Number Of Cost Function Evaluations Research Articles

Optimal Sizing of Hybrid Renewable Energy System Using Two-Stage Stochastic Programming

Stochastic programming has become increasingly vital in energy applications, especially in the context of the growing need for renewable energy solutions. This paper presents a significant advancement in this field by introducing an efficient and robust algorithm for optimally sizing hybrid renewable energy systems. Utilizing a two-stage stochastic programming approach, the proposed algorithm addresses the challenges posed by the unpredictability of renewable energy sources. The proposed solution leverages the three-block alternating direction method of multipliers (ADMM), a cutting-edge technique that facilitates parallel computation and enhances computational efficiency. The distinctiveness of this method lies in its ability to solve complex stochastic optimization problems without compromising the mathematical integrity of the model. This is achieved by applying first-order optimality conditions, ensuring both robustness and efficacy. To demonstrate the practical applicability and superiority of the algorithm, a case study was conducted in a rural area of South Africa. The proposed algorithm was applied to design an optimal hybrid renewable energy system, and its performance was compared against traditional methods such as progressive hedging and Monte Carlo techniques. Results affirm the superiority of the approach, saving approximately 8.16% capital cost when compared to progressive hedging. In addition, the proposed algorithm outperforms the Monte Carlo method both in terms of CPU time and the number of cost function evaluations.

Derivative-free search approaches for optimization of well inflow control valves and controls

AbstractDecisions regarding problem conceptualization, search approach, and how best to parametrize optimization methods for practical application are key to successful implementation of optimization approaches within georesources field development projects. This work provides decision support regarding the application of derivative-free search approaches for concurrent optimization of inflow control valves (ICVs) and well controls. A set of state-of-the-art approaches possessing different search features is implemented over two reference cases, and their performance, resource requirements, and specific method configurations are compared across multiple problem formulations for completion design. In this study, problem formulations to optimize completion design comprise fixed ICVs and piecewise-constant well controls. The design is optimized by several derivative-free methodologies relying on parallel pattern-search (tAPPS), population-based stochastic sampling (tPSO) and trust-region interpolation-based models (tDFTR). These methodologies are tested on a heterogeneous two-dimensional case and on a realistic case based on a section of the Olympus benchmark model. Three problem formulations are applied in both cases, i.e., one formulation optimizes ICV settings only, while two joint configurations also treat producer and injector controls as variables. Various method parametrizations across the range of cases and problem formulations exploit the different search features to improve convergence, achieve final objectives and infer response surface features. The scope of this particular study treats only deterministic problem formulations. Results outline performance trade-offs between parallelizable algorithms (tAPPS, tPSO) with high total runtime search efficiency and the local-search trust-region approach (tDFTR) providing effective objective gains for a low number of cost function evaluations. tAPPS demonstrates robust performance across different problem formulations that can support exploration efforts, e.g., during a pre-drill design phase while multiple independent tDFTR runs can provide local tuning capability around established solutions in a time-constrained post-drill setting. Additional remarks regarding joint completion design optimization, comparison metrics, and relative algorithm performance given the varying problem formulations are also made.

Initialisation of Optimisation Solvers for Nonlinear Model Predictive Control: Classical vs. Hybrid Methods

In nonlinear Model Predictive Control (MPC) algorithms, the number of cost-function evaluations and the resulting calculation time depend on the initial solution to the nonlinear optimisation task. Since calculations must be performed fast on-line, the objective is to minimise these indicators. This work discusses twelve initialisation strategies for nonlinear MPC. In general, three categories of strategies are discussed: (a) five simple strategies, including constant and random guesses as well as the one based on the previous optimal solution, (b) three strategies that utilise a neural approximator and an inverse nonlinear static model of the process and (c) four hybrid original methods developed by the authors in which an auxiliary quadratic optimisation task is solved or an explicit MPC controller is used; in both approaches, linear or successively linearised on-line models can be used. Efficiency of all methods is thoroughly discussed for a neutralisation reactor benchmark process and some of them are evaluated for a robot manipulator, which is a multivariable process. Two strategies are found to be the fastest and most robust to model imperfections and disturbances acting on the process: the hybrid strategy with an auxiliary explicit MPC controller based on a successively linearised model and the method which uses the optimal solution obtained at the previous sampling instant. Concerning the hybrid strategies, since a simplified model is used in the auxiliary controller, they perform much better than the approximation-based ones with complex neural networks. It is because the auxiliary controller has a negative feedback mechanism that allows it to compensate model errors and disturbances efficiently. Thus, when the auxiliary MPC controller based on a successively linearised model is available, it may be successfully and efficiently used for the initialisation of nonlinear MPC, whereas quite sophisticated methods based on a neural approximator are very disappointing.

An Improved Phenotype-Genotype Mapping for Solving Selective Assembly Problem Using Evolutionary Optimization Algorithms

Abstract Selective assembly is an assembly technique for producing high-quality assemblies from relatively lower quality mating parts. Developing the application of this technique to sheet metal assemblies in the automotive industry can improve the geometrical quality and reduce production costs significantly. Nevertheless, the required calculation time is the main obstacle against this development. To apply a selective assembly technique, an optimization problem of finding the optimal combination of mating parts should be solved. This problem is an MINLP optimization problem for selective assembly of sheet metals. This paper demonstrates that the phenotype-genotype mapping commonly used in most conventional selective assembly studies enlarges the search domain of the optimization. Thereafter, a new approach that makes the mapping one-to-one is proposed and applied to three selective assembly sample cases from the literature. Moreover, it is indicated that meta-heuristic methods are superior to MILP and MINLP methods in solving this problem, particularly for assemblies of more than two components and relatively large batch sizes. The results evidence that using the new method improves the convergence rate of meta-heuristics in solving the problem by reducing the number of cost function evaluations to 45% for sheet metal assemblies. This means reducing up-till 26 h of the optimization time for the presented sample cases.

A Comparison of Three Evolutionary Algorithms for the Optimization of Building Design

In building design, the need of optimization algorithms is considerably increasing due to the requirements of enhancing the overall performances, cost and sustainability objectives. An evolutionary algorithm coupled with building simulation code is often used. However, this approach is not widespread in actual application due to the high number of expensive simulation runs required by evolutionary algorithms. For this reason, the selection of an efficient and effective optimization algorithm becomes a key aspect in building design. In the literature there are several works analyzing the performance of different optimization algorithms, most of them by comparing the results obtained for the optimization of analytical test functions. However, there are no evidence-based studies deepening the efficiency and efficacy of these methods by comparing against the true solution of the discrete optimization problems on building design. This study compares the number of cost function evaluations and the percentage of the actual Pareto solutions of three algorithms used for the evaluation of the optimal refurbishment of three reference buildings for which the actual Pareto front is known through a brute-force approach.

A multi-layer line search method to improve the initialization of optimization algorithms

We introduce a novel metaheuristic methodology to improve the initialization of a given deterministic or stochastic optimization algorithm. Our objective is to improve the performance of the considered algorithm, called core optimization algorithm, by reducing its number of cost function evaluations, by increasing its success rate and by boosting the precision of its results. In our approach, the core optimization is considered as a sub-optimization problem for a multi-layer line search method. The approach is presented and implemented for various particular core optimization algorithms: Steepest Descent, Heavy-Ball, Genetic Algorithm, Differential Evolution and Controlled Random Search. We validate our methodology by considering a set of low and high dimensional benchmark problems (i.e., problems of dimension between 2 and 1000). The results are compared to those obtained with the core optimization algorithms alone and with two additional global optimization methods (Direct Tabu Search and Continuous Greedy Randomized Adaptive Search). These latter also aim at improving the initial condition for the core algorithms. The numerical results seem to indicate that our approach improves the performances of the core optimization algorithms and allows to generate algorithms more efficient than the other optimization methods studied here. A Matlab optimization package called “Global Optimization Platform” (GOP), implementing the algorithms presented here, has been developed and can be downloaded at: http://www.mat.ucm.es/momat/software.htm

Low-Complexity Soft-Output Quantum-Assisted Multiuser Detection for Direct-Sequence Spreading and Slow Subcarrier-Hopping Aided SDMA-OFDM Systems

Low-complexity suboptimal multiuser detectors (MUDs) are widely used in multiple access communication systems for separating users, since the computational complexity of the maximum likelihood (ML) detector is potentially excessive for practical implementation. Quantum computing may be invoked in the detection procedure, by exploiting its inherent parallelism for approaching the ML MUDs performance at a substantially reduced number of cost function evaluations. In this contribution, we propose a soft-output (SO) quantum-assisted MUD achieving a near-ML performance and compare it to the corresponding SO ant colony optimization MUD. We investigate rank deficient direct-sequence spreading (DSS) and slow subcarrier-hopping aided (SSCH) spatial division multiple access orthogonal frequency division multiplexing systems, where the number of users to be detected is higher than the number of receive antenna elements used. We show that for a given complexity budget, the proposed SO-Dürr-Høyer algorithm (DHA) QMUD achieves a better performance. We also propose an adaptive hybrid SO-ML/SO-DHA MUD, which adapts itself to the number of users equipped with the same spreading sequence and transmitting on the same subcarrier. Finally, we propose a DSS-based uniform SSCH scheme, which improves the system's performance by 0.5 dB at a BER of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-5</sup> , despite reducing the complexity required by the MUDs employed.

A Guided Hybrid Genetic Algorithm for Feature Selection with Expensive Cost Functions

We present a guided hybrid genetic algorithm for feature selection which is tailored to minimize the number of cost function evaluations. Guided variable elimination is used to make the stochastic backward search of the genetic algorithm much more efficient. Guiding means that a promising feature set is selected from a population and suggestions (for example by a trained Random Forest) are made which variable could be removed. It uses implicit diversity management and is able to return multiple optimal solutions if present, which might be important for interpreting the results. It uses a dynamic cost function that avoids prescribing an expected upper limit of performance or the number of features of the optimal solution. We illustrate the performance of the algorithm on artificial data, and show that the algorithm provides accurate results and is very efficient in minimizing the number of cost function evaluations.

GSR: A New Genetic Algorithm for Improving Source and Channel Estimates

In this paper, we introduce a new genetic algorithm, which allows us to refine the estimates of information source symbols and channel estimates obtained by any identification algorithm. Instead of searching the entire space, the proposed algorithm searches for the refined estimates in the subspaces near the initial estimate. Creation of initial guesses by using problem specific information and new specially tailored nonblind genetic operators, based on the ideas from schema theory, for realizing the proposed approach are described. The new genetic source symbol refinement (GSR) algorithm is tested to cope with rapidly varying finite-impulse response channels with additive noise model. The method is capable of offering fast convergence with directed search ability and exhibits a unique feature of automatic adjustment in the number of cost function evaluations with the varying signal-to-noise ratio (SNR). Computational results show that the GSR can achieve the bit-error-rate performance near to the simulated annealing bound. As compared with recent sophisticated alternatives for the problem, the GSR performance is superior over a wide range of SNR, with reduced complexity