This study focuses on the parameter estimation of an industrial activated sludge model using hyperparameter-tuned metaheuristic techniques. The data used in this study were collected on-site from a textile industry wastewater treatment plant. A Modified Activated Sludge Model (M-ASM) was the 'first-principle model’ selected and implemented with suitable assumptions. Advanced metaheuristic techniques, as Adaptive Tunicate Swarm Optimization (ATSO), Whale Optimization Algorithm (WOA), Rao-3 Optimization (Rao-3) and Driving Training Based Optimization (DTBO) were implemented. The hyperparameter tuning was performed with Bayesian Optimization (BO). Optimized metaheuristic algorithms were implemented for model-parameter identification. The Bayesian optimized Rao-3(BO-Rao-3) algorithm provided the best validation results, with a Mean Absolute Percentage Error (MAPE) value of 7.0141 and Normalized Root Mean Square Error (NRMSE) value of 0.2629. It also had the least execution time. BO-Rao-3 is 0.93% to 4.7% better than the other implemented hyperparameter-tuned metaheuristic techniques.
Many engineering application problems can be modeled as constrained multiobjective optimization problems (CMOPs), which have attracted much attention. In solving CMOPs, existing algorithms encounter difficulties in balancing conflicting objectives and constraints. Worse still, the performance of the algorithms deteriorates drastically when the size of the decision variables scales up. To address these issues, this study proposes a competitive and cooperative swarm optimizer for large-scale CMOPs. To balance conflict objectives and constraints, a bidirectional search mechanism based on competitive and cooperative swarms is designed. It involves two swarms, approximating the true Pareto front from two directions. To enhance the search efficiency in large-scale space, we propose a fast-converging competitive swarm optimizer. Unlike existing competitive swarm optimizers, the proposed optimizer updates the velocity and position of all particles at each iteration. Additionally, to reduce the search range of the decision space, a fuzzy decision variables operator is used. Comparison experiments have been performed on test instances with 100–1000 decision variables. Experiments demonstrate the superior performance of the proposed algorithm over five peer algorithms.
Real-world multi-objective engineering problems frequently involve uncertainties stemming from environmental factors, production inaccuracies, and other sources. A critical aspect of addressing these problems, termed Multi-Objective Robust Optimization (MORO) problems, is the development of solutions that are both optimal and resilient to uncertainties. This paper proposes addressing these uncertainties through the application of Stackelberg game models, a novel approach involving the interaction of two players. The Leader searches for optimal and robust solutions and the Follower generates uncertainties based on the Leader’s chosen solutions. The Follower seeks to tackle the most challenging uncertainties associated with the Leader’s candidate solutions. Additionally, this paper introduces a novel metric to assess the robustness of a given set of solutions concerning specified uncertainties.
Based on the proposed approach, a co-evolutionary algorithm is developed. A numerical study is then conducted to evaluate the algorithm by comparing its performance with those obtained by four benchmark algorithms on nine benchmark MORO problems. The numerical study also aims to assess its sensitivity to run parameter variations. The experimental results demonstrate the proposed approach’s effectiveness in identifying a non-dominated robust set of solutions.
Evolutionary neural architecture search (ENAS) and differentiable architecture search (DARTS) are all prominent algorithms in neural architecture search, enabling the automated design of deep neural networks. To leverage the strengths of both methods, there exists a framework called continuous ENAS, which alternates between using gradient descent to optimize the supernet and employing evolutionary algorithms to optimize the architectural encodings. However, in continuous ENAS, there exists a premature convergence issue accompanied by the small model trap, which is a common issue in NAS. To address this issue, this paper proposes a self-adaptive differential evolution algorithm for neural architecture search (SaDENAS), which can reduce the interference caused by small models to other individuals during the optimization process, thereby avoiding premature convergence. Specifically, SaDENAS treats architectures within the search space as architectural encodings, leveraging vector differences between encodings as the basis for evolutionary operators. To achieve a trade-off between exploration and exploitation, we integrate both local and global search strategies with a mutation scaling factor to adaptively balance these two strategies. Empirical findings demonstrate that our proposed algorithm achieves better performance with superior convergence compared to other algorithms.
Surrogate-assisted multi/many-objective evolutionary algorithms (SA-MOEAs) have shown significant progress in tackling expensive optimization problems. However, existing research primarily focuses on low-dimensional optimization problems. The main reason lies in the fact that some surrogate techniques used in SA-MOEAs, such as the Kriging model, are not applicable for exploring high-dimensional decision space. This paper introduces a surrogate-assisted multi-objective evolutionary algorithm with dimensionality reduction to address high-dimensional expensive optimization problems. The proposed algorithm includes two key insights. Firstly, we propose a dimensionality reduction framework containing three different feature extraction algorithms and a feature drift strategy to map the high-dimensional decision space into a low-dimensional decision space; this strategy helps to improve the robustness of surrogates. Secondly, we propose a sub-region search strategy to define a series of promising sub-regions in the high-dimensional decision space; this strategy helps to improve the exploration ability of the proposed SA-MOEA. Experimental results demonstrate the effectiveness of our proposed algorithm in comparison to several state-of-the-art algorithms.