Low-level Optimizations Research Articles

Modular product platforming with supply chain postponement decisions by leader-follower interactive optimization

Modular product platforming empowers product family design by identifying the common product platform and configuration of product variants for mass customization. The prevailing practice of fulfilling product families is to postpone certain customization modules in the downstream supply chain. Product platforming and postponement decisions are inherently coupled in terms of developing a modular product architecture to leverage product variety and the supply chain. This paper is motivated towards integrated decision making underlying modular product platforming (MPP) with supply chain postponement (SCP). The paper formulates integrated MPP and SCP decisions as a Stackelberg game that entails joint optimization for interactive evaluation of product modularity and supply chain fulfillment costs. A bilevel mixed 0–1 programming model is developed to characterize the leader-follower decision making process. Virtual compound modules are introduced to justifying which modules should be postponed. An upper level optimization problem is established for identification of basic modules and compound modules by maximizing customer-perceived utilities and postponement utilities of product families, whereas a lower level optimization problem deals with the selection of most appropriate postponement service providers for a minimal total supply chain cost. A nested genetic algorithm is developed to solve the bilevel joint optimization model. A case study of laser printer product platforming and supply chain postponement is reported to illustrate the feasibility and potential of the proposed decision model.

Strategies of data layout and cache writing for input-output optimization in high performance scientific computing: Applications to the forward electrocardiographic problem.

Input-output (I/O) optimization at the low-level design of data layout on disk drastically impacts the efficiency of high performance computing (HPC) applications. However, such a low-level optimization is in general challenging, especially when using popular scientific file formats designed with an emphasis on portability and flexibility. To reconcile these two aspects, we present a novel low-level data layout for HPC applications, fully independent of the number of dimensions in the dataset. The new data layout improves reading and writing efficiency in large HPC applications using many processors, and in particular during parallel post-processing. Furthermore, its combination with a cached write mode, in order to aggregate multiple writes into larger ones, substantially decreased the writing times of the proposed strategy. When applied to our simulation framework for the forward calculation of the human electrocardiogram, the combined strategy resulted in drastic improvements in I/O performance, of up to 40% in writing and 93–98% in reading for post-processing tasks. Given the generality of the proposed strategies and scientific file formats used, our results may represent significant improvements in I/O performance of HPC applications across multiple disciplines, reducing execution and post-processing times and leading to a more efficient use of HPC resource envelopes.

A Novel Bi-Level Framework for Fitting the Parameters in Cardiac Cellular Models.

Cardiac models constructed from sets of differential equations provide invaluable information about heart mechanism and disorder of both human and animals. As tuning the parameters is a profoundly important step of modeling, this paper presents a novel parametrization technique based on a bilevel framework that benefits from two solution approaches, namely mixed integer genetic algorithm (MIGA) and linear least squares (LLS). In the upper-level optimization step, the action potential (AP) of the model is fitted to the reference AP using MIGA. In the lower-level optimization step, the mismatch between the total current of the model and reference is minimized via a clamp concept-based linearization and LLS solution approach. Notably, the clamp concept can diminish the nonlinearity of the parameter fitting problem. The issue of dependency on initial parameters in the lower-level problem, as well as the sensitivity of model parameters to linearization, are circumvented by MIGA in the upper-level optimization. For evaluation of MIGA-LLS performance, two complex human ventricular models are employed. The results demonstrate that in comparison to the genetic algorithm (GA)-based approach, the proposed framework significantly reduces the average and variation of normalized root-mean-squared error (NRMSE) in terms of the AP and total current in different trials. Variability in the resulting parameter values is considerably decreased as well.

Gmxapi: a high-level interface for advanced control and extension of molecular dynamics simulations.

Molecular dynamics simulations have found use in a wide variety of biomolecular applications, from protein folding kinetics to computational drug design to refinement of molecular structures. Two areas where users and developers frequently need to extend the built-in capabilities of most software packages are implementing custom interactions, for instance biases derived from experimental data, and running ensembles of simulations. We present a Python high-level interface for the popular simulation package GROMACS that i) allows custom potential functions without modifying the simulation package code, ii) maintains the optimized performance of GROMACS and iii) presents an abstract interface to building and executing computational graphs that allows transparent low-level optimization of data flow and task placement. Minimal dependencies make this integrated API for the GROMACS simulation engine simple, portable and maintainable. We demonstrate this API for experimentally-driven refinement of protein conformational ensembles. LGPLv2.1 source and instructions are available at https://github.com/kassonlab/gmxapi. Supplementary data are available at Bioinformatics online.

Using Karush-Kuhn-Tucker proximity measure for solving bilevel optimization problems

A common technique to solve bilevel optimization problems is by reducing the problem to a single level and then solving it as a standard optimization problem. A number of single level reduction formulations exist, but one of the most common ways is to replace the lower level optimization problem with its Karush-Kuhn-Tucker (KKT) conditions. Such a reduction strategy has been widely used in the classical optimization as well as the evolutionary computation literature. However, KKT conditions contain a set of non-linear equality constraints that are often found hard to satisfy. In this paper, we discuss a single level reduction of a bilevel problem using recently proposed relaxed KKT conditions. The conditions are relaxed; therefore, approximate, but the error in terms of distance from the true lower level KKT point is bounded. There is a proximity measure associated to the new KKT conditions, which gives an idea of the KKT error and distance from the optimum. We utilize this reduction method within an evolutionary algorithm to solve bilevel optimization problems. The proposed algorithm is compared against a number of recently proposed approaches. The idea is found to lead to significant computational savings, especially, in the lower level function evaluations. The idea is promising and might be useful for further developments on bilevel optimization both in the domain of classical as well as evolutionary optimization research.

Analysis of the Effect of Parameter Variation on a Dynamic Cost Function for Distributed Energy Resources: A DER-CAM Case Study

This paper investigates the effect of selected strategies of distributed energy resources (DER) on an energy cost function that optimizes the distribution of distributed energy resources for a mid-rise apartment building. This is achieved through comparing parameter optimization results for both a high-level and low-level optimizer, respectively. The optimization process is carried out using the following approach: (1) a two-objective function is constructed with one objective function similar to that of the high-level optimizer (DER-CAM); (2) an evolutionary algorithm (EA) with modified selection capability is used to optimize the two-objective function problem in (1) for four selected cases of DER utilization that were previously optimized in DER-CAM; and (3) the optimization results of the low-level optimizer are compared with the outcome of DER-CAM optimization for the four selected cases. This is done to establish the capability of DER-CAM as an effective tool for optimal distributed energy resource allocation. Results obtained reveal the effect of load shifting and solar photovoltaic (PV) panels with power exporting capability on the optimization of the cost function. The Pareto-based MOEA approach has also proved to be effective in observing the interactions between objective function parameters. Mean inverted generational distance (MIGD) values obtained over 10 runs for each of the four cases that were considered show that a DER combination of PV panel, battery storage, heat pump, and load shifting outperforms the other strategies in 70% of the total simulation runs.

A multi-product green supply chain under government supervision with price and demand uncertainty

In this paper, a bi-level game-theoretic model is proposed to investigate the effects of governmental financial intervention on green supply chain. This problem is formulated as a bi-level program for a green supply chain that produces various products with different environmental pollution levels. The problem is also regard uncertainties in market demand and sale price of raw materials and products. The model is further transformed into a single-level nonlinear programming problem by replacing the lower-level optimization problem with its Karush–Kuhn–Tucker optimality conditions. Genetic algorithm is applied as a solution methodology to solve nonlinear programming model. Finally, to investigate the validity of the proposed method, the computational results obtained through genetic algorithm are compared with global optimal solution attained by enumerative method. Analytical results indicate that the proposed GA offers better solutions in large size problems. Also, we conclude that financial intervention by government consists of green taxation and subsidization is an effective method to stabilize green supply chain members’ performance.

Bilevel transmission expansion planning using second-order cone programming considering wind investment

This paper presents a new framework for bi-level multi-stage transmission expansion planning (TEP) considering wind investment. In the upper-level problem, the transmission and wind investment decisions are modeled, while in the lower-level problem, the market-clearing problem based on the alternating current-optimal power flow (AC-OPF) is formulated. Since the lower-level optimization problem is nonconvex, the second-order cone programming (SOCP) is applied to convexify this problem. Afterwards, the Karush-Kuhn-Tucker (KKT) optimality conditions are employed in order to convert the bi-level problem into a single-level problem. Due to the convexity of the lower-level problem, the KKT conditions are both necessary and sufficient. The whole problem is then solved by a commercial and powerful solver. To show the effectiveness and applicability of the proposed scheme, it is applied to two power systems, namely, IEEE 24-bus RTS and IEEE 118-bus. The numerical results illustrate the efficient performance of the proposed method. Furthermore, the results obtained from the AC-OPF-based market-clearing problem are compared with those obtained from the direct current-optimal power flow (DC-OPF)-based market-clearing problem, and the comparative analysis indicates that the latter may lead to inaccurate solutions.

Co-evolution of product family configuration and supplier selection: a game-theoretic bilevel optimisation approach

ABSTRACTJoint decision making of configuration design and supplier selection has been well recognised for successful development of modular product families. However, the prevailing practice for integrating supplier selection into product family design is limited to only one family generation and neglects the changes in customer demands and technological progress over time, which calls for a co-evolution design across product generations from a systematic perspective, instead of separating optima.In this paper, the co-evolution of configuration design and supplier selection for a product family is regarded as a distributed collaborative decision making, for which a Stackelberg game theoretic decision framework is proposed to model the interactions between product family planning in the current generation and product family re-planning in the next generation. Consistent with the Stackelberg game, a nonlinear bilevel optimisation model with a common deviation objective function, compromising an upper-level planning optimisation and a lower-level re-planning optimisation, is formulated. A corresponding nested bilevel genetic algorithm is developed to solve the optimisation model. A case study of mobile phone product family co-evolution with supplier selection is reported to illustrate the feasibility and potential of the proposed collaborative game theoretic approach.

Coordinated optimization of low-carbon product family and its manufacturing process design by a bilevel game-theoretic model

Abstract While increasing environmental issues arising from product development and manufacturing activities have attracted much attention from both academia and industry alike, few researches have addressed joint optimization of product family architecting (PFA) and its manufacturing process configuration (MPC) considering environmental concerns. Moreover, the hierarchical characteristics underlying these two optimization problems and complex interactions among PFA, MPC, and environmental concerns are failed to be revealed and addressed in the previous research. In this paper, a bilevel game-theoretic model for coordinating low-carbon PFA (L-CPFA) and low-carbon MPC (L-CMPC) is proposed. The L-CPFA decision by a designer (game-leader) is represented as an upper-level optimization problem for optimal configuration of module instances and architecture of compound modules and product variants from the perspectives of economic and environmental performances. The L-CMPC decision by a manufacturer (game-follower) is modeled as a lower-level optimization problem in order to determine the optimal low-carbon realization process planning of each primitive module, each compound module, and the assembly and transportation mode of each product variant according to the upper-level decision. A nonlinear, 0–1 integer bilevel programming model is developed, and then solved by a nested bilevel genetic algorithm (NBGA). A case study of a microwave oven product family is presented to demonstrate the feasibility and potential of the proposed model and algorithm. The results indicate that the carbon emissions have apparently impact on the optimal PFA and MPC decisions, and integrating low-carbon awareness into product family development activities is beneficial and advisable for enterprises to increase customer-perceived utilities and competitive advantages. Our proposed model can handle well the conflict and coordination between L-CPFA and L-CMPC, and balance well enterprise's benefits with environmental impacts triggered by development activities.

An optimization model to measure utility of joint and solo activities

The choice of ‘dining out with friends’ or ‘wrapping up unfinished tasks at work’ depends on the utility/satisfaction gained from performing each activity while being constrained by time and physical resources. In fact, such parameters as ‘type’, ‘time of day’, ‘duration’, ‘location’, ‘companionship’, and etc. are defining factors in quantifying the utility of activities - a challenging problem which has been the focus of research for many years. This paper proposes a methodology to estimate the parameters of utility distributions for joint and solo activities, along with the penalty values associated with the deviation of activity start time and duration from their modal values. The study utilizes travel survey data collected in Frauenfeld, Switzerland, over the period of six weeks in 2003. The proposed model is a bi-level optimization model, where the upper level maximizes the accuracy of the activity scheduling on the aggregate level and is measured using the outputs of lower level optimization models. Each lower level model is a variation of pickup and delivery problem and schedules activities for each individual in the population using the parameters of utility distribution and penalty values generated by the Genetic Algorithm. The results indicate that travelers are trying to be more consistent with their arrival time to work, school and pickup/drop off activities: the associated penalty values for deviation from the modal value for arrival time to work and school activities are high. Additionally, significant differences in the parameters of the estimated utility distribution for joint and solo activities are observed, reflecting the fact that utility gained from joint and solo activities are different and needs more in-depth investigation. The proposed methodology has the potential to be applied to any multiday travel survey data, which due to advances made in handheld smart devices and mobile applications are becoming more convenient to collect.

Performance Optimization Strategies for WRF Physics Schemes Used in Weather Modeling

Performance optimization in the petascale era and beyond in the exascale era has and will require modifications of legacy codes to take advantage of new architectures with large core counts and SIMD units. The Numerical Weather Prediction (NWP) physics codes considered here are optimized using thread-local structures of arrays (SOA). High-level and low-level optimization strategies are applied to the WRF Single-Moment 6-Class Microphysics Scheme (WSM6) and Global Forecast System (GFS) physics codes used in the NEPTUNE forecast code. By building on previous work optimizing WSM6 on the Intel Knights Landing (KNL), it is shown how to further optimize WMS6 and GFS physics, and GFS radiation on Intel KNL, Haswell, and potentially on future micro-architectures with many cores and SIMD vector units. The optimization techniques used herein employ thread-local structures of arrays (SOA), an OpenMP directive, OMP SIMD, and minor code transformations to enable better utilization of SIMD units, increase parallelism, improve locality, and reduce memory traffic. The optimized versions of WSM6, GFS physics, GFS radiation run 70, 27, and 23 faster (respectively) on KNL and 26, 18 and 30 faster (respectively) on Haswell than their respective original serial versions. Although this work targets WRF physics schemes, the findings are transferable to other performance optimization contexts and provide insight into the optimization of codes with complex physical models for present and near-future architectures with many core and vector units.

OPTIMIZATION OF THE ALGORITHM FOR DETERMINING THE HAUSDORFF DISTANCE FOR CONVEX POLYGONS

The paper provides a brief historical analysis of problems that use the Hausdorff distance; provides an analysis of the existing Hausdorff distance optimization elements for convex polygons; and demonstrates an optimization approach. The existing algorithm served as the basis to propose low-level optimization with super-operative memory, ensuring the finding a precise solution by a full search of the corresponding pairs of vertices and sides of polygons with exclusion of certain pairs of vertices and sides of polygons. This approach allows a significant acceleration of the process of solving the set problem.

A semivectorial bilevel programming approach to optimize electricity dynamic time-of-use retail pricing

Presently, residential electricity consumers are, in general, charged at flat or dual time-of-use tariffs along the day, which are defined by the retailer for long periods (e.g., one year). These pricing schemes do not convey price signals reflecting generation costs and grid conditions. Hence, consumers lack the incentives to engage in different consumption patterns using the flexibility they generally have in the operation of some end-use loads. Dynamic tariffs, i.e. energy prices varying possibly with significant magnitude in short periods of time, are expected to become an applicable pricing scheme in smart grids. In this setting, home energy management systems can play an important role to help end-users optimizing the usage of appliances to minimize energy costs without compromising comfort. This can be advantageous also from the perspective of grid management.A semivectorial bilevel programming approach is developed to model the interaction between electricity retailers and consumers in order to optimize electricity time-of-use retail pricing. The aim is to support the retailer in finding good decisions for the prices. The retailer (upper level decision maker) establishes dynamic time-of-use electricity prices to maximize profits. The consumer (lower level decision maker) responds by selecting, under that price setting, a load scheduling decision leading to a nondominated solution balancing his objectives of minimizing the electricity bill (cost dimension) and minimizing the dissatisfaction in face of his preferences and requirements (comfort dimension).The lower level optimization problem is formulated as a bi-objective mixed-integer linear programming problem. A hybrid approach is proposed, which consists of a genetic algorithm for the upper level problem and an exact solver to solve surrogate scalar problems at the lower level. A case study is presented and discussed.

Robust topology optimization under multiple independent unknown-but-bounded loads

The optimal designs obtained from the deterministic topology optimization without considering the loading uncertainties may become vulnerable, or even lead to catastrophic failures. A two-level optimization formulation is often used in the Robust Topology Optimization (RTO) under uncertain loads. Various approaches have been reported to identify the critical loads associated with the worst structure responses. Because Convex Model approaches apply convex approximations to the original non-convex model at the lower level, the optimal designs obtained by these methods are greatly dependent on the quality of the approximation. In this paper, a new formulation based on the Wolfe duality for the RTO problems with multiple independent unknown-but-bounded loads is proposed. Following the two-level formulation, the lower level optimization problem for the worst multiple independent uncertain loading case is transformed by the Wolfe duality. Both the first order necessary conditions and the second order sufficient conditions are derived rigorously to validate the solution optimality despite of the non-convexity associated with the lower level formulation. Numerical examples are also presented to demonstrate the proposed approach.

Bi-Level Model for Public Rail Transportation under Incomplete Data

AbstractThe increase of the utilization of public rail transportations is searched in directions for redistribution of the passenger travels between rail and bus transportation. The rail transport benefits by redistribution of the transportation flows on paths, predominantly supported by rails. The redistribution of the transportation is formalized by bi-level optimization problem. The upper level optimization estimates the maximal flow, which can be transported through a transportation network, supported both by bus and rail transports. The lower level optimization gives priority to the rail transport by decreasing the costs of flow distribution, using rail transport. This bi-level optimization problem was applied for the case of optimization of the rail exploitation in Bulgaria, defining priorities in transportation of the National transport scheme.

Reconfigurable Constant Multiplication for FPGAs

This paper introduces a new heuristic to generate pipelined run-time reconfigurable constant multipliers for field-programmable gate arrays (FPGAs). It produces results close to the optimum. It is based on an optimal algorithm which fuses already optimized pipelined constant multipliers generated by an existing heuristic called reduced pipelined adder graph (RPAG). Switching between different single or multiple constant outputs is realized by the insertion of multiplexers. The heuristic searches for a solution that results in minimal multiplexer overhead. Using the proposed heuristic reduces the run-time of the fusion process, which raises the usability and application domain of the proposed method of run-time reconfiguration. An extensive evaluation of the proposed method confirms a 9%–26% FPGA resource reduction on average compared to previous work. For reconfigurable multiple constant multiplication, resource savings of up to 75% can be shown compared to a standard generic lookup table based multiplier. Two low level optimizations are presented, which further reduce resource consumption and are included into an automatic VHDL code generation based on the FloPoCo library.

Bi-Level Programming Approach for the Optimal Allocation of Energy Storage Systems in Distribution Networks

Low-CO2-emission wind generation can alleviate the world energy crisis, but intermittent wind generation influences the reliability of power systems. Energy storage might smooth the wind power fluctuations and effectively improve system reliability. The contribution of energy storage to system reliability cannot be comprehensively assessed by the installed capacity of energy storage. The primary goal of this paper is to investigate the impact of the installed location and capacity of energy storage on power system reliability. Based on a bi-level programming approach, this paper presents a bi-level energy storage programming configuration model for energy storage capacity and location configuration. For upper-level optimization, a depth search method is utilized to obtain the optimal installed location of energy storage. For the lower-level optimization, the optimal capacity of energy storage is solved to meet the system reliability requirements. The influence of the contribution of energy storage location to system reliability is analyzed. The proposed model and method are demonstrated using the RBTS-Bus6 System and Nanao (NA) island distribution system in China. The results show the effectiveness and practicability of the proposed model and method.

Dynamic flux balance analysis with nonlinear objective function.

Dynamic flux balance analysis (DFBA) extends flux balance analysis and enables the combined simulation of both intracellular and extracellular environments of microbial cultivation processes. A DFBA model contains two coupled parts, a dynamic part at the upper level (extracellular environment) and an optimization part at the lower level (intracellular environment). Both parts are coupled through substrate uptake and product secretion rates. This work proposes a Karush-Kuhn-Tucker condition based solution approach for DFBA models, which have a nonlinear objective function in the lower-level part. To solve this class of DFBA models an extreme-ray-based reformulation is proposed to ensure certain regularity of the lower-level optimization problem. The method is introduced by utilizing two simple example networks and then applied to a realistic model of central carbon metabolism of wild-type Corynebacterium glutamicum.

Bi-Level Coordinated Configuration Optimization for Product-Service System Modular Design

Product-service systems (PSSs) deploy a selection of products and services in order to cope with diverse markets, so as to achieve a higher profit than would be possible by offering physical products alone. Modular design inherently contributes to the sustainability performance of PSS by material and resource reuse through the configuration of physical product and service modules. PSS configuration design is enacted through service configuration in line with product configuration; this entails two separate yet coordinated optimization problems, enabling customer satisfaction through service configuration and manufacturers’ sales profits through product configuration, respectively. Traditional multiobjective optimization approaches assume that the conflicting goals between customers and manufacturers can be aggregated into one single objective function through cooperative protocols, such as a weighted sum; in practice, this scarcely holds true. Consistent with game-theory decision-making, it is necessary to leverage the concerns of customers and manufacturers within a coherent framework of equilibrium solutions. This paper proposes a bi-level coordinated optimization framework to support PSS configuration design. An upper-level optimization problem is formulated for service configuration to act as a leader in the achievement of customer satisfaction, and a lower-level optimization problem is formulated for product configuration to act as a follower in an effort to enhance sales profits. Coordination between the upper and lower levels coincides with the tradeoffs underlying the conflicting goals that exist between customers and manufacturers. A constrained genetic algorithm is developed to solve the bi-level optimization model, and a case study of transformer PSS configuration design is reported to illustrate the feasibility and potential of bi-level coordinated configuration.