Stochastic programming based multi-arm bandit offloading strategy for internet of things

In order to solve the high latency of traditional cloud computing and the processing capacity limitation of Internet of Things(IoT)users,Multi-access Edge Computing(MEC)migrates computing and storage capabilities from the remote data center to the edge of network,providing users with computation services quickly and directly.In this paper,we investigate the impact of the randomness caused by the movement of the IoT user on decision-making for offloading,where the connection between the IoT user and the MEC servers is uncertain.This uncertainty would be the main obstacle to assign the task accurately.Consequently,if the assigned task cannot match well with the real connection time,a migration(connection time is not enough to process)would be caused.In order to address the impact of this uncertainty,we formulate the offloading decision as an optimization problem considering the transmission,computation and migration.With the help of Stochastic Programming(SP),we use the posteriori recourse to compensate for inaccurate predictions.Meanwhile,in heterogeneous networks,considering multiple candidate MEC servers could be selected simultaneously due to overlapping,we also introduce the Multi-Arm Bandit(MAB)theory for MEC selection.The extensive simulations validate the improvement and effectiveness of the proposed SP-based Multi-arm bandit Method(SMM)for offloading in terms of reward,cost,energy consumption and delay.The results showthat SMMcan achieve about 20%improvement compared with the traditional offloading method that does not consider the randomness,and it also outperforms the existing SP/MAB based method for offloading.

Foreign exchange trading and management with the stochastic dual dynamic programming method

We present a novel tool for generating speculative and hedging foreign exchange(FX)trading policies.Our solution provides a schedule that determines trades in each rebalancing period based on future currency prices,net foreign account positions,and incoming(outgoing)flows from business operations.To obtain such policies,we construct a multistage stochastic programming(MSP)model and solve it using the stochastic dual dynamic programming(SDDP)numerical method,which specializes in solving high-dimensional MSP models.We construct our methodology within an open-source SDDP package,avoiding implementing the method from scratch.To measure the performance of our policies,we model FX prices as a mean-reverting stochastic process with random events that incorporate stochastic trends.We calibrate this price model on seven currency pairs,demonstrating that our trading policies not only outperform the benchmarks for each currency,but may also be close to ex-post optimal solutions.We also show how the tool can be used to generate more or less conservative strategies by adjusting the risk tolerance,and how it can be used in a vari-ety of contexts and time scales,ranging from intraday speculative trading to monthly hedging for business operations.Finally,we examine the impact of increasing trade policy uncertainty(TPU)levels on our findings.Our findings show that the volatility of currencies from emerging economies rises in comparison to currencies from devel-oped markets.We discover that an increase in the TPU level has no effect on the aver-age profit obtained by our method.However,the risk exposure of the policies increases(decreases)for the group of currencies from emerging(developed)markets.

Multistage Stochastic Programming Model for the Portfolio Problem of a Property-Liability Insurance Company

The current portfolio model for property-liability insurance company is only single period that can not meet the practical demands of portfolio management, and the purpose of this paper is to develop a multiperiod model for its portfolio problem. The model is a multistage stochastic programming which considers transaction costs, cash flow between time periods, and the matching of asset and liability; it does not depend on the assumption for normality of return distribution. Additionally, an investment constraint is added. The numerical example manifests that the multiperiod model can more effectively assist the property-liability insurer to determine the optimal composition of insurance and investment portfolio and outperforms the single period one.

Improved Unit Commitment with Accurate Dynamic Scenarios Clustering Based on Multi-Parametric Programming and Benders Decomposition

Stochastic unit commitment is one of the most powerful methods to address uncertainty. However, the existingscenario clustering technique for stochastic unit commitment cannot accurately select representative scenarios,which threatens the robustness of stochastic unit commitment and hinders its application. This paper providesa stochastic unit commitment with dynamic scenario clustering based on multi-parametric programming andBenders decomposition. The stochastic unit commitment is solved via the Benders decomposition, which decouplesthe primal problem into the master problem and two types of subproblems. In the master problem, the committedgenerator is determined, while the feasibility and optimality of generator output are checked in these twosubproblems. Scenarios are dynamically clustered during the subproblem solution process through the multiparametric programming with respect to the solution of the master problem. In other words, multiple scenariosare clustered into several representative scenarios after the subproblem is solved, and the Benders cut obtainedby the representative scenario is generated for the master problem. Different from the conventional stochasticunit commitment, the proposed approach integrates scenario clustering into the Benders decomposition solutionprocess. Such a clustering approach could accurately cluster representative scenarios that have impacts on theunit commitment. The proposed method is tested on a 6-bus system and the modified IEEE 118-bus system.Numerical results illustrate the effectiveness of the proposed method in clustering scenarios. Compared withthe conventional clustering method, the proposed method can accurately select representative scenarios whilemitigating computational burden, thus guaranteeing the robustness of unit commitment.

Using Return and Risk Model for Choosing Perfect Portfolio Applied Study in Cairo Stock Exchange

Modern financial theory, commonly known as portfolio theory, provides an analytical framework for the investment decision to be made under uncertainty. It is a well-established proposition in portfolio theory that whenever there is an imperfect correlation between returns risk is reduced by maintaining only a portion of wealth in any asset, or by selecting a portfolio according to expected returns and correlations between returns. The major improvement of the portfolio approaches over prior received theory is the incorporation of 1) the riskiness of an asset and 2) the addition from investing in any asset. The theme of this paper is to discuss how to propose a new mathematical model like that provided by Markowitz, which helps in choosing a nearly perfect portfolio and an efficient input/output. Besides applying this model to reality, the researcher uses game theory, stochastic and linear programming to provide the model proposed and then uses this model to select a perfect portfolio in the Cairo Stock Exchange. The results are fruitful and the researcher considers this model a new contribution to previous models.

A Stochastic Programming Strategy in Microgrid Cyber Physical Energy System for Energy Optimal Operation

This paper focuses on the energy optimal operation problem of microgrids (MGs) under stochastic environment. The deterministic method of MGs operation is often uneconomical because it fails to consider the high randomness of unconventional energy resources. Therefore, it is necessary to develop a novel operation approach combining the uncertainty in the physical world with modeling strategy in the cyber system. This paper proposes an energy scheduling optimization strategy based on stochastic programming model by considering the uncertainty in MGs. The goal is to minimize the expected operation cost of MGs. The uncertainties are modeled based on autoregressive moving average (ARMA) model to expose the effects of physical world on cyber world. Through the comparison of the simulation results with deterministic method, it is shown that the effectiveness and robustness of proposed stochastic energy scheduling optimization strategy for MGs are valid. © 2014 Chinese Association of Automation.

A simulation-based two-stage interval-stochastic programming model for water resources management in Kaidu-Konqi watershed,China

This study presented a simulation-based two-stage interval-stochastic programming （STIP） model to support water resources management in the Kaidu-Konqi watershed in Northwest China. The modeling system coupled a distributed hydrological model with an interval two-stage stochastic programing （ITSP）. The distributed hydrological model was used for establishing a rainfall-runoff forecast system, while random parameters were pro- vided by the statistical analysis of simulation outcomes water resources management planning in Kaidu-Konqi The developed STIP model was applied to a real case of watershed, where three scenarios with different water re- sources management policies were analyzed. The results indicated that water shortage mainly occurred in agri- culture, ecology and forestry sectors. In comparison, the water demand from municipality, industry and stock- breeding sectors can be satisfied due to their lower consumptions and higher economic values. Different policies for ecological water allocation can result in varied system benefits, and can help to identify desired water allocation plans with a maximum economic benefit and a minimum risk of system disruption under uncertainty.

A NEW STOCHASTIC OPTIMAL CONTROL STRATEGY FOR HYSTERETIC MR DAMPERS

A new stochastic optimal control strategy for randomly excited quasi-integrable Hamiltonian systems using magneto-rheological (MR) dampers is proposed. The dynamic be- havior of an MR damper is characterized by the Bouc-Wen hysteretic model. The control force produced by the MR damper is separated into a passive part incorporated in the uncontrolled system and a semi-active part to be determined. The system combining the Bouc-Wen hysteretic force is converted into an equivalent non-hysteretic nonlinear stochastic control system. Then It?o stochastic di?erential equations are derived from the equivalent system by using the stochastic averaging method. A dynamical programming equation for the controlled di?usion processes is established based on the stochastic dynamical programming principle. The non-clipping nonlin- ear optimal control law is obtained for a certain performance index by minimizing the dynamical programming equation. Finally, an example is given to illustrate the application and e?ectiveness of the proposed control strategy.

Stochastic optimization of mine production scheduling with uncertain ore/metal/waste supply

Optimization of long-term mine production scheduling in open pit mines deals with the management of cash flows, typically in the order of hundreds of millions of dollars. Conventional mine scheduling utilizes optimization methods that are not capable of accounting for inherent technical uncertainties such as uncertainty in the expected ore/metal supply from the underground, acknowledged to be the most critical factor. To integrate ore/metal uncertainty into the optimization of mine production scheduling a stochastic integer programming(SIP) formulation is tested at a copper deposit. The stochastic solution maximizes the economic value of a project and minimizes deviations from production targets in the presence of ore/metal uncertainty. Unlike the conventional approach, the SIP model accounts and manages risk in ore supply, leading to a mine production schedule with a 29% higher net present value than the schedule obtained from the conventional, industry-standard optimization approach, thus contributing to improving the management and sustainable utilization of mineral resources.

Archery Algorithm:A Novel Stochastic Optimization Algorithm for Solving Optimization Problems

Finding a suitable solution to an optimization problem designed in science is a major challenge.Therefore,these must be addressed utilizing proper approaches.Based on a random search space,optimization algorithms can find acceptable solutions to problems.Archery Algorithm(AA)is a new stochastic approach for addressing optimization problems that is discussed in this study.The fundamental idea of developing the suggested AA is to imitate the archer’s shooting behavior toward the target panel.The proposed algorithm updates the location of each member of the population in each dimension of the search space by a member randomly marked by the archer.The AA is mathematically described,and its capacity to solve optimization problems is evaluated on twenty-three distinct types of objective functions.Furthermore,the proposed algorithm’s performance is compared vs.eight approaches,including teaching-learning based optimization,marine predators algorithm,genetic algorithm,grey wolf optimization,particle swarm optimization,whale optimization algorithm,gravitational search algorithm,and tunicate swarm algorithm.According to the simulation findings,the AA has a good capacity to tackle optimization issues in both unimodal and multimodal scenarios,and it can give adequate quasi-optimal solutions to these problems.The analysis and comparison of competing algorithms’performance with the proposed algorithm demonstrates the superiority and competitiveness of the AA.

Two-stage stochastic approach for spinning reserve allocation in dynamic economic dispatch

A novel approach was proposed to allocate spinning reserve for dynamic economic dispatch.The proposed approach set up a two-stage stochastic programming model to allocate reserve.The model was solved using a decomposed algorithm based on Benders' decomposition.The model and the algorithm were applied to a simple 3-node system and an actual 445-node system for verification,respectively.Test results show that the model can save 84.5 US $ cost for the testing three-node system,and the algorithm can solve the model for 445-node system within 5 min.The test results also illustrate that the proposed approach is efficient and suitable for large system calculation.

An Artificial Intelligence Approach for Solving Stochastic Transportation Problems

Recent years witness a great deal of interest in artificial intelligence(AI)tools in the area of optimization.AI has developed a large number of tools to solve themost difficult search-and-optimization problems in computer science and operations research.Indeed,metaheuristic-based algorithms are a sub-field of AI.This study presents the use of themetaheuristic algorithm,that is,water cycle algorithm(WCA),in the transportation problem.A stochastic transportation problem is considered in which the parameters supply and demand are considered as random variables that follow the Weibull distribution.Since the parameters are stochastic,the corresponding constraints are probabilistic.They are converted into deterministic constraints using the stochastic programming approach.In this study,we propose evolutionary algorithms to handle the difficulties of the complex high-dimensional optimization problems.WCA is influenced by the water cycle process of how streams and rivers flow toward the sea(optimal solution).WCA is applied to the stochastic transportation problem,and obtained results are compared with that of the new metaheuristic optimization algorithm,namely the neural network algorithm which is inspired by the biological nervous system.It is concluded that WCA presents better results when compared with the neural network algorithm.

Two-Stage Production Planning Under Stochastic Demand:Case Study of Fertilizer Manufacturing

Agriculture is a key facilitator of economic prosperity and nourishes the huge global population.To achieve sustainable agriculture,several factors should be considered,such as increasing nutrient and water efficiency and/or improving soil health and quality.Using fertilizer is one of the fastest and easiest ways to improve the quality of nutrients inland and increase the effectiveness of crop yields.Fertilizer supplies most of the necessary nutrients for plants,and it is estimated that at least 30%-50%of crop yields is attributable to commercial fertilizer nutrient inputs.Fertilizer is always a major concern in achieving sustainable and efficient agriculture.Applying reasonable and customized fertilizerswill require a significant increase in the number of formulae,involving increasing costs and the accurate forecasting of the right time to apply the suitable formulae.An alternative solution is given by two-stage production planning under stochastic demand,which divides a planning schedule into two stages.The primary stage has non-existing demand information,the inputs of which are the proportion of raw materials needed for producing fertilizer products,the cost for purchasing materials,and the production cost.The total quantity of purchased material and produced products to be used in the blending process must be defined to meet as small as possible a paid cost.At the second stage,demand appears under multiple scenarios and their respective possibilities.This stage will provide a solution for each occurring scenario to achieve the best profit.The two-stage approach is presented in this paper,the mathematical model of which is based on linear integer programming.Considering the diversity of fertilizer types,themathematicalmodel can advise manufacturers about which products will generate as much as profit as possible.Specifically,two objectives are taken into account.First,the paper’s thesis focuses on minimizing overall system costs,e.g.,including inventory cost,purchasing cost,unit cost,and ordering cost at Stage 1.Second,the thesis pays attention tomaximizing total profit based on information from customer demand,as well as being informed regarding concerns about system cost at Stage 2.

Approximation-Exact Penalty Function Method for Solving a Class of Stochastic Programming

We present an approximation-exact penalty function method for solving the single stage stochastic programming problem with continuous random variable. The original problem is transformed into a determinate nonlinear programming problem with a discrete random variable sequence, which is obtained by some discrete method. We construct an exact penalty function and obtain an unconstrained optimization. It avoids the difficulty in solution by the rapid growing of the number of constraints for discrete precision. Under lenient conditions, we prove the equivalence of the minimum solution of penalty function and the solution of the determinate programming, and prove that the solution sequences of the discrete problem converge to a solution to the original problem.

AN INEXACT LAGRANGE-NEWTON METHOD FOR STOCHASTIC QUADRATIC PROGRAMS WITH RECOURSE

In this paper,two-stage stochastic quadratic programming problems with equality constraints are considered.By Monte Carlo simulation-based approximations of the objective function and its first(second)derivative,an inexact Lagrange-Newton type method is proposed.It is showed that this method is globally convergent with probability one.In particular,the convergence is local superlinear under an integral approximation error bound condition.Moreover,this method can be easily extended to solve stochastic quadratic programming problems with inequality constraints.

Gaining-Sharing Knowledge Based Algorithm for Solving Stochastic Programming Problems

This paper presents a novel application of metaheuristic algorithmsfor solving stochastic programming problems using a recently developed gaining sharing knowledge based optimization (GSK) algorithm. The algorithmis based on human behavior in which people gain and share their knowledgewith others. Different types of stochastic fractional programming problemsare considered in this study. The augmented Lagrangian method (ALM)is used to handle these constrained optimization problems by convertingthem into unconstrained optimization problems. Three examples from theliterature are considered and transformed into their deterministic form usingthe chance-constrained technique. The transformed problems are solved usingGSK algorithm and the results are compared with eight other state-of-the-artmetaheuristic algorithms. The obtained results are also compared with theoptimal global solution and the results quoted in the literature. To investigatethe performance of the GSK algorithm on a real-world problem, a solidstochastic fixed charge transportation problem is examined, in which theparameters of the problem are considered as random variables. The obtainedresults show that the GSK algorithm outperforms other algorithms in termsof convergence, robustness, computational time, and quality of obtainedsolutions.

Stochastic Programming For Order Allocation And Production Planning

Stochastic demand is an important factor that heavily affects production planning.It influences activities such as purchasing,manufacturing,and selling,and quick adaption is required.In production planning,for reasons such as reducing costs and obtaining supplier discounts,many decisions must be made in the initial stage when demand has not been realized.The effects of non-optimal decisions will propagate to later stages,which can lead to losses due to overstocks or out-of-stocks.To find the optimal solutions for the initial and later stage regarding demand realization,this study proposes a stochastic two-stage linear program-ming model for a multi-supplier,multi-material,and multi-product purchasing and production planning process.The objective function is the expected total cost after two stages,and the results include detailed plans for purchasing and production in each demand scenario.Small-scale problems are solved through a deterministic equivalent transformation technique.To solve the problems in the large scale,an algorithm combining metaheuristic and sample average approximation is suggested.This algorithm can be implemented in parallel to utilize the power of the solver.The algorithm based on the observation that if the remaining quantity of materials and number of units of products at the end of the initial stage are given,then the problems of the first and second stages can be decomposed.

STOCHASTIC GENERALIZED GOAL PROGRAMMING

This thesis presents the combination of the stochastic programming and generalized goal programming. We puts forward several generalized goal programming models with stochastic parameter--stochastic generalized goal programming. Furthermore, we probe into the theory. and algorithm of these models. At last, this method was applied to an example of an industrial problem.

A Complex Algorithm for Solving a Kind of Stochastic Programming

Considering that the probability distribution of random variables in stochastic programming usually has incomplete information due to a perfect sample data in many real applications, this paper discusses a class of two-stage stochastic programming problems modeling with maximum minimum expectation compensation criterion (MaxEMin) under the probability distribution having linear partial information (LPI). In view of the nondifferentiability of this kind of stochastic programming modeling, an improved complex algorithm is designed and analyzed. This algorithm can effectively solve the nondifferentiable stochastic programming problem under LPI through the variable polyhedron iteration. The calculation and discussion of numerical examples show the effectiveness of the proposed algorithm.

Stochastic optimal control of cable vibration in plane by using axial support motion

A stochastic optimal control strategy for a slightly sagged cable using support motion in the cable axial direction is proposed. The nonlinear equation of cable motion in plane is derived and reduced to the equations for the first two modes of cable vibration by using the Galerkin method. The partially averaged Ito equation for controlled system energy is further derived by applying the stochastic averaging method for quasi-non-integrable Hamiltonian systems. The dynamical programming equation for the controlled system energy with a performance index is established by applying the stochastic dynamical programming principle and a stochastic optimal control law is obtained through solving the dynamical programming equation. A bilinear controller by using the direct method of Lyapunov is introduced. The comparison between the two controllers shows that the proposed stochastic optimal control strategy is superior to the bilinear control strategy in terms of higher control effectiveness and efficiency.