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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]

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]

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]

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]

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]

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]

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]

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.

• Artificial neural network is used to find significance of variables in optimization. • This approach replaces user-defined heuristic for repair-based constraint handling. • Convergence speed and diversity of solutions improves significantly. • Four bi-objective optimization problems are considered. • Validation with a few prominent optimization algorithms and constraint handling methods. Repairing infeasible solutions is a seldomly used constraint handling technique (CHT) in optimization because, with this technique, users must define ways to prevent constraint violation, which is difficult or impossible in many situations. To overcome this challenge, in this paper we propose an approach based on artificial neural networks to automatically discover variable-constraint mapping that specifies which variables must be modified if a constraint is violated. We embed this procedure into a recent repair-based CHT that uses members of the current population, either feasible or infeasible, to determine the new value for the repaired variables. Here, the CHT is modified to repair each constraint separately using a different solution that does not violate the same constraint. The entire technique is fully autonomous, meaning that a user does not provide any insights into the problem. The modified CHT is implemented in the Non-dominated Sorting Genetic Algorithm II (NSGA-II) and compared with four other multi-objective optimization algorithms and a few CHTs. Four test problems are considered: a mathematical benchmark problem, two truss problems and structural optimization of a chemical tanker. The tanker case is a real-world optimization problem with 94 variables and 376 nonlinear constraints. A minimum of 30 independent runs are performed with each algorithm, and various statistical results are shown. With the proposed automated mapping, the modified repair-assisted NSGA-II obtains significantly better results than NSGA-II with other CHTs on all test problems while outperforming all other algorithms and CHTs for the tanker. [ABSTRACT FROM AUTHOR]

In this paper, one MOEA/D variant using two crossover strategies (MOEA/D-TCS) and two constraint handling methods are proposed to deal with four combined cooling, heating, and power (CCHP) scenarios in summer and winter. MOEA/D-TCS maintains a balance between global search and local search by combining a modified spiral updating position of whale optimization algorithm and the simulated binary crossover of genetic algorithm, and it is able to obtain a wide and even Pareto set for each CCHP scenario. The two constraint handling methods enable infeasible solutions to get rid of infeasible regions over a short period of time, guaranteeing that the reserved solutions of MOEA/D-TCS satisfy all constraints. Experimental results show that each CCHP scenario with the battery has lower energy consumption, operation cost and carbon dioxide emission than the corresponding CCHP scenario without the battery, and hence the battery is helpful to the improvements of the flexibilities and efficiencies of energy cascade utilization for the CCHP systems in summer and winter. Also, MOEA/D-TCS performs better than the other seven multi-objective evolutionary algorithms and achieves larger hypervolumes and coverage rates for four CCHP scenarios. • The optimal dispatch of combined cooling, heating, and power is studied. • The battery is added to the combined cooling, heating, and power system. • A MOEA/D with two crossover strategies is presented for OD-CCHP. • The scenarios with the battery achieve small objective function values. • The improved MOEA/D outperforms the other methods for four OD-CCHPs. [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.

This paper aims at the optimal design of a system of small solid barrier-type stone dams in a semi-realistic study case, determining the number, location and height of dams and a borrow-pit (BP)'s location for benefit maximization and cost minimization of objectives: (a) maximum flood protection, (b) maximum underlying aquifers' artificial recharge, (c) minimum dams' construction cost and (d) minimum stonework transportation cost. The simplified conceptual model involves no hydraulic simulation; flow characteristics are not considered, while no dam is assumed to affect another dam's benefit/cost values. Hence, all partial benefit/cost values can be separately pre-calculated, for each one of the available dam locations for all available heights and BP locations, deriving from data concerning topography, geology/soil, land uses, construction and transportation costs. Any solution proposing a system of dams of various heights and a BP exhibits a total management value equal to the sum of the respective partial benefit/cost values of each dam. The multi-objective optimization problem is formulated into a single-objective minimization problem; the difference of costs minus benefits is to be minimized. Simple, elitist genetic algorithms (GAs) are used, coupled with sophisticated post-processing of results, able to produce optimized design solutions and strategies. HIGHLIGHTS Optimization of small dam system in mountainous stream basins.; Find optimal dams' locations and heights, and a borrow-pit's location.; Construction and stonework transport costs – flood protection and aquifer recharge benefits = minimum.; A simplified model allows the pre-calculation of benefits/costs and reduces computational load.; The ‘OptiDams’ tool serves as a decision-support tool in the design phase of relevant works.;

Abstract 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.

Traditional optimizers require several experimentations to fine tune parameters and this makes them problem dependent and can compound the general simulation problem. Penalty method which is commonly used to solve constrained well placement optimization problem requires extensive experimentation to set up the right penalty parameter. Poor parameter set up affects performance of optimization tool. In this article, Grey Wolf Optimizer (GWO) is implemented as well placement optimizer. Superiority of feasible solutions method was proposed for handling the minimum well distance constraint. Powell-Skolnick (CPF-1) and Deb (CPF-2) constraint techniques were considered and their performances were compared to Unconstrained Problem Formulation (UCPF). Two field development strategies (DS-1 and DS-2) were considered and implemented in SPE1 (unimodal system) and PUNQ-S3 (multimodal system) reservoir models to evaluate the performances of CPF-1, CPF-2 and UCPF. Results revealed that under SPE1, UCPF gave the highest average Net Present Value (NPV) for DS-1 and DS-2 but with majority of the solutions violating the constraints whilst under PUNQ-S3, CPF-1 and CPF-2 showed superior performances against UCPF. Among the constraint satisfaction, CPF-2 showed relatively superior performance than CPF-1 in all cases except under DS-2 in PUNQ-S3. [ABSTRACT FROM AUTHOR]

This study covers the output‐feedback model predictive control (MPC) of nonlinear systems subjected to stochastic disturbances and state chance constraints. The stochastic optimal control problem is solved in a stochastic dynamic programming fashion, and the output‐feedback control is performed with the extended Kalman filter. The information state is summarized as a dynamic Gaussian belief model. Thus, the stochastic Bellman equation is transformed into a deterministic equation using this model. The resulting constrained Bellman equation is solved using the proposed constrained, approximate dynamic programming algorithm. The algorithm is proved to have a Q‐superlinear local convergence rate. Numerical experiments show that the proposed algorithm can attain good control performance and reasonable chance‐constraint satisfaction and is computationally efficient owing to its dynamic programming structure. [ABSTRACT FROM AUTHOR]

An improved cross-entropy (CE) method assisted with a chaotic operator (CGSCE) is presented for solving the optimal power flow (OPF) problem. The introduction of the chaotic operator helps to enhance the exploration capability of the popular cross-entropy approach while the global best solution is preserved. To handle the constraints in the optimal power flow, an efficient constraint handling technique with no parameter adjustment is also introduced. The approach is tested on both the IEEE-30 bus system and the IEEE-57 bus system with different objective functions to verify its effectiveness in comparison with a few other methods reported in the literature. Simulation results confirm that the proposed method is capable of improving both the exploration ability and the convergence speed of the conventional cross-entropy method. It outperforms the original cross-entropy, its variant GSCE and other methods in most of the OPF study cases. [ABSTRACT FROM AUTHOR]

Genetic algorithms (GAs) are approximate solving methods that have been originally proposed to achieve unconstrained optimization. To handle constrained problems, which is the case for the majority of real-life circumstances, GAs must be equipped with a constraint-handling mechanism. Transformation functions (TFs) are among the constraint-handling approaches that intervene in the phenotypic space. In this paper, we study the impact of considering constraint priorities on the GA performance when it deals with heavily constrained problems. Priorities are set by integrating a constraint order into the TF definition. We consider different TF forms enhanced with a fuzzy inference engine to find the best constraint ordering. Finally, we conduct an experimental study to assess the performance of the proposed approach on the semi-supervised graph partitioning problem. The obtained results show with statistical evidence that the proposed fuzzy method is promising. • This article proposes a fuzzy constraint handling approach for the genetic algorithm (GA) to solve heavily constrained problems. • The fitness calculation uses transformation functions that reorder the constraints. • Constraint reordering allows the GA to penalize infeasible solutions without losing the good schemata they hide. • A fuzzy inference system seeks the best constraint prioritization to boost the genetic algorithm performances. • A comparative study investigates the performance of the proposed approach against state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Abstract 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.

Active-set approaches are commonly used in algorithms for constrained numerical optimization. We propose that active-set techniques can beneficially be employed for evolutionary black-box optimization with explicit constraints and present an active-set evolution strategy. We experimentally evaluate its performance relative to those of several algorithms for constrained optimization and find that the active-set evolution strategy compares favourably for the problem set under consideration. [ABSTRACT FROM AUTHOR]

This article proposes and suggested improves real-coded genetic algorithm (IRCGA) for optimal scheduling of thermal plants in coordination with fixed head hydro units. Genetic algorithm (GA) is based on inbred operation of human chromosomes. GA has the ability to establish the global or very close to the global optima. Here, in this article to heighten convergence speed and solution quality the IRCGA method has been recommended. Two different test systems have been used here to verify the effectiveness of the proposed IRCGA method. The results obtained from the emerged IRCGA method have been compared with other evolutionary techniques. The simulation results from different test systems demonstrate that the proposed IRCGA algorithm has the capability to generate better result. [ABSTRACT FROM AUTHOR]

The improvement of reservoir operation optimization (ROO) can lead to comprehensive economic benefits as well as sustainable development of water resources. To achieve this goal, an algorithm named wind-driven optimization (WDO) is first employed for ROO in this paper. An improved WDO(IWDO) is developed by using a dynamic adaptive random mutation mechanism, which can avoid the algorithm stagnation at local optima. Moreover, an adaptive search space reduction (ASSR) strategy that aims at improving the search efficiency of all evolutionary algorithms is proposed. The application results of the Goupitan hydropower station show that IWDO is an effective and viable algorithm for ROO and is capable of obtaining greater power generation compared to the classic WDO. Moreover, it is shown that the ASSR strategy can improve the search efficiency and the quality of scheduling results when coupled with various optimization algorithms such as IWDO, WDO and particle swarm optimization. HIGHLIGHTS A new algorithm named wind-driven optimization algorithm (WDO) is first introduced to reservoir operation optimization.; WDO is improved by two novel strategies.; One of the strategies mentioned in point 2 is also suitable for other algorithms to improve the efficiency of algorithms.;

Convergence, diversity and feasibility are three important issues when solving constrained multiobjective optimization problems (CMOPs). To deal with the balance among convergence, diversity and feasibility well, this article proposes a cooperative multiobjective evolutionary algorithm with propulsive population (CMOEA-PP) for solving CMOPs. CMOEA-PP has two populations, including propulsive population and normal population, and these two populations work cooperatively. Specifically, propulsive population focuses on convergence. Normal population gives priority to feasibility and is obligated to maintain diversity. To cross through the infeasible region and reach the Pareto front (PF), propulsive population does not consider constraints in the early stage and only considers constraints in the later stage. To further accelerate the speed of convergence, propulsive population only searches for corner solutions and center solutions, while normal population searches for the whole PF. As a result, propulsive population can cross through the infeasible region because of the lack of attention to feasibility. In addition, propulsive population also can guide and accelerate the convergence of the evolutionary process. Comprehensive experiment results on several sets of benchmark problems demonstrate that CMOEA-PP is better than existing state-of-the-art competitors. [ABSTRACT FROM AUTHOR]

Co-generation units (i.e., combined heat and power plants—CHPs) are playing an important role in fulfilling the heat and power demand in the energy system. Due to the depletion of fossil fuels and rising carbon footprints in the environment, it is necessary to develop some alternatives as well as energy efficient operating strategies. By utilising the waste heat from thermal plants, cogeneration units help to decrease energy generation costs as well as reduce emitted pollutants. The combined heat and power economic dispatch (CHPED) operation strategy is becoming an important optimisation task in the energy efficient operation of a power system. The optimisation of CHPED is quite complex due to the dual dependence of heat and power in the cogeneration units. The valve point loading effect and prohibited operating zones of a thermal power unit make the objective function non-linear and non-convex. In this work, to address these issues more effectively, the viable operational area of the CHP and power system network losses are considered for the optimal allocation of power output and heat generation. A metaheuristic optimisation algorithm is proposed to solve the CHPED to minimize the fuel supply, thus satisfying the constraints. To handle equality and inequality constraints, an external penalty factor-based constraint handling technique is used. The success of the proposed CHPED algorithm is tested on three considered cases. In all the cases, the results show the effectiveness in terms of solution accuracy and better convergence. [ABSTRACT FROM AUTHOR]

Solving constrained multiobjective optimization problems brings great challenges to an evolutionary algorithm, since it simultaneously requires the optimization among several conflicting objective functions and the satisfaction of various constraints. Hence, how to adjust the tradeoff between objective functions and constraints is crucial. In this article, we propose a dynamic selection preference-assisted constrained multiobjective differential evolutionary (DE) algorithm. In our approach, the selection preference of each individual is suitably switching from the objective functions to constraints as the evolutionary process. To be specific, the information of objective function, without considering any constraints, is extracted based on Pareto dominance to maintain the convergence and diversity by exploring the feasible and infeasible regions; while the information of constraint is used based on constrained dominance principle to promote the feasibility. Then, the tradeoff in these two kinds of information is adjusted dynamically, by emphasizing the utilization of objective functions at the early stage and focusing on constraints at the latter stage. Furthermore, to generate the promising offspring, two DE operators with distinct characteristics are selected as components of the search algorithm. Experiments on four test suites including 56 benchmark problems indicate that the proposed method exhibits superior or at least competitive performance, in comparison with other well-established methods. [ABSTRACT FROM AUTHOR]

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

The continuous berth allocation and quay crane assignment problem considers the size of berths and ships, the number of quay cranes, the dynamic ships and non-crossing constraints of quay cranes. In this work, a mixed-integer linear programming model of this problem is established, aiming at minimizing the total stay time and delay penalty of ships. To solve the model, the continuous berth is separated into discrete segments via a proposed discretization strategy. Thereafter, a large neighborhood search algorithm composed of the random removal operator and relaxed sorting-based insertion operator and a backtracking comparison-based constraint repair strategy are proposed. The effectiveness of the model and algorithm presented is verified via real-life instances with different characteristics, and the performances of different combinations of removal operators and insertion operators in the large neighborhood search algorithmic framework are analyzed. Numerical results show that the large neighborhood search algorithm can optimally solve the small-scale instances in a reasonable time. Meanwhile, the results of large-scale instances show that the large neighborhood search algorithm incorporating the discretization strategy is more efficient than other genetic algorithms based on continuous optimization. With the proposed approach, high-quality berth and quay crane allocation results can be obtained efficiently. [ABSTRACT FROM AUTHOR]

Many studies have shown that the effective mixture of feasible and infeasible solutions is beneficial to solve the constrained multi-objective optimization problems (CMOPs). So, it is of great importance to fully identify the valuable infeasible solutions that are helpful to find the constrained Pareto fronts. To achieve this, this paper evaluates the potential value of each infeasible solution from different aspects, and forms a criterion to fully identify the valuable infeasible solutions. Comparative analysis shows that compared with the existing constraint handling techniques, the proposed criterion is more effective in identifying valuable infeasible solutions. Accordingly, we embed the proposed criterion in the evolutionary algorithm and design a criterion-based constrained multi-objective algorithm for CMOPs. In the proposed algorithm, an archive preferring feasible solutions is used to record the best solutions, which are then mixed with the valuable infeasible solutions identified by the criterion to deal with the CMOPs. A series of simulation experiments on several benchmarks and engineering problem show the competitive performance of the proposed algorithm. Compared with the other state-of-the-art constrained evolutionary multi-objective optimization algorithms, the proposed algorithm performs better in dealing with different types of CMOPs, and it is the only one that can successfully deal with the problems that the initial population arises in the complex infeasible regions below the Pareto fronts. [ABSTRACT FROM AUTHOR]

The classical optimal power flow problem is usually formulated with only thermal generators, in which the fuel used to generate power is limited and emissions from the network system are often ignored. Due to several promising features like renewability, richness, and cleanness, renewable energy sources have been drew growing attention. As a result, more and more renewable energy sources are penetrated into the electrical grid. In this paper, the standard IEEE-30 bus system is modified by integrating renewable energy sources as the case study, where the traditional thermal generators on buses 5 and 11 are replaced by wind generators, and bus 13 is replaced by solar generators. In addition, to address the intermittence and uncertainty of renewable sources, the Weibull probability density function is used to calculate the available wind power. Meanwhile, the lognormal probability density function is employed to calculate the available solar power. The optimal power flow with stochastic wind and solar energy is formulated as a multi-objective optimization problem. A multi-objective evolutionary algorithm based on non-dominated sorting with constraint handling technique are presented to solve it. In addition, another larger test system i.e., IEEE-57 bus system is selected to further verify the performance of the proposed approach in handling large dimensional problem. Simulation results indicate that proposed approach can obtain competitive compromise solution on different optimization objectives. • OPF incorporating renewable energy sources such as wind and solar is formulated. • The intermittent and uncertain of wind and solar power is matched by different density function. • The superiority of feasible solutions (SF) is used to effectively handle constraints in OPF. • Two effective constraint multi-objective methods are proposed. [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.