Optimal operation of hydropower reservoir systems often needs to optimize multiple conflicting objectives simultaneously. The conflicting objectives result in a Pareto front, which is a set of non-dominated solutions. Non-dominated solutions cannot outperform each other on all the objectives. An optimization framework based on the multi-swarm comprehensive learning particle swarm optimization algorithm is proposed to solve the multi-objective operation of hydropower reservoir systems. Through adopting search techniques such as decomposition, mutation and differential evolution, the algorithm tries to derive multiple non-dominated solutions reasonably distributed over the true Pareto front in one single run, thereby facilitating determining the final tradeoff. The long-term sustainable planning of the Three Gorges cascaded hydropower system consisting of the Three Gorges Dam and Gezhouba Dam located on the Yangtze River in China is studied. Two conflicting objectives, i.e., maximizing hydropower generation and minimizing deviation from the outflow lower target to realize the system’s economic, environmental and social benefits during the drought season, are optimized simultaneously. Experimental results demonstrate that the optimization framework helps to robustly derive multiple feasible non-dominated solutions with satisfactory convergence, diversity and extremity in one single run for the case studied.

Comprehensive learning particle swarm optimization (CLPSO) is a powerful state-of-the-art single-objective metaheuristic. Extending from CLPSO, this paper proposes multiswarm CLPSO (MSCLPSO) for multiobjective optimization. MSCLPSO involves multiple swarms, with each swarm associated with a separate original objective. Each particle’s personal best position is determined just according to the corresponding single objective. Elitists are stored externally. MSCLPSO differs from existing multiobjective particle swarm optimizers in three aspects. First, each swarm focuses on optimizing the associated objective using CLPSO, without learning from the elitists or any other swarm. Second, mutation is applied to the elitists and the mutation strategy appropriately exploits the personal best positions and elitists. Third, a modified differential evolution (DE) strategy is applied to some extreme and least crowded elitists. The DE strategy updates an elitist based on the differences of the elitists. The personal best positions carry useful information about the Pareto set, and the mutation and DE strategies help MSCLPSO discover the true Pareto front. Experiments conducted on various benchmark problems demonstrate that MSCLPSO can find nondominated solutions distributed reasonably over the true Pareto front in a single run.

Multiswarm comprehensive learning particle swarm optimization (MSCLPSO) is a multiobjective metaheuristic recently proposed by the authors. MSCLPSO uses multiple swarms of particles and externally stores elitists that are nondominated solutions found so far. MSCLPSO can approximate the true Pareto front in one single run; however, it requires a large number of generations to converge, because each swarm only optimizes the associated objective and does not learn from any search experience outside the swarm. In this paper, we propose an adaptive particle velocity update strategy for MSCLPSO to improve the search efficiency. Based on whether the elitists are indifferent or complex on each dimension, each particle adaptively determines whether to just learn from some particle in the same swarm, or additionally from the difference of some pair of elitists for the velocity update on that dimension, trying to achieve a tradeoff between optimizing the associated objective and exploring diverse regions of the Pareto set. Experimental results on various two-objective and three-objective benchmark optimization problems with different dimensional complexity characteristics demonstrate that the adaptive particle velocity update strategy improves the search performance of MSCLPSO significantly and is able to help MSCLPSO locate the true Pareto front more quickly and obtain better distributed nondominated solutions over the entire Pareto front.

Comprehensive learning particle swarm optimization (CLPSO) and enhanced CLPSO (ECLPSO) are two literature metaheuristics for global optimization. ECLPSO significantly improves the exploitation and convergence performance of CLPSO by perturbation‐based exploitation and adaptive learning probabilities. However, ECLPSO still cannot locate the global optimum or find a near‐optimum solution for a number of problems. In this paper, we study further bettering the exploration performance of ECLPSO. We propose to assign an independent inertia weight and an independent acceleration coefficient corresponding to each dimension of the search space, as well as an independent learning probability for each particle on each dimension. Like ECLPSO, a normative interval bounded by the minimum and maximum personal best positions is determined with respect to each dimension in each generation. The dimensional independent maximum velocities, inertia weights, acceleration coefficients, and learning probabilities are proposed to be adaptively updated based on the dimensional normative intervals in order to facilitate exploration, exploitation, and convergence, particularly exploration. Our proposed metaheuristic, called adaptive CLPSO (ACLPSO), is evaluated on various benchmark functions. Experimental results demonstrate that the dimensional independent and adaptive maximum velocities, inertia weights, acceleration coefficients, and learning probabilities help to significantly mend ECLPSO’s exploration performance, and ACLPSO is able to derive the global optimum or a near‐optimum solution on all the benchmark functions for all the runs with parameters appropriately set.

Indirectly estimating global solar radiation is strongly nonlinear and needs to be addressed by machine learning. Sequentially developing a machine learning model can be very time consuming. Moreover, whether and how the exogenous meteorological, geographical and temporal variables affect regression accuracy still has not been well understood. This paper evaluates parallelized support vector regression (SVR) and nearest neighbor regression (NNR) models for estimating daily global solar radiation of the humid subtropical region in China using existing Python libraries on a multi-core central processing unit (CPU) and a graphical processing unit (GPU). Seven input variations are studied. Two variations are commonly adopted in literature, four variations contain meteorological, geographical and/or temporal features with bounded Pearson correlation coefficients (PCCs), and the other variation simply include all the available features. Experimental results demonstrate that: SVR and NNR are equally powerful for nonlinear regression, and the variation comprising features with absolute PCCs no less than 0.3 (i.e. just all the meteorological features) is able to achieve most accurate estimation; the GPU-parallelized SVR model can accelerate parameter calibration and prediction; compared with the CPU-parallelized and GPU-parallelized SVR models, the GPU-parallelized NNR model is much more efficient and rather more scalable with the increment of the number of data samples; and the CPU-parallelized NNR model consumes quite less parameter calibration time than the GPU-parallelized NNR model, owing to different methods adopted for determining distances and significant time wasted by the GPU-parallelized NNR model on repeatedly calculating required information during cross-validation.