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The number of research works on dynamic constrained optimization problems has been increasing rapidly over the past two decades. In this domain, many real-life decision problems need to be solved repeatedly with changing data and parameters. However, no research on dynamic problems with changes in the coefficients of the constraint functions has been reported. In this paper, to deal with such problems, a new evolutionary framework with multiple novel mechanisms is proposed. The new mechanisms are for (1) dealing with both linear and non-linear components in the constraint functions, (2) identifying the rate of change in the coefficients of the variables and (3) updating the population efficiently after every change occurs in the problem. To evaluate the performance of the proposed algorithm, we designed a new set of 13 dynamic benchmark problems, each of which consists of 20 dynamic changes and 3 different scenarios. The results demonstrate that the proposed algorithm significantly contributes in achieving good quality solutions, high feasibility rates and fast convergence in rapidly changing environments. In addition, the framework shows its capability of using different meta-heuristics to solve dynamic problems. [ABSTRACT FROM AUTHOR]

This paper presents a constrained adaptive dynamic programming (CADP) algorithm to solve general nonlinear nonaffine optimal control problems with known dynamics. Unlike previous ADP algorithms, it can directly deal with problems with state constraints. Firstly, a constrained generalized policy iteration (CGPI) framework is developed to handle state constraints by transforming the traditional policy improvement process into a constrained policy optimization problem. Next, we propose an actor-critic variant of CGPI, called CADP, in which both policy and value functions are approximated by multi-layer neural networks to directly map the system states to control inputs and value function, respectively. CADP linearizes the constrained optimization problem locally into a quadratically constrained linear programming problem, and then obtains the optimal update of the policy network by solving its dual problem. A trust region constraint is added to prevent excessive policy update, thus ensuring linearization accuracy. We determine the feasibility of the policy optimization problem by calculating the minimum trust region boundary and update the policy using two recovery rules when infeasible. The vehicle control problem in the path-tracking task is used to demonstrate the effectiveness of this proposed method. [ABSTRACT FROM AUTHOR]

Box-constrained optimization problems in the real m × n matrix space have been widely applied in big data mining. However, efficient solution of them is still a challenge. In this paper, a new nonmonotone line search rule is first proposed by extending the well-known ones and inheriting their advantages. Then, by analyzing and exploiting properties of this rule, a new nonmonotone spectral projected gradient algorithm is developed to solve the box-constrained optimization problems in the matrix space. Global convergence of the developed algorithm is also established. Numerical tests are conducted on a series of randomly generated test problems and those in the set of benchmark test problems. Compared with other existing nonmonotone line search rules, our rule shows its advantages in terms of the significantly reduced number of function evaluations and significantly reduced number of iterations. To further validate applicability of this research, we apply the studied optimization problem and the developed algorithm to solve the problems of image clustering. Numerical results demonstrate that the proposed method can generate better clustering results and is more robust than the similar ones available in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we propose an improved version of Twin SVM using a non-smooth optimization method. Twin SVM generally consists in determining two non-parallel planes by alternately solving two constrained optimization models. Solving this problem using the classical Lagrangian method has many limitations, notably: its only limited to handle Gaussian noise, generally exaggerates the influence of outliers and cannot handle unbalanced data, this due to the differentiability of the model. To circumvent these issues, we transform two-constraint optimization models using the penalty method into an unconstrained non-smooth optimization one. The non-smoothness nature of the problem has many advantages, but it requires special treatment, which is why we use the primal dual method to solve it, since it is the most appropriate and it is robust in terms of stability, convergence and speed (Lyaqini, Nachaoui and Hadri, 2022). To demonstrate the effectiveness of the proposed approach, several experiments were carried out on numerous UCI benchmarks, medical image and HandPD datasets. These experiments demonstrated the effectiveness and applicability of the proposed approach, with satisfactory results compared to the state of the art. [ABSTRACT FROM AUTHOR]

• Transform the max-bisection problem to a linearly constrained optimization problem. • Propose a deterministic annealing neural network algorithm by introducing a barrier function in square-root form. • Prove the existence of the integral minimum solution of the max-bisection problem in theory and the proof is simpler than other algorithms. • Experimental results show that the proposed method outperforms other methods. The max-bisection problem has extensive applications in network engineering, making it imperative to develop effective methods to solve this problem. However, the efficient computation on this problem remains challenging due to its NP-hard computational complexity. To address this question, in this paper, we transform the max-bisection problem to an artificial linearly constrained optimization problem and develop a modified deterministic annealing neural network algorithm by introducing a barrier function. The barrier parameter of this function acts as the temperature in the annealing process and decreases from a large positive number to zero. The initial value of the barrier parameter promises that the artificial problem is convex and can be easily solved at the beginning of the descending process. The solution to the original max-bisection problem is finally obtained through a descent algorithm, in which the bound limit of the solution is always satisfied as long as the iteration step length is less than one. We have proved the theoretical convergence of the proposed algorithm. Numerical results demonstrate that the proposed algorithm has several advantages over both the approximation algorithms and metaheuristic methods. [ABSTRACT FROM AUTHOR]

This study considers a constrained huge-scale optimization problem over networks where the objective is to minimize the sum of nonsmooth local loss functions. To solve this problem, many optimization algorithms have been proposed by employing (sub)gradient descent methods to handle high-dimensional data, but the computation of the entire sub(gradient) becomes a computational bottleneck. To reduce the computational burden of each agent and preserve privacy of data in time-varying networks, we propose a privacy-preserving decentralized randomized block-coordinate subgradient projection algorithm over time-varying networks, in which the coordinates of the subgradient vector is randomly chosen to update the optimized parameter and the partially homomorphic cryptography is used to protect the privacy of data. Further, we prove that our algorithm is convergent asymptotically. Moreover, the rates of convergence are also established by choosing appropriate step sizes, i.e., O (log K / K) under local strong convexity and O (log K / K) under local convexity, in which K represents the number of iterations. Meanwhile, we show that the privacy of data can be protected by the proposed algorithm. The results of experiments demonstrate the computational benefit of our algorithm on two real-world datasets. The theoretical results are also verified by different experiments. • This paper proposes a privacy-preserving decentralized randomized block-coordinate subgradient projection algorithm. • It proves that the proposed algorithm is asymptotically convergent. • It proves that the proposed algorithm can protect the privacy of data. • It proves that the rate of convergence is achieved, i.e., O (log K / K) and O (log K / K). [ABSTRACT FROM AUTHOR]

When solving constrained multiobjective optimization problems, it is crucial to deal with several conflicting objectives and various constraints simultaneously. To address these two issues, a constrained multiobjective differential evolution algorithm with an infeasible-proportion control mechanism is presented in this paper. Specifically, two populations are cooperatively employed in the evolution process. The first population is used to solve the original problem, that is, to explore the constrained Pareto front, while the second population is created to search for high-quality objective function information. Furthermore, differential evolution with two specific mutation strategies is employed to update each population. Cooperative strategies can not only balance diversity and convergence but also realize information exchange between the two populations provide new evolutionary directions. In addition, an infeasible-proportion control mechanism is used to gradually decrease the proportion of infeasible solutions in the second population. This enables the main population to pass through the infeasible region barrier in the early evolution stage and facilitates the search for a constrained Pareto front in the later evolution stage. Systematic experiments on 65 benchmark test functions show that the proposed algorithm is superior to or at least comparable to five well-established constrained multiobjective optimization methods. [ABSTRACT FROM AUTHOR]

• A cosh-based smoothing function is set to approximate complementary equation. • The smoothing approximation function is independent of users to suit large scale. • Multi-classes users are considered to optimize electricity prices in smart grid. • Nonsingularity of Jacobian and global and local quadratic convergence are proved. • Effectiveness of smoothing Newton pricing algorithm is shown by numerical results. In a smart grid system, different types of electricity users such as residential, commercial and industrial users have different utility functions. This paper proposes a nonlinear constrained optimization model for real-time pricing that maximizes the total utilities of all the different user groups. A Karush–Kuhn–Tucker equation system is employed to solve the model. However, it is a challenging task to solve the system due to the nonlinear complementary condition. To tackle the challenge, a cosh-based smoothing approximation function is proposed to substitute the nonlinear complementary condition. Subsequently, the smoothing Newton algorithm is developed to solve the new equation system. The global convergence and local quadratic convergence of the algorithm are proved. Numerical experiments are performed to test the smoothing method and compare the solutions of real-time pricing, fixed pricing and time-of-use pricing strategies applied in the smart grid system. The results show that the real-time pricing mechanism is the most suitable in saving energy and reducing peaks and troughs in energy consumption. This also indicates that it is effective to use the smoothing Newton algorithm to solve the problem of real-time electricity pricing for smart grid. We obtain that the smoothing approximation function is effective for the supply–demand balance constraints in smart grid. [ABSTRACT FROM AUTHOR]

Dynamic economic dispatch with valve-point effects (DED_ vpe) is a high-dimensional constrained optimization problem with non-convex and non-smooth characteristics. Hybrid methods are one of the most advanced methods to solve the problem. However, most of these methods improve the solution accuracy at the expense of algorithm robustness. This paper proposes an adaptive hybrid backtracking search optimization algorithm (AHBSA) for solving the DED_ vpe. The core idea of AHBSA lies in designing a suitable coupling structure based on the current best individual (called optimal partial coupling). The structure hybridizes an improved BSA mutation operator and the DE/best/1 operator with equal probability. The improved BSA mutation operator uses the current best individual and the historical population to update individual position, called BSA/best/old. It is also the first research work of extending BSA to the problem. In addition, an adaptive parameter control mechanism is proposed to select an appropriate 'mixrate' value for achieving better coupling. The performance of AHBSA is validated on six DED test cases of three systems. Experimental results demonstrate that, compared with some representative methods, AHBSA not only reduces the fuel cost but also ensures the robustness of the algorithm. • A hybrid method AHBSA is proposed to solve DED problem with valve-point effects. • An optimal partial coupling structure is designed in AHBSA. • BSA is the first attempt at solving DED problem. • Results on six benchmark DED test cases show AHBSA is competitive. [ABSTRACT FROM AUTHOR]

When evolutionary algorithms are employed to solve constrained optimization problems (COPs), how to efficiently make use of the information of some promising infeasible solutions is very important in the process of searching for the optimal feasible solution. In this paper, for selecting and making full use of some better infeasible solutions, a rankings-based fitness function method is designed. Specifically, the final fitness function of each individual is obtained by weighting two rankings, which are got after sorting the population based on the ɛ constraint technique and only based on the objective function, respectively. Furthermore, the weight is dynamically adjusted by considering the proportion of feasible solutions and generation information. By doing this, the tradeoff in constraints and objective can be addressed. Moreover, the promising offspring are generated by three differential evolution strategies with distinct characters to balance diversity and convergence. In addition, 116 benchmark problems from three test suites are used to evaluate the performance of the proposed method. Nine commonly used practical problems are selected to test the potential of the algorithm to solve real-world problems. Experimental results indicate that the proposed method shows superior or competitive to other state-of-the-art methods tailored for COPs. Moreover, the effectiveness of each introduced component in the proposed algorithm is investigated by the ablation study. • A new constrained evolutionary optimization algorithm is developed, denoted as DERFF. • Two rankings are got for each individual by two ways, one prefers constraint and the other prefers objective function. • The weight for summing these two rankings is dynamically adjusted by the proportion of feasible solutions and generation information. • Three evolutionary strategies are combined to balance the convergence and diversity of the population. • Experimental results indicate the effectiveness of the DERFF against other advanced algorithms. [ABSTRACT FROM AUTHOR]

Recently, decomposition has gained a wide interest in solving multi-objective optimization problems involving more than three objectives also known as Many-objective Optimization Problems (MaOPs). In the last few years, there have been many proposals to use decomposition to solve unconstrained problems. However, fewer is the amount of works that has been devoted to propose new decomposition-based algorithms to solve constrained many-objective problems. In this paper, we propose the ISC-Pareto dominance (Isolated Solution-based Constrained Pareto dominance) relation that has the ability to: (1) handle constrained many-objective problems characterized by different types of difficulties and (2) favor the selection of not only infeasible solutions associated to isolated sub-regions but also infeasible solutions with smaller CV (Constraint Violation) values. Our constraint handling strategy has been integrated into the framework of the Constrained Non-Dominated Sorting Genetic Algorithm-III (C-NSGA-III) to produce a new algorithm called Isolated Solution-based Constrained NSGA-III (ISC-NSGA-III). The empirical results have demonstrated that our constraint handling strategy is able to provide better and competitive results when compared against three recently proposed constrained decomposition-based many-objective evolutionary algorithms in addition to a penalty-based version of NSGA-III on the CDTLZ benchmark problems involving up to fifteen objectives. Moreover, the efficacy of ISC-NSGA-III on a real world water management problem is showcased. [ABSTRACT FROM AUTHOR]

Tree-Seed Algorithm (TSA) is a meta-heuristic optimization algorithm with good performance in solving continuous optimization problems. However, there is an imbalance between its exploration and exploitation when solving complex problems, mainly lack exploration. To overcome this problem, this paper proposes two tree migration mechanisms: triple-learning-based migration mechanism and sine-random-distribution migration mechanism. The target tree position is migrated by learning from the first three trees in the current iteration. The sine function is added to the tree migration formula to enhance the randomness of tree distribution. In order to verify these migration mechanisms, Triple Tree-Seed Algorithm (TriTSA) has been proposed and compared with TSA on 30 well-known test functions from IEEE CEC 2014. In addition, STSA, SCA, PSO, ABC, Jaya, and TLBO are adopted in some comparative experiments on different dimensions. The experiments show that the tree migration mechanism can improve the optimization capability of the original algorithm effectively. On all 30 benchmark test functions, TriTSA outperforms TSA on 10, 30, 50, and 100 dimensions by 70%, 90%, 90%, and 97% respectively. Finally, the proposed TriTSA is compared with TSA, ABC, PSO, and SCA on solving two classical engineering design problems. It is proved that the proposed algorithm is more applicable in solving practical problems. [ABSTRACT FROM AUTHOR]

This paper presents a versatile form-finding method for tensegrity structures that is based on solving a constrained optimization problem. A general constrained optimization model simulating the forming process of tensegrity structures is established firstly. Then it has been proved that the optimality conditions of this model are equivalent to the self-equilibrium equations of tensegrity structures. The dynamic relaxation technique with kinetic damping is incorporated into a so-called three-term method to solve this optimization problem, guaranteeing a stable and rapid convergent process. Besides the topology of the structure as well as the initial configuration given randomly, the input parameters of this method also include the power exponent of cable lengths— k , the weight coefficients of cables and the target lengths of struts in the objective function. The reasonable value of ' k ', to some extent dominating the effectiveness of this algorithm, is investigated qualitatively, combining with a set of illustrative examples of prismatic tensegrity structures. For cable-strut system with external supports, a twofold scheme to consider the corresponding boundary constraints is presented without increasing the number of constraint equations. Numerical examples show that the proposed method has a huge capacity of searching for free-form tensegrity structures with large members and complicated topology. [ABSTRACT FROM AUTHOR]