complementary effects of both archives, we develop a restricted mating selection mechanism that adaptively chooses appropriate mating parents from them according to their evolution status. Comprehensive experiments on a series of benchmark problems and a real-world case study fully demonstrate the competitiveness of our proposed algorithm, in comparison to five state-of-the-art constrained evolutionary multiobjective optimizers. [ABSTRACT FROM AUTHOR]

Real-world engineering design problems, like structural optimization, can be characterized as a multi-objective optimization when two or more conflicting objectives are in the problem formulation. The differential evolution (DE) algorithm is nowadays one of the most popular meta-heuristics to solve optimization problems in continuous search spaces and has attracted much attention in multi-objective optimization due to its simple implementation and efficiency when solving real-world problems. A recent paper has shown that GDE3, a well-known DE-based algorithm, performs efficiently when solving structural multi-objective optimization problems. Also an adaptive penalty technique called APM was adopted to handle constraints. However, the authors did not investigate the contribution of this technique and that of the GDE3 algorithm separately. So, in this work, the results obtained by GDE3 equipped with the APM scheme (denoted here by GDE3 + APM) are compared with those found by the original GDE3 in order to investigate the advantages and limitations of this constraint handling technique in those problems. The results of the GDE3 + APM are also compared with the most commonly used multi-objective meta-heuristic, namely NSGA-II, in order to comparatively evaluate the quality of the solutions obtained with respect to other algorithms from the literature. The analysis indicates that GDE3 + APM is more efficient than both GDE3 and NSGA-II in most performance metrics used when solving the structural multi-objective optimization problems considered here, suggesting that the GDE3 + APM algorithm is promising in this area, and that the APM technique makes a considerable contribution to its performance. [ABSTRACT FROM AUTHOR]

Iterative learning control (ILC) is a high-performance tracking control design method for systems operating in a repetitive manner. This paper proposes a novel design methodology that extends the recently developed point-to-point ILC framework to allow automatic via-point time allocation within a given point-to-point tracking task, leading to significant performance improvements, e.g., energy reduction. The problem is formulated into an optimization framework with via-point temporal constraints and a reference tracking requirement, for which a two-stage design approach is developed. This yields an algorithmic solution, which minimizes input energy based on norm optimal ILC and gradient minimization. The algorithm is further expanded to incorporate system constraints into the design, prior to experimental validation on a gantry robot test platform to confirm its feasibility in practical applications. [ABSTRACT FROM AUTHOR]

This paper focuses on the constraint handling for induction machines (IMs) using model predictive control (MPC) to enhance the optimality. Commonly, the constraints of IMs are represented by stator current and voltage limits, which are described as quadratic inequality in dq-frame. Due to the spherical feature, the constraints have to be replaced by approximation by polygon in order to get a standard form of quadratic programming (QP). In this paper, a novel approach is proposed to convert the quadratic inequalities into linear ones without approximation, whereat the inequality is parameter-varying. To tackle this parameter-varying inequality, the multiparametric quadratic program (mp-QP) algorithm for reference tracking is utilized and extended. To ensure the optimization problem solved in real time, an explicit MPC (EMPC) via mp-QP is applied instead of any online numerical solver. [ABSTRACT FROM PUBLISHER]

This paper proposes a meta-heuristic algorithm named as quasi-oppositional self-learning teacher-learner-based-optimization (QOSLTLBO) for solving non-convex economic load dispatch (ELD) problem. The ELD problem is an essential concern of power system and its main objective is to allocate optimal power generation to each generating unit so as to minimize the total cost of generation while satisfying all constraints available in the system. The problem considered in this paper is a non-convex quadratic generation cost of the units (with or without valve-point loading effects) with power balance and generation limits as the system constraints. This model of generation cost is a continuous model of the ELD problem. The proposed algorithm includes a quasi-oppositional approach for better initialization of population. A self-learning phase is added after teacher phase and learner phase of basic teacher-learner-based-optimization (TLBO) algorithm to improve the convergence rate. To prove the efficacy and robustness of proposed algorithm, it is applied to solve ELD problem on different standard IEEE generator systems and the results, thus obtained are compared with other state-of-art algorithms. The minimum total cost of generation in all the cases are obtained from the proposed algorithm which proves its effectiveness over others. The additional advantage of the proposed QOSLTLBO algorithm is that it is kept free from algorithm-specific parameters like basic TLBO. [ABSTRACT FROM AUTHOR]

To achieve ideal force control of a functional autonomous exoskeleton, sensitivity amplification control is widely used in human strength augmentation applications. The original sensitivity amplification control aims to increase the closed-loop control system sensitivity based on positive feedback without any sensors between the pilot and the exoskeleton. Thus, the measurement system can be greatly simplified. Nevertheless, the controller lacks the ability to reject disturbance and has little robustness to the variation of the parameters. Consequently, a relatively precise dynamic model of the exoskeleton system is desired. Moreover, the human-robot interaction (HRI) cannot be interpreted merely as a particular part of the driven torque quantitatively. Therefore, a novel control methodology, so-called probabilistic sensitivity amplification control, is presented in this paper. The innovation of the proposed control algorithm is two-fold: distributed hidden-state identification based on sensor observations and evolving learning of sensitivity factors for the purpose of dealing with the variational HRI. Compared to the other state-of-the-art algorithms, we verify the feasibility of the probabilistic sensitivity amplification control with several experiments, i.e., distributed identification model learning and walking with a human subject. The experimental result shows potential application feasibility. [ABSTRACT FROM AUTHOR]

This paper proposes an efficient approach for constraint handling in multi-objective particle swarm optimization. The particles population is divided into two non-overlapping populations, named infeasible population and feasible population. The evolution process in each population is done independent of the other one. The infeasible particles are evolved in the constraint space toward feasibility. During evolution process, if an infeasible particle becomes a feasible one, it migrates to feasible population. In a parallel process, the particles in feasible population are evolved in the objective space toward Pareto optimality. At each generation of multi-objective particle swarm optimization, a leader should be assigned to each particle to move toward it. In the proposed method, a different leader selection algorithm is proposed for each population. For feasible population, the leader is selected using a priority-based method in three levels and for infeasible population, a leader replacement method integrated by an elitism-based method is proposed. The proposed approach is tested on several constrained multi-objective optimization benchmark problems, and its results are compared with two popular state-of-the-art constraint handling multi-objective algorithms. The experimental results indicate that the proposed algorithm is highly competitive in solving the benchmark problems. [ABSTRACT FROM AUTHOR]