Simulation-based Objective Function Research Articles

A two-stage stochastic programming approach for dynamic OD estimation using LBSN data

Estimating origin–destination (OD) demand is essential for urban transport management and traffic control systems. With the ubiquity of smartphones, location based social networks (LBSN) data has emerged as a new rich data source with broad urban spatial and temporal coverage highly suitable for OD estimation. Its nature of confirmed trip purpose (activity) and activity chain host makes it more advantageous than other data (e.g., household travel surveys and traffic network detection). On the other hand, LBSN data is a more direct and accurate representation of demand patterns and can remove the significant burden of developing traffic models and estimating simulation-based objective functions. However, thus far, most LBSN-based estimation models only focus on static (day-level) OD estimation, making less use of those characteristics. To this end, this paper establishes a two-stage stochastic programming (TSSP) framework integrating the activity chains to model activity-level dynamic mobility flows using LBSN data. The first-stage model aims to minimize the errors introduced by the inter-zone OD flows alongside the expected errors of the check-in patterns. The second-stage model attempts to minimize the errors produced by the considered check-in pattern scenarios. Markov chain Monte Carlo (MCMC) sampling is used to generate plausible check-in scenarios. A generalized Benders decomposition (GBD) algorithm is presented to solve the two-stage stochastic programming model. We conduct the experiments on the case study of Tokyo, Japan, under the employment of the generalized least squares (GLS) estimator. The results show that algorithm convergence can be guaranteed within several iterations. The approach can provide satisfactory estimations of check-in patterns, zonal production and attraction, and OD flows. Furthermore, multiple objective function states are tested for evaluating the completeness of the proposed framework and exploring its potential for simplification and extension. Incorporating specific penalty terms into the objective function also provides a way to verify the reliability of the two-stage structure and validate the effectiveness of the model. Finally, we discuss the model enhancement from the perspectives of online OD estimation by integrating with LBSN simulations, network-wide OD extrapolation using appropriate scaling methods, and removing the user-side data requirement by leveraging activity chain modeling. The proposed framework provides a novel and effective approach to OD demand estimation using LBSN data.

Efficient Simulation-Based Toll Optimization for Large-Scale Networks

This paper proposes a simulation-based optimization technique for high-dimensional toll optimization problems of large-scale road networks. We formulate a novel analytical network model. The latter is embedded within a metamodel simulation-based optimization (SO) algorithm. It provides analytical and differentiable structural information of the underlying problem to the SO algorithm. Hence, the algorithm no longer treats the simulator as a black box. The analytical model is formulated as a system of nonlinear equations that can be efficiently evaluated with standard solvers. The dimension of the system of equations scales linearly with network size. It scales independently of the dimension of the route choice set and of link attributes such as link length. Hence, it is a scalable formulation suitable for the optimization of large-scale networks. For instance, the model is used in the case study of the paper for toll optimization of a Singapore network with more than 4,050 OD (origin-destination) pairs and 18,200 feasible routes. The corresponding analytical model is implemented as a system of 860 nonlinear equations. The analytical network model is validated based on one-dimensional toy network problems. It captures the main trends of the simulation-based objective function and, more importantly, accurately locates the global optimum for all experiments. The proposed SO approach is then used to optimize a set of 16 tolls for the network of expressways and major arterials of Singapore. The proposed method is compared with a general-purpose algorithm. The proposed method identifies good quality solutions at the very first iteration. The benchmark method identifies solutions with similar performance after 2 days of computation or similarly after more than 30 points have been simulated. The case study indicates that the analytical structural information provided to the algorithm by the analytical network model enables it to (i) identify good quality solutions fast and (ii) become robust to both the quality of the initial points and to the stochasticity of the simulator. The final solutions identified by the proposed algorithm outperform those of the benchmark method by an average of 18%.

Parallel surrogate-assisted optimization: Batched Bayesian Neural Network-assisted GA versus q-EGO

Surrogate-based optimization is widely used to deal with long-running black-box simulation-based objective functions. Actually, the use of a surrogate model such as Kriging or Artificial Neural Network allows to reduce the number of calls to the CPU time-intensive simulator. Bayesian optimization uses the ability of surrogates to provide useful information to help guiding effectively the optimization process. In this paper, the Efficient Global Optimization (EGO) reference framework is challenged by a Bayesian Neural Network-assisted Genetic Algorithm, namely BNN-GA. The Bayesian Neural Network (BNN) surrogate is chosen for its ability to provide an uncertainty measure of the prediction that allows to compute the Expected Improvement of a candidate solution in order to improve the exploration of the objective space. BNN is also more reliable than Kriging models for high-dimensional problems and faster to set up thanks to its incremental training. In addition, we propose a batch-based approach for the parallelization of BNN-GA that is challenged by a parallel version of EGO, called q-EGO. Parallel computing is a highly important complementary way (to surrogates) to deal with the computational burden of simulation-based optimization. The comparison of the two parallel approaches is experimentally performed through several benchmark functions and two real-world problems within the scope of Tuberculosis Transmission Control (TBTC). The study presented in this paper proves that parallel batched BNN-GA is a viable alternative to q-EGO approaches being more suitable for high-dimensional problems, parallelization impact, bigger data-bases and moderate search budgets. Moreover, a significant improvement of the solutions is obtained for the two TBTC problems tackled.

A splitting algorithm for simulation-based optimization problems with categorical variables

ABSTRACTIn the design of complex products, some product components can only be chosen from a finite set of options. Each option then corresponds to a multidimensional point representing the specifications of the chosen components. A splitting algorithm that explores the resulting discrete search space and is suitable for optimization problems with simulation-based objective functions is presented. The splitting rule is based on the representation of a convex relaxation of the search space in terms of a minimum spanning tree and adopts ideas from multilevel coordinate search. The objective function is underestimated on its domain by a convex quadratic function. The main motivation is the aim to find—for a vehicle and environment specification—a configuration of the tyres such that the energy losses caused by them are minimized. Numerical tests on a set of optimization problems are presented to compare the performance of the algorithm developed with that of other existing algorithms.

Efficient solution of many instances of a simulation-based optimization problem utilizing a partition of the decision space

This paper concerns the solution of a class of mathematical optimization problems with simulation-based objective functions. The decision variables are partitioned into two groups, referred to as variables and parameters, respectively, such that the objective function value is influenced more by the variables than by the parameters. We aim to solve this optimization problem for a large number of parameter settings in a computationally efficient way. The algorithm developed uses surrogate models of the objective function for a selection of parameter settings, for each of which it computes an approximately optimal solution over the domain of the variables. Then, approximate optimal solutions for other parameter settings are computed through a weighting of the surrogate models without requiring additional expensive function evaluations. We have tested the algorithm’s performance on a set of global optimization problems differing with respect to both mathematical properties and numbers of variables and parameters. Our results show that it outperforms a standard and often applied approach based on a surrogate model of the objective function over the complete space of variables and parameters.

A Simulation-Based Optimization Algorithm for Dynamic Large-Scale Urban Transportation Problems

This paper addresses large-scale urban transportation optimization problems with time-dependent continuous decision variables, a stochastic simulation-based objective function, and general analytical differentiable constraints. We propose a metamodel approach to address, in a computationally efficient way, these large-scale dynamic simulation-based optimization problems. We formulate an analytical dynamic network model that is used as part of the metamodel. The network model formulation combines ideas from transient queueing theory and traffic flow theory. The model is formulated as a system of equations. The model complexity is linear in the number of road links and is independent of the link space capacities. This makes it a scalable model suitable for the analysis of large-scale problems. The proposed dynamic metamodel approach is used to address a time-dependent large-scale traffic signal control problem for the city of Lausanne. Its performance is compared to that of a stationary metamodel approach. The proposed approach outperforms the stationary approach. This comparison illustrates the added value of providing the algorithm with analytical dynamic problem-specific structural information. The performance of a signal plan derived by the proposed approach is also compared to that of an existing signal plan for the city of Lausanne, and to that of a signal plan derived by a mainstream commercial signal control software. The proposed method can systematically identify signal plans with good performance. The online appendix is available at https://doi.org/10.1287/trsc.2016.0717 .

Efficient calibration techniques for large-scale traffic simulators

Road transportation simulators are increasingly used by transportation stakeholders around the world for the analysis of intricate transportation systems. Model calibration is a crucial prerequisite for transportation simulators to reliably reproduce and predict traffic conditions. This paper considers the calibration of transportation simulators. The methodology is suitable for a broad family of simulators. Its use is illustrated with stochastic and computationally costly simulators. The calibration problem is formulated as a simulation-based optimization (SO) problem. We propose a metamodel approach. The analytical metamodel combines information from the simulator with information from an analytical differentiable and tractable network model that relates the calibration parameters to the simulation-based objective function. The proposed algorithm is validated by considering synthetic experiments on a toy network. It is then used to address a calibration problem with real data for a large-scale network: the Berlin metropolitan network with over 24300 links and 11300 nodes. The performance of the proposed approach is compared to a traditional benchmark method. The proposed approach significantly improves the computational efficiency of the calibration algorithm with an average reduction in simulation runtime until convergence of more than 80%. The results illustrate the scalability of the approach and its suitability for the calibration of large-scale computationally inefficient network simulators.

Optimized Design of Autonomous Inflow-Control Devices for Gas and Water Coning

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 173203, “Optimized Design of Autonomous Inflow-Control Devices for Gas and Water Coning,” by Terry W. Stone, Terje Moen, David A. Edwards, Alexander Shadchnev, and Kashif Rashid, Schlumberger, and Geir Frode Kvilaas and Kjell Christoffersen, Det Norske Oljeselskap, prepared for the 2015 SPE Reservoir Simulation Symposium, Houston, 23–25 February. The paper has not been peer reviewed. Several designs for autonomous inflow-control devices (AICDs) are available. One forces inflowing fluids to enter gates, depending on inertial and viscous forces of the various fluids. Another is an autonomous valve in the shape of a free-floating disk that restricts the flow rate of low-viscosity fluids and is primarily used to choke gas and water inflow. Recently, a device with water-swellable rubber inside the nozzle has been proposed, but it is not yet commercially available. The comparative properties and abilities of these designs are the focus of this paper. Well Model, Reservoir Simulator, and Optimizer The well model used in this work is part of a next-generation parallel commercial reservoir simulator and features a flexible multisegmented well topology, enhanced robustness for difficult problems, and extensive well-model options. It forms part of a scalable parallel commercial reservoir simulator. Optimizations carried out in this work used an optimizer developed to alleviate the computational cost in an optimization study where simulation-based objective functions are expensive to evaluate. When compared with several other commonly used optimizers, it was demonstrated that this optimizer outperformed others significantly. Modeling Inflow-Control Devices (ICDs) Various ICD designs include those with nozzle orifices, tubes, and helices. Unlike ICDs, AICDs may or may not have moving parts but they can change or modify their state in response to inflow. Design of the AICD determines the particular unwanted fluids that are delayed. There are a number of types available commercially, including a floating flapper, an oil- selector valve, an autonomous inflow-control valve, the rate-controlled-production (RCP) valve, and a fluidic diode valve. Another design recently proposed is based on inclusion of water-swellable rubber within the nozzle, but this is not yet commercially available. Both ICDs and AICDs are often deployed in a compartment whose edges are sealed with a packer, and are placed in the tubing wall between an annulus and main production stream.

A Metamodel Simulation-based Optimization Approach for the Efficient Calibration of Stochastic Traffic Simulators

This work considers the calibration of stochastic microscopic traffic simulators. It formulates the calibration problem as a simulation-based optimization (SO) problem, and uses metamodel SO ideas. The main idea is to embed within the calibration algorithm an analytical problem-specific description of how the calibration parameters are related to the simulation-based objective function. Preliminary results on a toy network are presented. Ongoing work applies these ideas to the calibration of a Berlin metropolitan area network.

An adaptive-topology ensemble algorithm for engineering optimization problems

Modern engineering design optimization often relies on computer simulations to evaluate candidate designs, a scenario which formulates the problem of optimizing a computationally expensive black-box functions. In such problems, there will often exist candidate designs which cause the simulation to fail, and this can degrade the optimization effectiveness. To address this issue, this paper proposes a new optimization algorithm which incorporates classifiers into the optimization search. The classifiers predict which candidate design are expected to cause the simulation to fail, and their prediction is used to bias the search towards valid designs, namely, for which the simulation is expected to succeed. However, the effectiveness of this approach strongly depends on the type of metamodels and classifiers being used, but due to the high cost of evaluating the simulation-based objective function it may be impractical to identify by numerical experiments the most suitable types of each. Leveraging on these issues, the proposed algorithm offers two main contributions: (a) it uses ensembles of both metamodels and classifiers to benefit from a diversity of predictions of different metamodels and classifiers, and (b) to improve the search effectiveness, it continuously adapts the ensembles’ topology during the search. The performance of the proposed algorithm was evaluated using an engineering problem of airfoil shape optimization. Performance analysis of the proposed algorithm using an engineering problem of airfoil shape optimization shows that: (a) incorporating classifiers into the search was an effective approach to handle simulation failures (b) using ensembles of metamodels and classifiers, and updating their topology during the search, improved the search effectiveness in comparison to using a single metamodel and classifier, and (c) it is beneficial to update the topology of the metamodel ensemble in all problem types, and it is beneficial to update the classifier ensemble topology in problems where simulation failures are prevalent.

Improvement of power system stability using genetically optimized SVC controller

Single machine infinite bus (SMIB) power system and multi-machine power system (MMPS) stability improvement by tuning of static var compensator (SVC) based controller parameters are investigated in the proposed method. The design problem is formulated as an optimization problem with a time-domain simulation-based objective function and real-coded genetic algorithm is used for searching optimal controller parameters. SMIB power system and MMPS models are developed using MATLAB’s SIMULINK which incorporates SVC controller. A fault is created on the transmission line. The simulation results of SMIB power system and MMPS without SVC controller and with SVC controller are presented. The simulation results are analyzed which show that the power system becomes unstable on the occurrence of the fault if SVC controller is not used. This paper proves the effectiveness of the proposed design. Thus the proposed method enhances the power system stability.

Derivative-based hybrid heuristics for continuous-time simulation optimization

The topic of simulation–optimization has not been fundamentally tackled by many continuous-time modeling and simulation tools, yet. Common simulation-based optimization problems are usually coupled with standard optimization algorithms like any other simulation-free nonlinear optimization problems. While such couplings are usually based on many state-of-the-art software engineering concepts with a high-level user interface for flexible incorporation of simulation and optimization, the design of specialized optimization strategies targeting simulation-based objective functions is lacked within many simulation–optimization tools. In this work, new redefinition of Non Linear Programming (NLP) problems in the context of continuous-time simulation optimization is presented. Then, the modified optimization problems are efficiently tackled using derivative-based hybrid heuristics. In order to specify, illustrate and implement such heuristics, a new terminology is proposed. According to the proposed terminology, derivative-based hybrid strategies are implemented by hybridizing naive multistart derivative-based optimization methods with population-based metaheuristics. It is shown that the adoption of derivative-based optimization methods within hybrid optimization strategies significantly improves the solution quality of continuous-time simulation optimization problems.

An adaptive multiquadric radial basis function method for expensive black-box mixed-integer nonlinear constrained optimization

Many real-world optimization problems comprise objective functions that are based on the output of one or more simulation models. As these underlying processes can be time and computation intensive, the objective function is deemed expensive to evaluate. While methods to alleviate this cost in the optimization procedure have been explored previously, less attention has been given to the treatment of expensive constraints. This article presents a methodology for treating expensive simulation-based nonlinear constraints alongside an expensive simulation-based objective function using adaptive radial basis function techniques. Specifically, a multiquadric radial basis function approximation scheme is developed, together with a robust training method, to model not only the costly objective function, but also each expensive simulation-based constraint defined in the problem. The article presents the methodology developed for expensive nonlinear constrained optimization problems comprising both continuous and integer variables. Results from various test cases, both analytical and simulation-based, are presented.

Integer simulation based optimization by local search

Abstract Simulation-based optimization combines simulation experiments used to evaluate the objective and/or constraint functions with an optimization algorithm. Compared with classical optimization, simulation based optimization brings its specific problems and restrictions. These are discussed in the paper. Evaluation of the objective function is based on time consuming, typically repeated simulation experiments. So we believe that the main objective in selecting the optimization algorithm is minimization of the number of objective function evaluations. In this paper we concentrate on integer optimization that is typical in simulation context. Local search algorithms that try to minimize the number of objective function evaluations are described. Examples with both analytical and simulationbased objective functions are used to demonstrate the performance of the algorithms.

An adaptive multi-modal optimization algorithm for simulation-based design of power-electronic circuits

This article introduces a non-gradient optimization algorithm for the simulation-based design of nonlinear power-electronic circuits where multiple local minima may exist. The algorithm steers a simultaneous search for multiple optima by generating a multi-resolution mesh in the search space. It adaptively increases its resolution only in regions where the presence of local optima is likely, thus offering significant savings in the number of (simulation-based) objective-function evaluations. The algorithm's relatively low computational intensity, its independence of local gradient information and its capability to discover multiple local minima simultaneously make it appealing for the optimization of expensive black-box functions. The article shows an implementation of the algorithm in MATLAB® and links it to the PSCAD®/EMTDC transient simulation program. Examples of the application of the proposed algorithm for both analytical and simulation-based objective functions are included.

Robust coordinated design of excitation and STATCOM-based controller using genetic algorithm

Power system stability enhancement via robust coordinated design of a power system stabiliser (PSS) and a static synchronous compensator (STATCOM)-based stabiliser is thoroughly investigated in this paper. The coordination among the proposed damping stabilisers and the STATCOM internal AC and DC voltage controllers as well as the current regulator has also been taken into consideration. The coordinated design problem is formulated as an optimisation problem with a time-domain simulation-based objective function and genetic algorithm (GA) is employed to search for optimal controller parameters. The proposed stabilisers are tested on a weakly connected power system with different disturbances and loading conditions. The non-linear simulation results show the effectiveness and robustness of the proposed control schemes over a wide range of loading conditions and disturbances. Further, the proposed design approach is found to be robust and improves stability effectively even under small disturbance and unbalanced fault conditions.

The Objective Function of Simulation Estimators Near the Boundary of the Unstable Region of the Parameter Space

The paper examines the role of stability constraints in estimation by dynamic simulation. In particular, it analyzes the behavior of the objective function on either side of the boundary of the stability region of the parameter space. The main finding is that stability constraints may be ignored because the simulation-based objective function contains a built-in penalty to enforce stability. A key caveat, however, is that the dynamic stability of the auxiliary model that defines the moment conditions must be checked and enforced. An attempt to fit via simulation to moments defined by a dynamically unstable auxiliary model can be expected to lead to an ill-behaved objective function.