Sequential Optimization Approach Research Articles

R2ogs5: Calibration of Numerical Groundwater Flow Models with Bayesian Optimization in R.

Large-scale and high-resolution groundwater models are currently becoming increasingly important in order to clarify the extent to which climate trends and extreme weather affect the groundwater balance regionally. As a result, the parameterization of groundwater models is becoming more detailed and more complex, making conventional calibration methods too time-consuming. Moderating the computational demand to find optimal solutions for the resulting potentially multi-modal objective function requires intelligent and efficient global optimization methods. Moreover, the increasing use of modern scripting languages R and Python to craft environmental analysis workflows calls to integrate groundwater flow simulators in such. Here we introduce and exemplify r2ogs5, a tool that integrates version 5 of the open-source simulation software OpenGeoSys into the programming language R. r2ogs5 allows for calibration of numerical groundwater flow models with a sequential model-based optimization approach that combines Bayesian optimization (BO) with surrogate modeling. Here, we describe the structure and function of r2ogs5 as well as the implemented calibration method. We then demonstrate the calibration method by calibrating 4 and 12 parameters of two simple groundwater flow models. The results indicate that this method needs fewer runs of the groundwater flow model than conventional gradient search and Latin hypercube sampling in case of the 12 parameter model. We believe that our method offers the potential to calibrate computationally expensive groundwater flow models. r2ogs5 supports groundwater flow modelers to access the statistical analysis and visualization capabilities of the R language and is a valuable tool for geoscientists already using R.

Largest small polygons: a sequential convex optimization approach

A small polygon is a polygon of unit diameter. The maximal area of a small polygon with $n=2m$ vertices is not known when $m\ge 7$. Finding the largest small $n$-gon for a given number $n\ge 3$ can be formulated as a nonconvex quadratically constrained quadratic optimization problem. We propose to solve this problem with a sequential convex optimization approach, which is an ascent algorithm guaranteeing convergence to a locally optimal solution. Numerical experiments on polygons with up to $n=128$ sides suggest that the optimal solutions obtained are near-global. Indeed, for even $6 \le n \le 12$, the algorithm proposed in this work converges to known global optimal solutions found in the literature.

Integrated line planning and train timetabling through price-based cross-resolution feedback mechanism

Railway line planning and train timetabling are two key planning steps that determine the operating cost and passenger service quality of a railway operator under the infrastructure capacity limitations. Traditionally, the line planning and train timetabling problems are solved sequentially at the strategic and tactical level, respectively. In this study, by introducing two types of binary decision variables, we first propose a unified integer linear programming (ILP) model for the integrated optimization of line planning and train timetabling. The line planning problem is modeled using ILP to satisfy passenger demand, whereas the cyclic train timetabling problem is formulated as a multi-commodity network flow model with a side track capacity constraint. The two types of binary decision variables are coupled by a cross-resolution consistency constraint, which ensures the conformity of the line planning and train timetabling decisions. Furthermore, a dual decomposition mechanism based on the Alternating Direction Method of Multipliers (ADMM) is developed to dualize the cross-resolution consistency and track capacity constraints, such that the original ILP model is decomposed into a line planning sub-problem and a set of train-specific sub-problems. After the linearization of the quadratic penalty terms in the ADMM, each sub-problem contains the Lagrangian relaxation price information based on the cross-resolution consistency constraint. Moreover, the primal and dual solutions are obtained by iteratively and efficiently solving the line planning sub-problem using a commercial solver, and each train-specific sub-problem through a tailored forward dynamic programming algorithm. Furthermore, a real-life case study is conducted based on the Beijing–Shanghai high-speed railway corridor to verify the efficiency and effectiveness of the proposed model and algorithm. The results of the numerical experiments demonstrate that the ADMM can achieve significantly smaller optimality gaps than Lagrangian relaxation, and the integrated optimization approach can improve the objective value by 5.78% on average compared with the sequential optimization approach.

Control Co-Design of Lithium-Ion Batteries for Enhanced Fast-Charging and Cycle Life Performances

Abstract As enablers of electric vehicles, lithium-ion batteries are drawing much attention for their high energy density and low self-discharge. However, “range anxiety” has remained a significant hindrance to its further development. As an alternative to increasing capacity, fast charging seems a reasonable solution. However, challenges remain due to the conflict between high charging rate and excessive capacity loss. In the past, enormous efforts have been carried out to resolve the dispute between high charging rates and large capacity losses by either improving the battery design or optimizing the charging/discharging protocols. In contrast, this study proposes a novel control co-design framework with adaptive surrogate modeling to address the challenges and to generate the systematic optimal battery design and the corresponding charging protocol simultaneously. The proposed method is ideal for lithium-ion battery systems to offer the improved performances as compared with traditional sequential optimization approaches due to the integration of strong coupling effects between electrode design and control optimization. The integrated adaptive surrogate modeling technique allows model reduction for efficient optimal control and simulation solutions. Meanwhile, it preserves an accurate mapping from the first-principle model to the reduced-order model. A hybrid model like this captures the multiscale nature of the cell, that is, micro-scale parameters affect the macro-scale behavior. It reduces the computational cost significantly. The battery co-design problem is formulated as a nested problem, where the inner-loop solves an open-loop optimal control problem and the outer-loop optimizes the plant design variables. The results show that system-level optimal design can be obtained for minimized charging time at various levels of health requirement.

A cost effective approach to design of energy efficient residential buildings

The objective of this study is to identify cost-optimal efficiency packages at several levels of building energy savings. A two-story residential building located in Jordan is selected as a case study. DesignBuilder software is used to predict the annual energy usage of a two-story residence in Irbid, Jordan. Real-time experimental data from a single isolated controlled room was used to verify the proposed model. In addition to energy analysis, the economic, environmental, and social benefits of the proposed design have been investigated. The sequential search optimization approach is used to estimate the minimum cost of the building while considering various design scenarios. In addition, the impact of various energy conservation techniques on residential buildings is assessed, and the payback period for each program is calculated. Ultimately, the optimal combination of design to achieve energy efficiency measures has been identified in several climate regions. The simulations results predict that the annual electricity consumption can be reduced up to 50% if the proper combinations of energy conservation measures are selected at the lowest cost. The payback period is 9.3 years. Finally, energy efficiency measures can lead to a total of 9470 jobs/year job opportunities.The study provide practical framework to link between energy performance criteria and economic goals of building. Linking the energy performance requirements to economic targets provides guidelines for homeowners, contractors, and policymakers for making a suitable decision regarding the retrofitting of existing residential buildings. The study focuses on developing new methodologies that support minimizing costs during a building's lifecycle while maximizing environmental benefits which can not be identified by a series of parametric analyses using individual energy-efficient measures.

NEXTorch: A Design and Bayesian Optimization Toolkit for Chemical Sciences and Engineering.

Automation and optimization of chemical systems require well-informed decisions on what experiments to run to reduce time, materials, and/or computations. Data-driven active learning algorithms have emerged as valuable tools to solve such tasks. Bayesian optimization, a sequential global optimization approach, is a popular active-learning framework. Past studies have demonstrated its efficiency in solving chemistry and engineering problems. We introduce NEXTorch, a library in Python/PyTorch, to facilitate laboratory or computational design using Bayesian optimization. NEXTorch offers fast predictive modeling, flexible optimization loops, visualization capabilities, easy interfacing with legacy software, and multiple types of parameters and data type conversions. It provides GPU acceleration, parallelization, and state-of-the-art Bayesian optimization algorithms and supports both automated and human-in-the-loop optimization. The comprehensive online documentation introduces Bayesian optimization theory and several examples from catalyst synthesis, reaction condition optimization, parameter estimation, and reactor geometry optimization. NEXTorch is open-source and available on GitHub.

Energy management strategies for a zero-emission hybrid domestic ferry

The paper presents three approaches for the sizing and control of a maritime hybrid power-plant equipped with proton exchange membrane fuel cells and batteries. The study focuses on three different power-plant configurations, including the energy management strategy and the power-plant component sizing. The components sizing is performed following the definition of the energy management strategy using the sequential optimization approach. These configurations are tested using a dynamic model developed in Simulink. The simulations are carried out to validate the technical feasibility of each configuration for maritime use. Each energy management strategy is developed to allow for the optimization of a chosen set of parameters, such as hydrogen consumption and fuel cell degradation. It is observed that in the hybrid power-plant optimization there are always trade-offs, and the optimization should be carried out by prioritizing primary factors the ship owner considers most important for day-to-day operations.

Reliability-based design optimization of structural systems under stochastic excitation: An overview

This article presents a brief survey on some of the latest developments in the area of reliability-based design optimization of structural systems under stochastic excitation. The contributions are grouped into three main categories, namely, sequential optimization approaches, stochastic search based techniques, and schemes based on augmented reliability spaces. The different approaches are described and summarized. In addition, remarks are provided about their range of application, advantages, disadvantages, relevance, and potential research directions. The literature review indicates that computational aspects play a key role in the solution of this class of optimization problems. Besides, this overview suggests that methods for optimal design in stochastic structural dynamics are no longer restricted to academic-type of problems but they can be used as tools in a class of engineering design problems as well.

Optimization of Methanol Synthesis under Forced Periodic Operation

Traditionally, methanol is produced in large amounts from synthesis gas with heterogeneous Cu/ZnO/Al2O3 catalysts under steady state conditions. In this paper, the potential of alternative forced periodic operation modes is studied using numerical optimization. The focus is a well-mixed isothermal reactor with two periodic inputs, namely, CO concentration in the feed and total feed flow rate. Exploiting a detailed kinetic model which also describes the dynamics of the catalyst, a sequential NLP optimization approach is applied to compare optimal steady state solutions with optimal periodic regimes. Periodic solutions are calculated using dynamic optimization with a periodicity constraint. The NLP optimization is embedded in a multi-objective optimization framework to optimize the process with respect to two objective functions and generate the corresponding Pareto fronts. The first objective is the methanol outlet flow rate. The second objective is the methanol yield based on the total carbon in the feed. Additional constraints arising from the complex methanol reaction and the practical limitations are introduced step by step. The results show that significant improvements for both objective functions are possible through periodic forcing of the two inputs considered here.

Optimization design of metamaterial vibration isolator with honeycomb structure based on multi-fidelity surrogate model

The hexagonal periodic structure of the honeycomb is a magic product of nature and shows great mechanical potential. In this work, a type of metamaterial vibration isolator with a honeycomb structure is proposed. The strain, deformation, and natural frequency of the vibration isolator are calculated by the two-dimensional plane finite element model and the simulation accuracies are validated by the experiments. As the design of the metamaterial vibration isolator involves time-consuming finite-element simulation, a multi-fidelity sequential optimization approach based on feasible region analysis (MF-FA) is proposed. In the proposed method, the refined and coarse mesh models are developed as the high- and low-fidelity models, and a two-phase multi-fidelity updating strategy is carried out. In the first phase, sample points are added to the constraint boundary to find the feasible solution quickly, in the second phase, the quality of the feasible optimization solution is gradually improved in the feasible region until it converges to the global optimal solution. Finally, the optimized metamaterial vibration isolator is manufactured and its superiority is validated. Results illustrate that the proposed approach can obtain a desirable optimum, whose natural frequency error between the experimental and the expected value is improved by 12.67% compared with the initial design.

Application of particle swarm optimization and genetic algorithm for optimization of a southern Iranian oilfield

Optimization of the placement and operational conditions of oil wells plays an important role in the development of the oilfields. Several automatic optimization algorithms have been used by different authors in recent years. However, different optimizers give different results depending on the nature of the problem. In the current study, a comparison between the genetic algorithm and particle swarm optimization algorithms was made to optimize the operational conditions of the injection and production wells and also to optimize the location of the injection wells in a southern Iranian oilfield. The current study was carried out with the principal purpose of evaluating and comparing the performance of the two most used optimization algorithms for field development optimization on real-field data. Also, a comparison was made between the results of sequential and simultaneous optimization of the decision variables. Net present value of the project was used as the objective function, and the two algorithms were compared in terms of the profitability incremental added to the project over twelve years. First, the production rate of the producers was optimized, and then water alternating gas injection wells were added to the field at locations determined by engineering judgment. Afterward, the location, injection rate, and water alternating gas ratio of the injectors were optimized sequentially using the two algorithms. Next, the production rate of the producers was optimized again. Finally, a simultaneous optimization was done in two manners to evaluate its effect on the optimization results: simultaneous optimization of the last two steps and simultaneous optimization of all decision variables. Results showed the positive effect of the algorithms on the profitability of the project and superiority of the particle swarm optimization over the genetic algorithm at every stage. Also, simultaneous optimization was beneficial at finiding better results compared to sequential optimization approach. In the end, a sensitivity analysis was made to specify the most influencing decision variable on the project’s profitability.

A Direct Optimization Algorithm for Problems with Differential-Algebraic Constraints: Application to Heat and Mass Transfer

In this article, an optimization task with nonlinear differential-algebraic equations (DAEs) is considered. As a main result, a new solution procedure is designed. The computational procedure represents the sequential optimization approach. The proposed algorithm is based on a multiple shooting parametrization method. Two main aspects of a generalized parametrization approach are analyzed in detail: a control function and DAE model parametrization. A comparison between the original and modified DAEs is made. The new algorithm is applied to solve an optimization task in heat and mass transfer engineering.

Multi-Objective Sequential Forest Management Under Risk Using a Markov Decision Process-Pareto Frontier Approach

Forests play an important role in many different cycles (carbon sink, biodiversity, timber) and, consequently, in regulating the global climate system. Moreover, forests are the source of a wide range of goods and services to human societies and, as a result, the decisions made by forest owners affect forest ecosystems. Since forests are currently threatened by climate change, there is a need to provide support to forest owners for managing forests under risk, taking conflicting objectives into account. This study focuses on developing an explicit multiple-objective and sequential forest management model under risk. The multi-objective sequential optimization approach used here is based on the concept of Pareto optimality, and the computation of the Pareto frontier (the set of non-dominated solutions), instead of a single solution. We consider a Markov Decision Process (MDP) model to evaluate forest management policies under different criteria, and to generate the Pareto frontier. The framework is applied to the management of a private forest located in southwestern France. We identify optimal forest management practices for each objective separately and trade-off policies considering all objectives jointly. We analyze the forest management policies located on the Pareto frontier, yielding different trade-offs among the conflicting objectives. Our framework makes it possible to envision all possible trade-offs, and to understand how a trade-off policy takes each objective into account. It is hoped that this information will help in analyzing potential policy implications for forest management, taking the provision of multiple forest ecosystem services into consideration.

A Sequential Optimization Approach in Tactical Planning for Value Creation in the Forest Products Industry

Strategic, tactical, and operation-level forest management plans are commonly formulated by forest planners following even-flow yield principles. Although strategic planning ensures a sustained supply of timber over the long term, it disregards individual mills’ requirements, which leads to discrepancy between supply and demand. We hypothesize that a value-based timber allocation decision, which accounts for individual mills’ demands during tactical level planning, reduces such discrepancy by increasing value over the entire supply chain. Three types of linear programming models were constructed: Model A—status quo volume-maximization model, Model B—supply chain net present value-maximization (NPV) model, and Model C—a novel approach with sub-models embedded that maximize the NPV of individual mills in the allocation decision. Our results showed that only 58% of the annual allowable cut was profitable and the mean net revenue per harvested area was $2455 ha−1 using Model A. The respective values using Models B and C were 64% and $3890 ha−1 and 96% and $4040 ha−1, respectively, showing that Model C generated the highest net revenue for all mills. Such a method of value-based sequential optimization (Model C) will be crucial in sustainable use of forest products and sustaining future bioeconomy, particularly for managing mixed species stands that contain timber suitable for manufacturing a wide range of products with different market values.

Lightweight design of cylindrical stiffened shells in launch vehicles by a dual-elite population sequential approximation optimization approach

A nonlinear displacement-controlled loading dynamic method is employed to investigate the deformed shape evolution of stiffened shells from prebuckling to postbuckling field until collapse. Because of the time-consuming postbuckling analysis, the dual-elite population sequential approximation optimization (SAO) approach is proposed. A novel determination method of Gaussian kernel widths based on moment estimates is proposed to enhance the augmented radial basis function surrogate model. A novel adaptive parallel infilling strategy is then developed to balance the capabilities of local and global optimization. A dual-elite population strategy is further developed to exploit the information from already acquired sampling points. Finally, the framework of the proposed SAO approach, which is implemented in a distributed parallel way on high-performance clusters to further diminish computation costs, is presented. The efficiency of the algorithm is validated by the postbuckling lightweight optimization of a cylindrical stiffened shell, resulting in a reduction of 12.3% of the initial weight.

Simultaneous and sequential stochastic optimization approaches for pumped storage plant scheduling with random breakdowns

This paper addresses a pumped-storage stations scheduling problem. The study contribution is three-fold. First, a new service-related multi-objective function is proposed. The model aims to minimize the supply-demand disparity function and the pump maintenance cost in terms of the number of pump switches. Second, the proposed mathematical formulation considers individual units scheduling and random breakdowns. Furthermore, this work considers the electricity demand uncertainty in hourly and daily basis. Third, a new sequential two-stage formulation is proposed. The Sample Average Approximation method is applied to handle the grid demand uncertainty, stochastic failures and unplanned maintenance of pumping units. Goal programming is applied at the second-stage to handle the conflicting objective functions and avoid the model infeasibility. A case study data based on the Ingula pumped-storage station in South Africa is used to test the performance of the proposed approach. A comparison between the two-stage sequential approach and a simultaneous approach showed the superior performance of the two-stage sequential approach in terms of modeling complexity and computational time. Furthermore, experimental analysis showed that involving more pumping/generating units could improve the service level by reducing Disparity Index. Moreover, the two-stage sequential approach showed a superior performance even for the larger size instances.

An extended Two-Stage Sequential Optimization approach: Properties and performance

This paper looks into nonlinear non convex stochastic unconstrained optimization with finite simulation budget. Our work builds upon the Two-Stage Sequential Optimization (TSSO) algorithm that addresses the class of problems of interest by using the modified nugget effect kriging (MNEK) meta-model and proposing a budget allocation followed by a two-stage sequential procedure. Despite its efficiency and performance, we have observed that, given a finite budget, the choice of the number of replications per iteration, currently left to the user, is particularly critical for the algorithm performance. A fixed a-priori assignment can affect the ability to control the algorithm making it particularly sensitive to the initial settings. In this paper, we propose the extended TSSO (eTSSO). Specifically, a general simulation budget allocation scheme is proposed with the objective to balance the need of accurate function estimations to improve the selection in the search stage, with the need to explore the solution space. The new scheme adaptively, and recursively, increases the simulation budget based upon information iteratively returned by the optimizer itself. We analyze the asymptotic properties of eTSSO. Subsequently, we propose four alternative variants of the general allocation that we empirically analyze by comparing the quality of the estimated optimum input combination and the corresponding estimated optimum output against TSSO and other state of the art algorithms.

Enhancement of SPSA algorithm performance using reservoir quality maps: Application to coupled well placement and control optimization problems

Determination of optimal well location is a vital step in the design of an efficient field development plan which aims to maximize the hydrocarbon recovery and profits from the project. This step has become further complicated as the well control parameters are also introduced into the problem which is known as coupled well placement and control optimization problem. As the number of optimization variable increases, computational cost also increases and it becomes a serious challenge, especially in high resolution reservoir models since the optimization process becomes very time demanding. Simultaneous Perturbation Stochastic Approximation (SPSA) has been introduced as an efficient algorithm in finding the optimum solution for problems with a large number of variables. In this work, SPSA algorithm has been modified using reservoir quality maps to enhance and accelerate finding the good solutions with a minimum number of function evaluation which is desirable for high-resolution reservoir models and high dimensional optimization problems. In this modification, reservoir quality maps are employed to navigate production wells toward high potential areas instead of random movement in standard SPSA. The modified algorithm is tested for joint well placement and control optimization problem using both simultaneous and sequential optimization approach in a synthetic and two benchmark models. The results show that modified SPSA outperforms standard SPSA both in terms of final result and convergence trend. Also, in most cases, simultaneous well placement and control optimization approach gives better results compared to sequential approaches for both algorithms.

Joint design of beamforming and time switching/power splitting for wireless-powered multi-antenna dual-relay network

In this paper, we consider a wireless-powered dual-relay network consisting of one multi-antenna source, two single-antenna energy-constrained relays and one single-antenna destination without direct source to destination link. In order to establish the communication flow, the energy-constrained relays harvest energy from the radio frequency transmitted by the source firstly, then exploit the harvested energy to forward the source information to the destination based on distributed space time coding (DSTC). Under this network architecture, three decode-and-forward (DF) technique-based relaying protocols, i.e., time switching-based relaying (TSR) protocol, power splitting-based relaying (PSR) protocol, and hybrid relaying (HR) protocol, are considered to drive the energy transfer and information transmission. To maximize the network throughput, the joint design for the optimal energy and information beamforming vectors employed at the source, the optimal time switching, and power splitting ratios under these three protocols are investigated and solved efficiently by employing simple sequential optimization approach or alternating optimization approach. Simulations are conducted to show the superior performance achieved by our proposed scheme. Moreover, we find that the TSR protocol outperforms the PSR protocol in the low signal-to-noise ratio (SNR) region, while the latter outperforms the former in the high SNR region. And the HR protocol achieves the best performance in any SNR region. At the same time, the effect of the relays’ locations on the throughput performance of these three protocols is also investigated.

Optimization of an Absorption-Based Biogas Upgrading and Liquefaction Process

The present work proposes a methodology for optimization of a liquefied biomethane (LBM) production plant. The LBM production plant comprises amine-based absorption upgrading followed by a single expander refrigeration cycle. The processes were modeled using Aspen HYSYS® and optimized through a Sequential Quadratic Programming algorithm. Any changes in the operating conditions of the upgrading process will affect the cooling demand in the liquefaction, while the opposite is not true. Based on this, a sequential optimization approach starting with the upgrading process is proposed. In order to accommodate the connection between the processes, different objective functions were formulated for the sequential optimization approach. The results from the sequential approach were compared with an overall optimization approach, where the entire LBM plant was optimized simultaneously. The results indicate that the same solution was obtained both for the sequential approach and the simultaneous approach. For the sequential approach, however, the best result was observed when the interaction between the upgrading and liquefaction processes was accounted for by considering the effect of the upgrading process on the exergy requirement in the liquefaction process.