Stochastic optimization for modeling physiological time series: application to the heart rate response to exercise

Stochastic optimization is applied to the problem of optimizing the fit of a model to the time series of raw physiological (heart rate) data. The physiological response to exercise has been recently modeled as a dynamical system. Fitting the model to a set of raw physiological time series data is, however, not a trivial task. For this reason and in order to calculate the optimal values of the parameters of the model, the present study implements the powerful stochastic optimization method ALOPEX IV, an algorithm that has been proven to be fast, effective and easy to implement. The optimal parameters of the model, calculated by the optimization method for the particular athlete, are very important as they characterize the athlete's current condition. The present study applies the ALOPEX IV stochastic optimization to the modeling of a set of heart rate time series data corresponding to different exercises of constant intensity. An analysis of the optimization algorithm, together with an analytic proof of its convergence (in the absence of noise), is also presented.     

Stochastic optimization for the calculation of the optimal critical curve from experimental data in a model of the process of regaining balance after perturbation from quiet stance

We demonstrate the successful application of ALOPEX stochastic optimization to the problem of calculating the optimal critical curve in a dynamical systems model of the process of regaining balance after perturbation from quiet stance. Experimental data provide the time series of angles for which the subjects were able to regain balance after an initial perturbation. The optimal critical curve encloses all data points and has a minimum distance from the border points of the data set. We demonstrate the results of the optimization firstly using the traditional cost function of chi-square distance. We then successfully introduce a modified cost function that fits the model to the experimental data by taking into account the specific requirements of the model. By use of the proposed cost function, combined with the efficiency of our optimization method, an optimal critical curve is calculated even in the cases of very asymmetric data sets that lie within the capabilities of the existing model.     

PANMIN: sequential and parallel global optimization procedures with a variety of options for the local search strategy

We present two sequential and one parallel global optimization codes, that belong to the stochastic class, and an interface routine that enables the use of the Merlin/MCL environment as a non-interactive local optimizer. This interface proved extremely important, since it provides flexibility, effectiveness and robustness to the local search task that is in turn employed by the global procedures. We demonstrate the use of the parallel code to a molecular conformation problem.

Program summary

Title of program: PANMINCatalogue identifier: ADSUProgram summary URL:http://cpc.cs.qub.ac.uk/summaries/ADSUProgram obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandComputer for which the program is designed and others on which it has been tested: PANMIN is designed for UNIX machines. The parallel code runs on either shared memory architectures or on a distributed system. The code has been tested on a SUN Microsystems ENTERPRISE 450 with four CPUs, and on a 48-node cluster under Linux, with both the GNU g77 and the Portland group compilers. The parallel implementation is based on MPI and has been tested with LAM MPI and MPICHInstallation: University of Ioannina, GreeceProgramming language used: Fortran-77Memory required to execute with typical data: Approximately O(n²) words, where n is the number of variablesNo. of bits in a word: 64No. of processors used: 1 or manyHas the code been vectorised or parallelized?: Parallelized using MPINo. of bytes in distributed program, including test data, etc.: 147163No. of lines in distributed program, including the test data, etc.: 14366Distribution format: gzipped tar fileNature of physical problem: A multitude of problems in science and engineering are often reduced to minimizing a function of many variables. There are instances that a local optimum does not correspond to the desired physical solution and hence the search for a better solution is required. Local optimization techniques can be trapped in any local minimum. Global Optimization is then the appropriate tool. For example, solving a non-linear system of equations via optimization, one may encounter many local minima that do not correspond to solutions, i.e. they are far from zeroMethod of solution: PANMIN is a suite of programs for Global Optimization that take advantage of the Merlin/MCL optimization environment [1,2]. We offer implementations of two algorithms that belong to the stochastic class and use local searches either as intermediate steps or as solution refinementRestrictions on the complexity of the problem: The only restriction is set by the available memory of the hardware configuration. The software can handle bound constrained problems. The Merlin Optimization environment must be installed. Availability of an MPI installation is necessary for executing the parallel codeTypical running time: Depending on the objective functionReferences: [1] D.G. Papageorgiou, I.N. Demetropoulos, I.E. Lagaris, Merlin-3.0. A multidimensional optimization environment, Comput. Phys. Commun. 109 (1998) 227-249. [2] D.G. Papageorgiou, I.N. Demetropoulos, I.E. Lagaris, The Merlin Control Language for strategic optimization, Comput. Phys. Commun. 109 (1998) 250-275.     

Stochastic optimization for the detection of changes in maternal heart rate kinetics during pregnancy

The stochastic optimization method ALOPEX IV has been successfully applied to the problem of detecting possible changes in the maternal heart rate kinetics during pregnancy. For this reason, maternal heart rate data were recorded before, during and after gestation, during sessions of exercises of constant mild intensity; ALOPEX IV stochastic optimization was used to calculate the parameter values that optimally fit a dynamical systems model to the experimental data. The results not only demonstrate the effectiveness of ALOPEX IV stochastic optimization, but also have important implications in the area of exercise physiology, as they reveal important changes in the maternal cardiovascular dynamics, as a result of pregnancy.     

Stochastic optimization for a tip-tilt adaptive correcting system

We present computer simulations of a tip-tilt adaptive optics system, where stochastic optimization is applied to the problem of dynamic compensation of atmospheric turbulence. The system uses a simple measure of the light intensity that passes through a mask and is recorded on the image plane, to generate signals for the tip-tilt mirror. A feedback system rotates the mirror adaptively and in phase with the rapidly changing atmospheric conditions. Computer simulations and a series of numerical experiments investigate the implementation of the method in the presence of drifting atmosphere. In particular, the study examines the system's sensitivity to the rate of change of the atmospheric conditions and investigates the optimal size of the mirror's masking area and the algorithm's optimal degree of stochasticity.     

A Multiobjective Optimization Model for Dynamic Reconfiguration of Ring Topologies with Stochastic Load

In this paper we describe a heuristic procedure to generate solutions to a multiobjective stochastic, optimization problem for a dynamic telecommunications network. Generating Pareto optimal solutions can be difficult since the optimization problem is computationally challenging and moreover the network must be reconfigured in near real time, for example, to recover connectivity after a severe weather event. There are two main contributions of this paper. First, we show mathematically how a certain deterministic equivalent optimization problem can be solved instead of the stochastic one, thus facilitating computations. Second, we test our heuristic under a wide set of simulated conditions (e.g., atmospheric obscuration due to differing levels of cloud cover, different demand patterns) and show that it achieves near Pareto optimality in a short amount of time.     

3级网状随机性库存控制策略的仿真优化

研究了多制造商,多分销商和多零售商的3级网状随机性库存系统的(r,Q)库存控制策略问题.由于该系统具有顾客到达时间服从泊松分布,随机顾客需求量,随机顾客购买行为,随机订货时间和制造商生产容量有限制等特点,使得解析方法很难描述系统中的多种复杂随机因素并无法求解有效的库存控制策略.为此建立了以总成本最小为目标的数学模型,运用了基于仿真的优化方法,通过将仿真方法与粒子群优化算法相结合对问题进行求解.最后通过仿真实例与比较,验证了模型和基于仿真的粒子群优化方法的可行性和有效性.也表明了基于仿真的优化方法在供应链管理中的适用性.     

面向全局搜索的自适应领导者樽海鞘群算法

针对实际配送过程中客户需求、车辆服务时间随机可变,提出带软时间窗的随机需求和随机服务时间的车辆路径问题.以配送车辆行驶路径为研究对象,建立基于配送成本、时间惩罚成本、修正成本的配送车辆路径优化模型,并提出一种混合禁忌搜索算法.该算法将最近邻算法和禁忌搜索算法相结合,将时间窗宽度及距离作为最近邻算法中节点选择标准;并对禁忌搜索算法中禁忌长度等构成要素进行自适应调整,引入自适应惩罚系数.实验结果表明,改进后的混合禁忌搜索算法具有较强的寻优能力、较高的鲁棒性,同时算法所得车辆行驶路径受客户需求变动影响较小.     

模糊需求下时间依赖型车辆路径优化

针对客户需求模糊且有时间窗约束的时间依赖型车辆路径问题(TDVRP),基于先预优化后重调度的思想构建模型.在预优化阶段,依据可信性理论构建模糊机会约束优化模型处理客户点模糊需求;针对不同时间段道路的交通情况,采用Ichoua速度时间依赖函数表征车辆的行驶速度,并设计自适应大规模邻域搜索算法(ALNS)对其求解.在重调度阶段,应用随机模拟算法模拟客户点的真实需求,采用点重调度策略对预优化方案进行调整.通过改进的Solomon算例实验验证模型和算法的有效性.研究成果可丰富TDVRP问题的相关研究,为现实配送方案的优化决策提供理论依据.     

Analyzing a lost-sale stochastic inventory model with Markov-modulated demands: A simulation-based optimization study

A consumer demand that presents auto-correlated components is a class of demand commonly found in competitive markets in which consumers may develop preferences for certain products which influence their willingness to purchase them again. This behavior may be observed in inventory systems whose products are subject to promotion plans in which mechanisms that incentivize the demand are implemented. Inventory systems that ignore these dependency components may severely impair their performance. This paper analyzes a stochastic inventory model where the control review system is periodic, is categorized as a lost-sale case, and is exposed to this class of auto-correlated demand pattern. The demand for products is characterized as a discrete Markov-modulated demand in which product quantities of the same item may relate to one another according to an empirical probability distribution. A simulation-based optimization that combines simulated annealing, pattern search, and ranking and selection (SAPS&RS) methods to approximate near-optimal solutions to this problem is employed. Lower and upper bounds for a range of near-optimal solutions are determined by the pattern search step enhanced by ranking and selection—indifferent zone. Results indicate that inventory performance significantly declines as the autocorrelation increases and is disregarded.     

A new real-coded stochastic Bayesian optimization algorithm for continuous global optimization

Estimation of distribution algorithms are considered to be a new class of evolutionary algorithms which are applied as an alternative to genetic algorithms. Such algorithms sample the new generation from a probabilistic model of promising solutions. The search space of the optimization problem is improved by such probabilistic models. In the Bayesian optimization algorithm (BOA), the set of promising solutions forms a Bayesian network and the new solutions are sampled from the built Bayesian network. This paper proposes a novel real-coded stochastic BOA for continuous global optimization by utilizing a stochastic Bayesian network. In the proposed algorithm, the new Bayesian network takes advantage of using a stochastic structure (that there is a probability distribution function for each edge in the network) and the new generation is sampled from the stochastic structure. In order to generate a new solution, some new structure, and therefore a new Bayesian network is sampled from the current stochastic structure and the new solution will be produced from the sampled Bayesian network. Due to the stochastic structure used in the sampling phase, each sample can be generated based on a different structure. Therefore the different dependency structures can be preserved. Before the new generation is generated, the stochastic network’s probability distributions are updated according to the fitness evaluation of the current generation. The proposed method is able to take advantage of using different dependency structures through the sampling phase just by using one stochastic structure. The experimental results reported in this paper show that the proposed algorithm increases the quality of the solutions on the general optimization benchmark problems.     

Simulation optimization approach for hybrid flow shop scheduling problem in semiconductor back-end manufacturing

This study presents a simulation optimization approach for a hybrid flow shop scheduling problem in a real-world semiconductor back-end assembly facility. The complexity of the problem is determined based on demand and supply characteristics. Demand varies with orders characterized by different quantities, product types, and release times. Supply varies with the number of flexible manufacturing routes but is constrained in a multi-line/multi-stage production system that contains certain types and numbers of identical and unrelated parallel machines. An order is typically split into separate jobs for parallel processing and subsequently merged for completion to reduce flow time. Split jobs that apply the same qualified machine type per order are compiled for quality and traceability. The objective is to achieve the feasible minimal flow time by determining the optimal assignment of the production line and machine type at each stage for each order. A simulation optimization approach is adopted due to the complex and stochastic nature of the problem. The approach includes a simulation model for performance evaluation, an optimization strategy with application of a genetic algorithm, and an acceleration technique via an optimal computing budget allocation. Furthermore, scenario analyses of the different levels of demand, product mix, and lot sizing are performed to reveal the advantage of simulation. This study demonstrates the value of the simulation optimization approach for practical applications and provides directions for future research on the stochastic hybrid flow shop scheduling problem.     

On stochastic dynamic programming for solving large-scale planning problems under uncertainty

The stochastic dynamic programming approach outlined here, makes use of the scenario tree in a back-to-front scheme. The multi-period stochastic problems, related to the subtrees whose root nodes are the starting nodes (i.e., scenario groups), are solved at each given stage along the time horizon. Each subproblem considers the effect of the stochasticity of the uncertain parameters from the periods of the given stage, by using curves that estimate the expected future value (EFV) of the objective function. Each subproblem is solved for a set of reference levels of the variables that also have nonzero elements in any of the previous stages besides the given stage. An appropriate sensitivity analysis of the objective function for each reference level of the linking variables allows us to estimate the EFV curves applicable to the scenario groups from the previous stages, until the curves for the first stage have been computed. An application of the scheme to the problem of production planning with logical constraints is presented. The aim of the problem consists of obtaining the planning of tactical production over the scenarios along the time horizon. The expected total cost is minimized to satisfy the product demand. Some computational experience is reported. The proposed approach compares favorably with a state-of-the-art optimization engine in instances on a very large scale.     

Finite Horizon Minimax Optimal Control of Stochastic Partially Observed Time Varying Uncertain Systems

We consider a linear-quadratic problem of minimax optimal control for stochastic uncertain control systems with output measurement. The uncertainty in the system satisfies a stochastic integral quadratic constraint. To convert the constrained optimization problem into an unconstrained one, a special S-procedure is applied. The resulting unconstrained game-type optimization problem is then converted into a risk-sensitive stochastic control problem with an exponential-of-integral cost functional. This is achieved via a certain duality relation between stochastic dynamic games and risk-sensitive stochastic control. The solution of the risk-sensitive stochastic control problem in terms of a pair of differential matrix Riccati equations is then used to establish a minimax optimal control law for the original uncertain system with uncertainty subject to the stochastic integral quadratic constraint. Date received: May 13, 1997. Date revised: March 18, 1998.     

需求随机的变质性产品生产计划模型

研究了能力约束的有限计划展望期生产计划问题,各周期的需求随机,库存产品存在变质且变质率为常数。建立了问题的期望值模型,目标函数为极小化生产准备成本、生产成本、库存成本的期望值。提出了随机模拟、遗传算法和启发式算法相结合的求解算法。用数值实例对模型和算法进行了验证,优化结果表明模型和算法是有效的。     

An effective heuristic algorithm for the maximum satisfiability problem

Stochastic local search algorithms (SLS) have been increasingly applied to approximate solutions of the weighted maximum satisfiability problem (MAXSAT), a model for solutions of major problems in AI and combinatorial optimization. While MAXSAT instances have generally a strong intrinsic dependency between their variables, most of SLS algorithms start the search process with a random initial solution where the value of each variable is generated independently with the same uniform distribution. In this paper, we propose a new SLS algorithm for MAXSAT based on an unconventional distribution known as the Bose-Einstein distribution in quantum physics. It provides a stochastic initialization scheme to an efficient and very simple heuristic inspired by the co-evolution process of natural species and called Extremal Optimization (EO). This heuristic was introduced for finding high quality solutions to hard optimization problems such as colouring and partitioning. We examine the effectiveness of the resulting algorithm by computational experiments on a large set of test instances and compare it with some of the most powerful existing algorithms. Our results are remarkable and show that this approach is appropriate for this class of problems.     

Stochastic Model of the Electric Power Purchase System on a Railway Segment

Proposed was a mathematical optimization model of the power supply system of a railway segment where the electric power is bought from more than one supplier with allowance for the random demand. Consideration was given to several time periods with different tariffs for electric power. The system model represents a two-step problem of stochastic programming with a quantile criterion. At its first step, a primary purchase plan is generated. At the second step, an additional purchase is done to compensate for the lack of electric power arising because of the random demand. The model takes into consideration the losses arising at transmitting the electric power from the supplier to the segment, as well as the pent-up demand. The total operational costs of the power supply system under consideration are minimized. An algorithm was proposed to solve the problem by reducing the stated problem by discretizing the probabilistic measure and confidence method to the problem of mixed integer linear programming. A model example was discussed.     

Exploring the economic consequences of letting a supplier hold reserve storage

We consider a single-item, periodic review inventory control problem with discrete non-stationary stochastic demand. The time horizon is finite and all shortages at the downstream level are backordered. There are two modes of supply: a normal supplier and a reserve storage supply. The reserve storage is capacitated and the downstream buyer can only order the entire inventory in the reserve storage or nothing. If the reserve storage is empty, it takes a fixed time interval before it is replenished again. Provided that the reserve storage is fully replenished it can be used at any time period, whereas orders to the normal supplier can only be issued at specific time periods. The lead time from the reserve storage is shorter than from the normal supplier, but using the reserve storage is more expensive than using the normal supplier. We use stochastic dynamic programming to specify an exact model of the problem. We also develop an approximate model which is computationally faster than the first model. The models are then used to analyze numerically the sensitivity with respect to key parameters like the reserve storage size and unit purchase cost. This paper is motivated by a problem presented during contacts with a leading Danish provider of communications solutions.     

Marking optimization of stochastic timed event graphs using IPA

This paper addresses the marking optimization of stochastic timed event graphs, where the transition firing times are generated by random variables with general distributions. The marking optimization problem consists of obtaining a given cycle time while minimizing a p-invariant criterion. We propose two heuristic algorithms, both starting from the optimal solution to the associated deterministic problem and iteratively adding tokens to adequate places as long as the given cycle time is not obtained. Infinitesimal perturbation analysis of the average cycle time with respect to the transition firing times is used to identify the appropriate places in which new tokens are added at each iteration. Numerical results show that the heuristic algorithms provide solutions better than the ones obtained by the existing methods.     

Energy reduction of stochastic time-constrained robot stations

This paper looks at the problem of reducing the energy use of robot movements in a robot station with stochastic execution times, while keeping the productivity of the station. The problem is formulated as a stochastic optimization problem, that constrains the makespan of the station to meet a deadline with a high probability. The energy use of the station is a function of the execution times of the robot operations, and the goal is to reduce this energy use by finding the optimal execution times and operation order. A theoretical motivation to why the stochastic variables in the problem, under some conditions, can be approximated as independent and normally distributed is presented, together with a derivation of the max function of stochastic variables. This allows the stochastic optimization problem to be approximated with a deterministic version, that can be solved with a commercial solver. The accuracy of the deterministic approximation is evaluated on multiple numerical examples, which show that the method successfully reduces the energy use, while the deadlines of the stations are met with high probabilities.