Composite Objective Function Research Articles

An Imperialist Competitive Algorithm-Based Multi-Objective Optimization for Voltage Source Converter High-Voltage Direct Current Stations Control in Multi-Terminal HVDC Grids

This article presents a multi-objective-based imperialist competitive algorithm (ICA) for optimal tuning of voltage source converter (VSC) stations control parameters in multi-terminal high-voltage direct current (MT-HVDC) grid. The key objective here is to enhance the control performance of the MT-HVDC grid VSC-HVDC stations under dynamic situations. As VSC-HVDC stations are non-linear apparatuses of the MT-HVDC grids, conventional methods for the tuning of the control parameters which are commonly based on approximated linear plant models do not reach to optimal results. Therefore, as the main contribution of this research, an effective ICA-based multi-objective optimization technique is adopted for optimal tuning of the VSC-HVDC stations control parameters. The proposed composite objective function in this algorithm consists of both inner and outer loop parameter optimization characteristics. A fuzzification technique is used in this study to normalize all objective functions and to find the optimal solution. To confirm the merits of the presented optimization method, a detailed model of a four-terminal MT-HVDC grid is developed and its transient and steady-state performance in case of classically and ICA tuned have been studied and compared.

A comparative study in aquifer parameter estimation using MFree point collocation method with evolutionary algorithms

Abstract In this study, we present a comparative assessment of simulation-optimization (S-O) models to estimate aquifer parameters such as transmissivity, longitudinal dispersivity, and transverse dispersivity. The groundwater flow and contaminant transport processes are simulated using the mesh-free radial basis point collocation method (RPCM). Four different S-O models are developed by combining the RPCM model separately with genetic algorithm (GA), differential evolution (DE), cat swarm optimization (CSO), and particle swarm optimization (PSO). The objective of the S-O model is to minimize a composite objective function with transmissivity, longitudinal dispersivity, and transverse dispersivity as decision variables. Hydraulic head and contaminant concentration at observation points are the state variables. The S-O models are used to estimate aquifer parameters of a confined aquifer with nine zones. It is found that RPCM-based DE, CSO, and PSO models are more accurate in estimating aquifer parameters than RPCM-GA. However, for noisy observed data, the RPCM-CSO model outperforms other models. The efficiency of the RPCM-CSO model over other models is further established by performing reliability analysis to the noisy observed data set. The comparative study reflects the efficacy of CSO over GA, DE, and PSO.

Online Learning With Inexact Proximal Online Gradient Descent Algorithms

We consider non-differentiable dynamic optimization problems such as those arising in robotics and subspace tracking. Given the computational constraints and the time-varying nature of the problem, a low-complexity algorithm is desirable, while the accuracy of the solution may only increase slowly over time. We put forth the proximal online gradient descent (OGD) algorithm for tracking the optimum of a composite objective function comprising of a differentiable loss function and a non-differentiable regularizer. An online learning framework is considered and the gradient of the loss function is allowed to be erroneous. Both, the gradient error as well as the dynamics of the function optimum or target are adversarial and the performance of the inexact proximal OGD is characterized in terms of its dynamic regret, expressed in terms of the cumulative error and path length of the target. The proposed inexact proximal OGD is generalized for application to large-scale problems where the loss function has a finite sum structure. In such cases, evaluation of the full gradient may not be viable and a variance reduced version is proposed that allows the component functions to be sub-sampled. The efficacy of the proposed algorithms is tested on the problem of formation control in robotics and on the dynamic foreground-background separation problem in video.

Supply chain network optimization with consideration of raw material and final product substitutions driven by price and carbon emissions

PurposeThis paper aims to develop a bi-objective mixed integer non-linear programing model to optimize the supply chain networks consisting of raw material providers, final product manufacturers and distribution centers. Raw material substitution caused by varying raw material supply amounts, prices and carbon emissions and final product substitution due to different product prices and carbon emissions are considered.Design/methodology/approachThe proposed model aims to achieve total profit maximization and total carbon emission minimization. The objective function of carbon emissions is converted into a maximization problem by changing minimum to maximum. The composite objective function is the weighted sum of the bias value of each objective function. The model is then solved using software Lingo12.FindingsNumerical analysis results show that an increase in the number of alternate raw materials for original raw material helps improve supply chain network performance, and variation in that number causes detectable but not significant changes in downstream final product substitution results.Originality/valueThe major differences between this work and existing research are as follows: first, although previous research considered carbon emissions in supply chain network optimization, it has not considered the substitution effects of products or raw materials. This paper considers the substitution of both raw material and productions. Second, the item substitution considered by previous research is derived from inventory shortage or price difference of original items. However, the substitution considered in the present paper is a response to differences in purchase price, production cost and carbon emissions for items.

A flexible coordinate descent method

We present a novel randomized block coordinate descent method for the minimization of a convex composite objective function. The method uses (approximate) partial second-order (curvature) information, so that the algorithm performance is more robust when applied to highly nonseparable or ill conditioned problems. We call the method Flexible Coordinate Descent (FCD). At each iteration of FCD, a block of coordinates is sampled randomly, a quadratic model is formed about that block and the model is minimized approximately/inexactly to determine the search direction. An inexpensive line search is then employed to ensure a monotonic decrease in the objective function and acceptance of large step sizes. We present several high probability iteration complexity results to show that convergence of FCD is guaranteed theoretically. Finally, we present numerical results on large-scale problems to demonstrate the practical performance of the method.

An Emergency Energy Management for AC/DC Micro-grids in Industrial Park

Abstract Industrial parks have the trend to be designed to operate as microgrids with renewable distributed generations and battery storage. In this paper, an energy management system is proposed for AC/DC microgrids. This paper introduces a mixed-integer nonlinear programming method to realize the multiple objectives of emergency energy management. Combined with the comprehensive consideration of the amount of load supply, the cost of power generation and the utilization of battery storage, as well as the number of the switch operation, this paper establishes a composite objective function by synthetically evaluating several criteria. Then, examples are given to illustrate the effectiveness of the proposed method by considering the islanded mode with a generator fault.

A note on the accelerated proximal gradient method for nonconvex optimization

We improve a recent accelerated proximal gradient (APG) method in [Li, Q., Zhou, Y., Liang, Y. and Varshney, P. K., Convergence analysis of proximal gradient with momentum for nonconvex optimization, in Proceedings of the 34th International Conference on Machine Learning, Sydney, Australia, PMLR 70, 2017] for nonconvex optimization by allowing variable stepsizes. We prove the convergence of the APG method for a composite nonconvex optimization problem under the assumption that the composite objective function satisfies the Kurdyka-Łojasiewicz property.

PPCOF: A Robust Proportion-Preserving Composite Objective Function for Scale-Invariant Multi-Objective Optimization

This paper aims at introducing a proportion-preserving composite ob-jective function for multi-objective optimization, namely, PPCOF, and validating its eciency through demonstrating its applicability to opti- mization of the kinetostatic performance of planar parallel mechanisms. It exempts the user from both specifying preference factors and conduct- ing decision-making. It consists of two terms. The rst one adds the normalized objective functions up, where the extrema are resulted from single-objective optimization. To making the composite objective func- tion steer the variations of the objective functions while preserving ra- tional proportions between them, as the main contribution of the paper, it is sought that the normalized objective functions take closely similar values, to which end, they are juxtaposed inside a vector, which is then scaled such that its Euclidean norm-2 is equal to that of the vector of all ones with the same dimensions, and then the second term is constructed as the addition of penalty factors standing for the absolute value of the di erence between each element of the foregoing vector from 1. Based on the experimental results, with a considerably smaller computational cost, the PPCOF obtains an optimal solution that is not dominated by any point from a set of Pareto-optimal solutions o ered by NSGA-II.

Complexity bounds for primal-dual methods minimizing the model of objective function

We provide Frank-Wolfe (≡ Conditional Gradients) method with a convergence analysis allowing to approach a primal-dual solution of convex optimization problem with composite objective function. Additional properties of complementary part of the objective (strong convexity) significantly accelerate the scheme. We also justify a new variant of this method, which can be seen as a trust-region scheme applying the linear model of objective function. Our analysis works also for a quadratic model, allowing to justify the global rate of convergence for a new second-order method. To the best of our knowledge, this is the first trust-region scheme supported by the worst-case complexity bound.

Distributed Gaussian mixture model-based particle filter method for chemical pollution source localization with sensor network

Chemical pollution source localization with statistical estimation algorithm in sensor networks, which was also known as source parameters estimation, has an important significance in fields such as pollution environmental monitoring and control. In this paper, a distributed Gaussian mixture dispersion model based particle filter method was proposed for the chemical pollution source localization problem. At the same time, we designed a composite information objective function for sensor scheduling scheme, which comprised of information utility measurement and energy consumption measurement. At last, in order to balance the source localization accuracy and energy consumption, a dynamical sensor radius adjusting method was given for sensor nodes scheduling. Simulation and experiment results show that the proposed method could determine the position of chemical pollution source, compared to UKF, the distributed Gaussian mixture particle filter method was suggested because it could get a significant reduction in the required numbers of sensor nodes and less energy to achieve the desired performance with less time.

Control of underground blast induced building vibration by shape-memory-alloy rubber bearing (SMARB)

Summary This paper focuses on the performance of shape-memory-alloy rubber bearings (SMARBs) compared to conventional lead-plug or New-Zealand (N-Z) bearings in control of building vibration due to underground blast induced ground motion (BIGM). The performance is evaluated with regard to maximum acceleration and isolator displacement obtained by nonlinear time history analysis. In doing so the Bouc–Wen's model is used to represent the nonlinear behaviour of the N-Z bearing and the superelastic behaviour of nickel–titanium-based shape-memory alloy is represented by the Graesser–Cozzarelli model. The underground BIGM input is modelled by exponentially decaying function. It is observed that though the N-Z bearing is fairly effective in controlling the structural accelerations due to BIGM without excessive bearing displacements, there remains a problem with the residual bearing displacements. The latter, however, is found to be dealt with very effectively by the SMARB. Furthermore, the procedure to obtain the optimum design parameters of the base isolators under study is obtained by optimizing two mutually conflicting objective functions, that is, the minimization of peak acceleration as well as peak bearing displacement by converting the multiobjective optimization problem to a single composite objective function. The improved and robust control performance of SMARB compared to N-Z bearing is elucidated through numerical study by considering a five-storied shear building frame.

Inverse truss design as a conic mathematical program with equilibrium constraints

We formulate an inverse optimal design problem as a Mathematical Programming problem with Equilibrium Constraints (MPEC). The equilibrium constraints are in the form of a second-order conic optimization problem. Using the so-called Implicit Programming technique, we reformulate the bilevel optimization problem as a single-level nonsmooth nonconvex problem. The major part of the article is devoted to the computation of a subgradient of the resulting composite objective function. The article is concluded by numerical examples demonstrating, for the first time, that the Implicit Programming technique can be efficiently used in the numerical solution of MPECs with conic constraints on the lower level.

Smoothed $$\ell _1$$ ℓ 1 -regularization-based line search for sparse signal recovery

$$\ell _1$$ -regularization-based sparse recovery has received a considerable attention over the last decade. In this paper, a solver called SQNSR is proposed to recover signals with high dynamic range. SQNSR utilizes linear search strategy and quasi-Newton step to the solve composite objective function for the sparse recovery problem. Since $$\ell _1$$ -norm-regularized item is nonsmooth, smoothing technique is introduced to obtain an approximate smoothed function. The sufficient and necessary condition is also derived for the feasible smoothed objective function. By limiting the step length in each iteration, the convergence of SQNSR is guaranteed to obtain the sparsest solution. Numerical simulations are implemented to test the performance of the proposed approach and verify the theoretical analysis.

Drop test simulation and surrogate-based optimization of a dishwasher mechanical structure and its packaging module

A drop test simulation of the mechanical structure of a redesigned dishwasher is performed by using a detailed finite element (FE) model. The nonlinear explicit FE code LS-DYNA® is used for the drop impact simulations. The FE model is validated through real tests of two drop scenarios (vertical and inclined to the side). An optimization study is performed in order to determine the optimum design variables for better crash performance. The effects of geometric parameters and material properties on the weights of certain components (ie, dogleg plate and bottom foam) are investigated. A surrogate-based optimization approach is used to find optimum values for the dogleg plate thickness, bottom foam density and increment of the bottom foam height to minimize the weights of both components. Two different surrogate models are used to predict optimization problem constraints that have a crucial role in the crash performance of the dishwasher mechanical structure and packaging module: the polynomial response surface and radial basis functions. The results showed that the dogleg plate mass can be slightly reduced and the bottom foam mass can be significantly reduced in order to obtain the optimum dishwasher configuration and better crashworthiness. The weights of the dogleg plate and bottom foam could be lowered by as much as 5.95 and 24.8 %, respectively. Finally, multi-objective optimization is performed by minimizing a composite objective function that provides a compromise between the weights of both components. The results showed that weight reductions of 2.3 and 21.5 % could be obtained for the dogleg plate and bottom foam, respectively.

Optimum crashworthiness design of tapered thin-walled tubes with lateral circular cutouts

In this paper, the effects of introducing lateral circular cutouts on crash performances of tapered thin-walled tubes are explored within a simulation-driven surrogate-based multi-objective optimization framework. The crash performances of the tubes are measured using the crush force efficiency (CFE) and the specific energy absorption (SEA) criteria, which are computed using the finite element analysis code LS-DYNA. Surrogate-based optimization approach is followed to find out that optimum values of the wall thickness, the taper angle, the cutout diameter and the numbers of cutouts in horizontal and vertical directions to maximize CFE and SEA. Four different surrogate models are used: polynomial response surfaces, radial basis functions, and Kriging models with zeroth- and first-order trend models. It is found that the optimum CFE of the tubes with lateral circular cutouts is 27.4% larger than the optimum CFE of the tubes without cutouts. It is also found that the optimum SEA of the tubes with lateral circular cutouts is 26.4% larger than the optimum SEA of the tubes without cutouts. It is observed that the optimum SEA design has slightly reduced wall thickness, significantly reduced taper angle, significantly increased cutout diameter, increased number of cutouts in horizontal direction and slightly reduced number of cutouts in vertical direction compared to the optimum CFE design. In addition, multi-objective optimization of the tubes is performed by maximizing a composite objective function that provides a compromise between CFE and SEA. It is found that the CFE dominates the behavior of composite objective function.

Stochastic Intermediate Gradient Method for Convex Problems with Stochastic Inexact Oracle

In this paper, we introduce new methods for convex optimization problems with stochastic inexact oracle. Our first method is an extension of the Intermediate Gradient Method proposed by Devolder, Glineur and Nesterov for problems with deterministic inexact oracle. Our method can be applied to problems with composite objective function, both deterministic and stochastic inexactness of the oracle, and allows using a non-Euclidean setup. We estimate the rate of convergence in terms of the expectation of the non-optimality gap and provide a way to control the probability of large deviations from this rate. Also we introduce two modifications of this method for strongly convex problems. For the first modification, we estimate the rate of convergence for the non-optimality gap expectation and, for the second, we provide a bound for the probability of large deviations from the rate of convergence in terms of the expectation of the non-optimality gap. All the rates lead to the complexity estimates for the proposed methods, which up to a multiplicative constant coincide with the lower complexity bound for the considered class of convex composite optimization problems with stochastic inexact oracle.

Penalized composite quantile estimation for censored regression model with a diverging number of parameters

ABSTRACTThis article considers the variable selection in censored composite quantile regression with a diverging number of parameters. We propose a sparse weighted composite quantile regression objective function based on inverse censoring probability weighting and smoothly clipped absolute deviation penalty. Under some mild conditions, we get consistency and “Oracle Property” of the proposed estimator. Moreover, we use an iterative algorithm to minimize the proposed objective function, and a modified Bayesian information criterion for tuning parameter selection. Some simulations and real data examples are provided to examine the performance of our procedure.

Identification of some nonsmooth evolution systems with illustration on adhesive contacts at small strains

A class of evolution quasi-static systems which leads, after a suitable time discretization, to recursive non-linear programs, is considered and optimal control or identification problems governed by such systems are investigated. The resulting problem is an evolutionary Mathematical Programs with Equilibrium Constraints. A subgradient information of the (in general nonsmooth) composite objective function is evaluated and the problem is solved by the implicit programming approach. The abstract theory is illustrated on an identification problem governed by delamination of a unilateral adhesive contact of elastic bodies discretized by finite-element method in space and a semiimplicit formula in time. Being motivated by practical tasks, an identification problem of the fracture toughness and of the elasticity moduli of the adhesive is computationally implemented and tested numerically on a two-dimensional example. Other applications including frictional contacts or bulk damage, plasticity or phase transformations are outlined.

An Adaptive Multipoint Formulation for Robust Parametric Optimization

The performance of a system designed for given functioning conditions often seriously degrades, when operated at other conditions. Therefore, a system operating over a continuous range of conditions should be designed over this range. The aerodynamic shape optimization of an aircraft at multiple altitudes, angles of attack and Mach numbers is a typical case in aerospace. This paper links parametric and multipoint optimizations by the sampling of the operating condition ranges. It is demonstrated that this discrete set of operating conditions, used to formulate a composite objective function, must adequately be chosen. An algorithm is proposed to select these conditions, which ensures a minimal computational cost to the robust optimization. Wing aerodynamic multipoint optimizations using a lifting line model and Reynolds-averaged Navier---Stokes equations, derived with a discrete adjoint formulation, are given as examples.

Automatic Calibration Tool for Hydrologic Simulation Program-FORTRAN Using a Shuffled Complex Evolution Algorithm

Hydrologic Simulation Program-Fortran (HSPF) model calibration is typically done manually due to the lack of an automated calibration tool as well as the difficulty of balancing objective functions to be considered. This paper discusses the development and demonstration of an automated calibration tool for HSPF (HSPF-SCE). HSPF-SCE was developed using the open source software “R”. The tool employs the Shuffled Complex Evolution optimization algorithm (SCE-UA) to produce a pool of qualified calibration parameter sets from which the modeler chooses a single set of calibrated parameters. Six calibration criteria specified in the Expert System for the Calibration of HSPF (HSPEXP) decision support tool were combined to develop a single, composite objective function for HSPF-SCE. The HSPF-SCE tool was demonstrated, and automated and manually calibrated model performance were compared using three Virginia watersheds, where HSPF models had been previously prepared for bacteria total daily maximum load (TMDL) development. The example applications demonstrate that HSPF-SCE can be an effective tool for calibrating HSPF.