Search

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]

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]

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 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]

Economic dispatch (ED) has received considerable interest in the field of energy management and optimization. The problem aims to determine the most cost-effective power allocation strategy that satisfies the power demand and all physical constraints of the power system. To solve this problem, we propose an algorithm based on differential evolution and adopt a hybrid mutation strategy, a linear population size reduction mechanism, and an improved single-unit repair mechanism. Experimental results confirmed that these mechanisms are useful for performance improvement. The proposed algorithm (L -HMDE) showed good performance when compared with more than 90 algorithms in solving 22 test cases. It could provide high-quality solutions stably and efficiently. In addition to designing a good algorithm, we present a review of over 100 papers and highlight their algorithm features. We also provide a comprehensive collection of test cases in the literature. Through careful examination and verification, data coefficients of these test cases and solutions to them are included in this paper as a useful reference for researchers who are interested in this problem. • A differential evolution-based algorithm (L-HMDE) is proposed to address the economic dispatch problem. • The L-HMDE integrates a hybrid mutation strategy, a population size reduction mechanism, and an improved repair procedure. • It shows good solution quality and high efficiency when compared with more than 90 existing algorithms on 22 test cases. • A comprehensive collection of test cases and solutions is also provided. [ABSTRACT FROM AUTHOR]

Iterative learning control (ILC) is a high-performance control design method for systems working in a repetitive manner. ILC has traditionally focused on tracking a reference defined at all points over a finite-time interval; recent developments have begun to exploit the design freedom unlocked by tracking only a finite number of distinct time instants driven by the needs of, e.g., robotic pick-and-place tasks. This paper proposes a generalized ILC paradigm, which extends and unifies the scope of existing design frameworks by amalgamating previous task descriptions and embedding system constraints on the input and output. A novel solution is then derived using a successive projection method, which provides well-defined convergence properties. The proposed design framework is illustrated by applying it to a spatial reference tracking problem with experimental results on a gantry robot testing platform demonstrating its effectiveness. [ABSTRACT FROM AUTHOR]

A Linear Time Invariant (LTI) energy-maximising control strategy for Wave Energy Converters (WECs) is proposed in this paper. Using the fundamental requirement of impedance-matching, the controller is tuned to maximise the energy obtained under polychromatic wave excitation. Given the LTI nature of the proposed controller, the design and implementation procedure is significantly simpler than well-established energy-maximising controllers, including state-of-the-art numerical optimisation routines, which are predominant in this field. Additionally, a LTI constraint handling mechanism is provided. The effectiveness of both the LTI control strategy and the constraint handling mechanism are assessed using regular and irregular waves in unconstrained and constrained cases. The resulting performance is compared to those obtained using existing WEC optimal control strategies. Finally, the benefits, in terms of power production, for both the controller and the constraint handling mechanism are explicitly highlighted by means of an application case. [ABSTRACT FROM AUTHOR]

A generic constraint handling framework for use with any swarm-based optimization algorithm is presented. For swarm optimizers to solve constrained optimization problems effectively modifications have to be made to the optimizers to handle the constraints, however, these constraint handling frameworks are often not universally applicable to all swarm algorithms. A constraint handling framework is therefore presented in this paper that is compatible with any swarm optimizer, such that a user can wrap it around a chosen swarm algorithm and perform constrained optimization. The method, called separation-sub-swarm, works by dividing the population based on the feasibility of individual agents. This allows all feasible agents to move by existing swarm optimizer algorithms, hence promoting good performance and convergence characteristics of individual swarm algorithms. The framework is tested on a suite of analytical test function and a number of engineering benchmark problems, and compared to other generic constraint handling frameworks using four different swarm optimizers; particle swarm, gravitational search, a hybrid algorithm and differential evolution. It is shown that the new framework produces superior results compared to the established frameworks for all four swarm algorithms tested. Finally, the framework is applied to an aerodynamic shape optimization design problem where a shock-free solution is obtained. [ABSTRACT FROM AUTHOR]

The sensitivity of the initial guess in terms of optimizer based on an hp-adaptive pseudospectral method for solving a space maneuver vehicle's (SMV) trajectory optimization problem has long been recognized as a difficult problem. Because of the sensitivity with regard to the initial guess, it may cost the solver a large amount of time to do the Newton iteration and get the optimal solution or even the local optimal solution. In this paper, to provide the optimizer a better initial guess and solve the SMV trajectory optimization problem, an initial guess generator using a violation learning differential evolution algorithm is introduced. A new constraint-handling strategy without using penalty function is presented to modify the fitness values so that the performance of each candidate can be generalized. In addition, a learning strategy is designed to add diversity for the population in order to improve the convergency speed and avoid local optima. Several simulation results are conducted by using the combination algorithm; simulation results indicated that using limited computational efforts, the method proposed to generate initial guess can have better performance in terms of convergence ability and convergence speed compared with other approaches. By using the initial guess, the combinational method can also enhance the quality of the solution and reduce the number of Newton iteration and computational time. Therefore, the method is potentially feasible for solving the SMV trajectory optimization problem. [ABSTRACT FROM AUTHOR]

Discussions on how to make effective use of advance information on target changes are discussed relatively rarely in the predictive control literature. While earlier work has indicated that the default solutions from conventional predictive control algorithms are often poor, very little work has proposed systematic alternatives. This paper proposes an embedding structure for utilising advance information on target changes within an optimum predictive control law. The proposed embedding is shown to be systematic and beneficial. Moreover, it allows for easy extension to deal with more challenging scenarios such as unreachable set points and guarantees of convergence/stability in the uncertain case. [ABSTRACT FROM AUTHOR]

Mixed-variable optimization problems consist of the continuous, integer, and discrete variables generally used in various engineering optimization problems. These variables increase the computational cost and complexity of optimization problems due to the handling of variables. Moreover, there are few optimization algorithms that give a globally optimal solution for non-differential and non-convex objective functions. Initially, the Jaya algorithm has been developed for continuous variable optimization problems. In this paper, the Jaya algorithm is further extended for solving mixed-variable optimization problems. In the proposed algorithm, continuous variables remain in the continuous domain while continuous domains of discrete and integer variables are converted into discrete and integer domains applying bound constraint of the middle point of corresponding two consecutive values of discrete and integer variables. The effectiveness of the proposed algorithm is evaluated through examples of mixed-variable optimization problems taken from previous research works, and optimum solutions are validated with other mixed-variable optimization algorithms. The proposed algorithm is also applied to two-plane balancing of the unbalanced rigid threshing rotor, using the number of balance masses on plane 1 and plane 2. It is found that the proposed algorithm is computationally more efficient and easier to use than other mixed optimization techniques. [ABSTRACT FROM AUTHOR]

The objective of this paper is to introduce with a quaternion orientation based quadrotor that can be controlled by Model Predictive Control (MPC). As MPC offers promising performance in different industrial applications, quadrotor can be another suitable platform for the application of MPC. The present study consistently adopts unit quaternion approach for quadrotor orientation in order to avoid any axes overlapping problem, widely known as singularity problem whereas Euler angle orientation approach is unable to resolve so. MPC works based on the minimal cost function that includes the attitude error and consequently, the cost function requires quaternion error in order to proceed with process of MPC. Therefore, the main contribution of this study is to introduce a newly developed cost function for MPC because by definition, quaternion error is remarkably different from the attitude error of Euler angle. As a result, a unit quaternion based quadrotor with MPC can ascertain a smooth singularity-free flight that is influenced by model uncertainty. MATLAB and Simulink environment has been used to validate the cost function for quaternion by simulating several trajectories. [ABSTRACT FROM AUTHOR]

The dynamic economic dispatch problem is a high-dimensional complex constrained optimization problem that determines the optimal generation from a number of generating units by minimizing the fuel cost. Over the last few decades, a number of solution approaches, including evolutionary algorithms, have been developed to solve this problem. However, the performance of evolutionary algorithms is highly dependent on a number of factors, such as the control parameters, diversity of the population, and constraint-handling procedure used. In this paper, a self-adaptive differential evolution and a real-coded genetic algorithm are proposed to solve the dynamic dispatch problem. In the algorithm design, a new heuristic technique is introduced to guide infeasible solutions towards the feasible space. Moreover, a constraint-handling mechanism, a dynamic relaxation for equality constraints, and a diversity mechanism are applied to improve the performance of the algorithms. The effectiveness of the proposed approaches is demonstrated on a number of dynamic economic dispatch problems for a cycle of 24 h. Their simulation results are compared with each other and state-of-the-art algorithms, which reveals that the proposed method has merit in terms of solution quality and reliability. [ABSTRACT FROM AUTHOR]

This paper proposes an adaptive uniform search framework designed for constrained multi-objective optimization. The framework comprises three key components: a global uniform exploration strategy, a local greedy exploitation strategy, and a search switch mechanism. These components work together to facilitate comprehensive exploration of promising areas while maintaining a balance between global exploration and local exploitation. Specifically, the global uniform exploration strategy ensures even distribution within promising areas, preventing any oversights during exploration. The local greedy exploitation strategy divides these areas into sub-areas and employs a feasibility-led constraint handling technique to enhance efficiency in identifying optimal solutions. Additionally, the search switch dynamically adjusts the search strategy between global exploration and local exploitation. Numerical simulations on various benchmark suites and real-world problem demonstrate the strong performance of the framework in addressing constrained multi-objective optimization problems. The comparison results show that compared with eight recently proposed algorithms, the proposed framework is more robust in solving diverse constrained multi-objective optimization problems. • GUE removes close individuals, promoting even distribution. • LGE divides areas for effective local optimization. • A novel switch adapts search between GUE and LGE. [ABSTRACT FROM AUTHOR]

Abstract 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.

Deep reinforcement learning (RL) has emerged as a promising approach to solving sequential optimization problems that involve high dimensional state/action space and stochastic uncertainties. Unfortunately, many such problems, especially those related to process control, involve state constraints (typically expressed as inequality constraints) that are difficult to handle. Most RL application studies have incorporated inequality constraints into the training by adding penalty terms for violating the constraints to the reward function. However, while training neural networks to learn the value (or Q) function, one can run into numerical difficulties caused by sharp changes in the value function (VF) at the constraint boundary. This problem can lead to an array of issues including getting stuck in local minima and slow convergence during training which ultimately manifest as poor closed-loop performance when training samples are limited. In this paper, we first examine the effect of the penalty function form on the neural network training performance in deep RL algorithms. To address the slow convergence, we propose a dynamic penalty (DP) approach where the penalty factor is gradually and systematically increased as the iteration episodes proceed during training. The agents trained by a Deep Q-Learning algorithm with the proposed approach were compared with agents trained with other constant penalty functions in a vehicle control problem and in a battery management control problem. Results show that the DP approach can help improve the accuracy of the VF approximation, leading to superior results in the constraint satisfaction and in the degree of violation. [ABSTRACT FROM AUTHOR]

Constraint normalization ensures consistency in scaling for each constraint in an optimization problem. Most constraint handling studies only address the issue to deal with constraints and use problem information to scale the constraints. In this paper, we propose a hybrid evolutionary algorithm—Constraint Handling with Individual Penalty Approach (CHIP)—which scales all constraints adaptively without any problem specific information from the user. Penalty parameters for all constraints are estimated adaptively by considering overall constraint violation as a helper objective for minimization and as a result any number of constraints can be dealt without incurring proportional computational cost. The efficiency of the proposed method is demonstrated using 23 test problems and two problems from engineering optimization. The constrained optimum and function evaluations of CHIP method are inspected with five recently developed evolutionary-based constraint handling methods. The simulation results show that the proposed CHIP mechanism is very efficient, faster and comparable in the aspect of accuracy against other recently developed methods. [ABSTRACT FROM AUTHOR]

Many real-world problems in engineering and process synthesis tend to be highly dimensional and nonlinear, even involve conflicting multiple objectives and subject to many constraints, which makes the feasible regions narrow; hence, it is hard to be solved by traditional constraint handling techniques used in evolutionary algorithms. To handle this issue, this paper presents a multi-objective differential evolution with dynamic hybrid constraint handling mechanism (MODE-DCH) for tackling constrained multi-objective problems (CMOPs). In MODE-DCH, global search model and local search model combined with different constraint handling methods are proposed, and they are executed dynamically based on the feasibility proportion of the population. In the early stage that the feasible ratio is low, the local search model focuses on dragging the population into feasible regions rapidly, while the global search model is used to refine the whole population in the later stage. The two major modules of the algorithm cooperate together to balance the convergence and distribution of Pareto-optimal front. To demonstrate the effectiveness of MODE-DCH, the proposed algorithm is applied on several well-known CMOPs and two engineering problems compared with two other state-of-the-art multi-objective algorithms. The performance indicators show that MODE-DCH is an effective method to solve CMOPs. [ABSTRACT FROM AUTHOR]

Almost all real-world optimisation problems are constrained. Solving constrained problems is difficult for optimisation techniques. In this paper, different constraint handling strategies used in heuristic optimisation algorithms and especially particle swarm optimisation (PSO) are reviewed. Since PSO is a very common optimisation algorithm, this paper can provide a broad view to researchers in related field and help them to identify the appropriate constraint handling strategy for their own optimisation problem. [ABSTRACT FROM AUTHOR]

The rate of penetration (ROP) is one of the key parameters related to the efficiency of the drilling process. Within the confines of operational limits, the drilling parameters affecting the ROP should be optimized to drill more efficiently and safely, to reduce the overall cost of constructing the well. In this study, a data-driven optimization method called Extremum Seeking (ES) is employed to automatically find and maintain the optimal weight on bit (WOB) which maximizes the ROP. The ES algorithm is a model-free method that gathers information about the current downhole conditions by automatically performing small tests with the WOB and executing optimization actions based on the test results. In this paper, this optimization method is augmented with a combination of a predictive and a reactive constraint handling technique to adhere to operational limitations. These methods of constraint handling are demonstrated for a maximal limit imposed on the surface torque, but the methods are generic and can be applied to various drilling parameters. The proposed optimization scheme has been tested with experiments on a downscaled drilling rig and simulations on a high-fidelity drilling simulator of a full-scale drilling operation. The experiments and simulations show the method's ability to steer the system to the optimum and to handle constraints and noisy data, resulting in safe and efficient drilling at high ROP. [ABSTRACT FROM AUTHOR]

In software testing, optimal testing resource allocation problems (OTRAPs) are important when seeking a good tradeoff between reliability, cost, and time with limited resources. There have been intensive studies of OTRAPs using multiobjective evolutionary algorithms (MOEAs), but little attention has been paid to the constraint handling. This paper comprehensively investigates the effect of the constraint handling on the performance of nondominated sorting genetic algorithm II (NSGA-II) for solving OTRAPs, from both theoretical and empirical perspectives. The heuristics for individual repairs are first proposed to handle constraint violations in NSGA-II, based on which several properties are derived. Additionally, the Z-score based Euclidean distance is adopted to estimate the difference between solutions. Finally, the above methods are evaluated and the experiments show several results. 1) The developed heuristics for constraint handling are better than the Existing Strategy in terms of the capacity and coverage values. 2) The Z-score operation obtains better diversity values and reduces repeated solutions. 3) The modified NSGA-II for OTRAPs (called NSGA-II-TRA) performs significantly better than the existing MOEAs in terms of capacity and coverage values, which suggests that NSGA-II-TRA could obtain more and higher quality testing-time-allocation schemes, especially for large, complex datasets. 4) NSGA-II-TRA is robust according to the sensitivity analysis results. [ABSTRACT FROM PUBLISHER]

The application of cold-formed steel channel sections for portal frames becomes more popular for industrial and residential purposes. Experimental tests showed that such structures with long-span up to 20 m can be achieved when knee brace joints are included. In this paper, the influence of knee brace configuration on the optimum design of long-span cold-formed steel portal frames is investigated. The cold-formed steel portal frames are designed using Eurocode 3 under ultimate limit states. A novel method in handling design constraints integrated with genetic algorithm is proposed for searching the optimum design of cold-formed steel portal frames. The result showed that the proposed routine for design optimization effectively searched the near global optimum solution with the computational time is approximate 50% faster than methods being popularly used in literature. The optimum configuration for knee brace joint can reduce the section size of rafter and so the lighter frame could be obtained especially for long-span portal frame. The minimum weight of main frame obtained from optimization process is approximate 19.72% lighter than a Benchmark Frame used in the full-scale experimental test. [ABSTRACT FROM AUTHOR]

The testing of configurations with constraints still faces a great challenge. Although artificial intelligence (AI)-based algorithms perform better than greedy algorithms on -way testing because of the good searching ability of optimal solutions, only a few AI-based algorithms can support constraints currently. Moreover, the AI-based algorithms can only ignore the conflicting candidate test cases subject to constraints, even though they are optimal. In this paper, we demonstrate two novel particle swarm optimization (PSO)-based constraint test cases generation (PCTG) methods. In the two methods, the strategies of avoiding the selection of conflicting test cases and replacing conflicting test cases are applied to handle constraints, respectively. They guide the process of searching for optimal solutions from different perspectives, according to different handling of constraints. We evaluate the availability of these two methods with some excellent existing strategies in terms of performance. The evaluation results indicate that our proposed methods, in most cases, outperform other strategies as far as the generated constraints covering array sizes. [ABSTRACT FROM AUTHOR]

In recent years, artificial immune system (AIS) algorithms is considered to be an effective method to solve the multiobjective optimization problems (MOPs), such as multimedia delivery problem. Though a decent number of solution algorithms have been proposed for MOPs, far less progress has been made for constrained multiobjective optimization problems (CMOPs), which demands a combination of constraints handling technique and search algorithm, e.g. Nondominated Neighbor Immune Algorithm (NNIA). In this paper, we propose a hybrid constraint handling technique of adaptive penalty function and objectivization of constraint violations. In our approach, the dominant population is updated via a method of objectivization of constraint violations and proportional reduction while a modified adaptive penalty function method based on the structure of the search algorithm (NNIA) is utilized to update the active population. We combine the proposed hybrid constraint handling method with NNIA to form the proposed Constrained Nondominated Neighbor Immune Algorithm (C-NNIA) to address the constrained multiobjective optimization problems. To our knowledge, it is the first time NNIA has been applied as the search algorithm for CMOPs. Numerical simulations indicate that the proposed algorithm outperforms the current state-of-the-art algorithms, i.e. NSGA-II-WTY, in both convergence and diversity. [ABSTRACT FROM AUTHOR]

Abstract 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.

Many real-world optimization problems, particularly engineering ones, involve constraints that make finding a feasible solution challenging. Numerous researchers have investigated this challenge for constrained single- and multi-objective optimization problems. In particular, this work extends the boundary update (BU) method proposed by Gandomi and Deb (Comput. Methods Appl. Mech. Eng. 363:112917, 2020) for the constrained optimization problem. BU is an implicit constraint handling technique that aims to cut the infeasible search space over iterations to find the feasible region faster. In doing so, the search space is twisted, which can make the optimization problem more challenging. In response, two switching mechanisms are implemented that transform the landscape along with the variables to the original problem when the feasible region is found. To achieve this objective, two thresholds, representing distinct switching methods, are taken into account. In the first approach, the optimization process transitions to a state without utilizing the BU approach when constraint violations reach zero. In the second method, the optimization process shifts to a BU method-free optimization phase when there is no further change observed in the objective space. To validate, benchmarks and engineering problems are considered to be solved with well-known evolutionary single- and multi-objective optimization algorithms. Herein, the proposed method is benchmarked using with and without BU approaches over the whole search process. The results show that the proposed method can significantly boost the solutions in both convergence speed and finding better solutions for constrained optimization problems. [ABSTRACT FROM AUTHOR]