Solving large-scale, constrained, and nonlinear optimization problems is crucial for the Internet of Things (IoT) due to its wide range of real-life applications. However, there is no unified approach for handling constraints and optimizing objective functions. This article proposes a tri-objective general framework (TriGF) and an efficient differential evolution (DE) method enhanced with adaptive gradient-based mutation (AGM), termed AGM-DE. Within the TriGF, AGM-DE explores the entire feasible region by considering both constraints and the objective function. The goal is to achieve global optimality and fast convergence for the self-assembly of satellite IoT devices under constraints. AGM is an adaptive refinement technique that uses gradient information to reduce the search space and speed up optimization. In our AGM approach, we incorporate gradient information from the objective function to mitigate the negative effects of classic constraint-based gradient descent and reduce its inherent greediness. To validate AGM-DE’s effectiveness, we conducted extensive simulations on 57 benchmark problems with diverse dimensions and constraints. The results demonstrate AGM-DE’s exceptional ability to manage constraints in 56 of these 57 test functions, outperforming five leading methods in optimization efficacy and consistency. We also assessed AGM-DE’s application in optimizing IoT device self-assembly within a satellite layout, subject to heat pipe constraints. Comparative analyses highlight AGM-DE’s robustness and superior search capabilities in deriving layout schemes. Remarkably, these schemes outperform existing best known solutions for IoT configurations involving 40 to 90 nodes with 80 to 180 variables, confirming AGM-DE’s suitability for a wide range of large-scale constrained IoT challenges.

Recently, gradient-based repair methods have been commonly introduced into constraint-handling techniques to handle linear and non-linear constraints. These gradient-based repair methods are only designed to reduce constraint violations, and they do not act on the objective function in the repairing process. Nevertheless, the gradient descent optimization method is originally proposed to optimize the objective function without constraints. Motivated by this consideration, this study develops an improved gradient-based repair method that incorporates the objective function to handle the constraints and optimize the objective function simultaneously. The proposed repair method is integrated into a multiobjective differential evolution framework to investigate its effectiveness. Experiments have been conducted on 57 real-world constrained benchmark test functions. The empirical result shows that, compared to the selected state-of-the-art algorithms, our proposed gradient-based repair method can assist the adopted constrained optimization approach to obtain high-quality feasible solutions.

Many real-world optimization problems are inherently constrained, presenting significant challenges to the application of evolutionary algorithms. Successfully managing these constraints while simultaneously optimizing the objective function requires a considerable degree of population diversity. To address this, we have developed a methodology that effectively combines an$\varepsilon$-constraint-handling method with a niching technique. The$\varepsilon$-constraint- handling method is specifically designed to manage constraints, while the niching technique aims to preserve pop-ulation diversity. In our approach, a constrained optimization problem is transformed into a tri-objective optimization challenge, introducing two additional objectives: the density objective and the overall constraint objective. The density objective is a particularly innovative aspect of our method, as it prolongs the survival of promising yet infeasible solutions. This prolongation aids the evolutionary search in converging towards the feasible region from various directions, thereby increasing the chances of identifying optimal solutions. Moreover, an improved gradient repair mutation strategy, based on a successful information reuse approach, is implemented to further refine promising solutions. To evaluate the effectiveness of our method, we tested it on 30 real-world constrained optimization problems from the CEC 2020 benchmark test suite. The results demonstrate that our approach either exceeds or is equivalent to the performance of current state-of-the-art constrained optimization algorithms.

In recent years, surrogate-assisted evolutionary algorithms have gained considerable success in addressing expensive constrained optimization problems. While significant focus has been directed toward optimization challenges with inequality constraints, the domain of expensive equality-constrained optimization also necessitates attention, as equality constraints are frequently encountered in traditional constrained optimization problems. Recognizing this gap, this study introduces an innovative approach that integrates a multilayer perceptron regression-based surrogate with a gradient descent-based repair method and differential evolution to address these challenges effectively. Our contributions are threefold: 1) We develop a multilayer perceptron-based surrogate model that concurrently approximates the objective function and equality constraints, 2) We employ a gradient descent-based repair method to adeptly manage the challenging equality constraints, and 3) We propose a hybrid local search scheme that enhances the solution refinement process. The combined use of the multilayer perceptron-based surrogate and gradient descent-based local search works in concert with differential evolution to guide the population toward the feasible region. This approach enables the evolutionary search, supported by the surrogate model, to extensively explore potential feasible regions. Our experimental results underscore the potential and efficacy of the proposed surrogate-assisted evolutionary algorithm in solving such complex optimization problems.

Economic dispatching of generating units in a power system can significantly reduce the energy cost of the system. However, the economic dispatch (ED) problem is highly constrained, and often has disconnected feasible regions because of various physical features. Enhancing population diversity is critical for the evolutionary approach to fully explore and exploit the feasible regions. In this article, we propose a density-enhanced multiobjective evolutionary approach to solve ED problem. An ED problem is first transformed into a tri-objective optimization problem, and then multiobjective optimization techniques are employed to fully optimize the constraints and cost function simultaneously. The first two objectives are derived from the original ED problem, while the third one is a novel density objective constructed by niching methods to enhance population diversity. These three objectives are optimized simultaneously by a dynamic dominance relation, which can make a good balance among feasibility, diversity, and convergence. To evaluate the performance of this proposed approach, 22 benchmark problems and seven real-world ED problems with different features are tested in this article. The experimental results show that our approach performs better than or at least competitive to the state-of-the-art algorithms, especially on large-scale ED problems.