We are investigating the distributed optimization problem,where a network of nodes works together to minimize a global objective that is a finite sum of their stored local functions.Since nodes exchange optimization p...We are investigating the distributed optimization problem,where a network of nodes works together to minimize a global objective that is a finite sum of their stored local functions.Since nodes exchange optimization parameters through the wireless network,large-scale training models can create communication bottlenecks,resulting in slower training times.To address this issue,CHOCO-SGD was proposed,which allows compressing information with arbitrary precision without reducing the convergence rate for strongly convex objective functions.Nevertheless,most convex functions are not strongly convex(such as logistic regression or Lasso),which raises the question of whether this algorithm can be applied to non-strongly convex functions.In this paper,we provide the first theoretical analysis of the convergence rate of CHOCO-SGD on non-strongly convex objectives.We derive a sufficient condition,which limits the fidelity of compression,to guarantee convergence.Moreover,our analysis demonstrates that within the fidelity threshold,this algorithm can significantly reduce transmission burden while maintaining the same convergence rate order as its no-compression equivalent.Numerical experiments further validate the theoretical findings by demonstrating that CHOCO-SGD improves communication efficiency and keeps the same convergence rate order simultaneously.And experiments also show that the algorithm fails to converge with low compression fidelity and in time-varying topologies.Overall,our study offers valuable insights into the potential applicability of CHOCO-SGD for non-strongly convex objectives.Additionally,we provide practical guidelines for researchers seeking to utilize this algorithm in real-world scenarios.展开更多
This paper considers distributed stochastic optimization,in which a number of agents cooperate to optimize a global objective function through local computations and information exchanges with neighbors over a network...This paper considers distributed stochastic optimization,in which a number of agents cooperate to optimize a global objective function through local computations and information exchanges with neighbors over a network.Stochastic optimization problems are usually tackled by variants of projected stochastic gradient descent.However,projecting a point onto a feasible set is often expensive.The Frank-Wolfe(FW)method has well-documented merits in handling convex constraints,but existing stochastic FW algorithms are basically developed for centralized settings.In this context,the present work puts forth a distributed stochastic Frank-Wolfe solver,by judiciously combining Nesterov's momentum and gradient tracking techniques for stochastic convex and nonconvex optimization over networks.It is shown that the convergence rate of the proposed algorithm is O(k^(-1/2))for convex optimization,and O(1/log_(2)(k))for nonconvex optimization.The efficacy of the algorithm is demonstrated by numerical simulations against a number of competing alternatives.展开更多
The contribution deals with the optimization of a sequential preventive maintenance schedule of a technical device. We are given an initial time-to-failure probability distribution, model of changes of this distributi...The contribution deals with the optimization of a sequential preventive maintenance schedule of a technical device. We are given an initial time-to-failure probability distribution, model of changes of this distribution after maintenance actions, as well as the costs of maintenance, of a device acquisition, and of the impact of failure. The maintenance timing and, eventually, its extent, are the matter of optimization. The objective of the contribution is two-fold: first, to formulate a proper (random) objective function evaluating the lifetime of the maintained device relatively to maintenance costs;second, to propose a numerical method searching for a maintenance policy optimizing selected characteristics of this objective function. The method is based on the MCMC random search combined with simulated annealing. It is also shown that such a method is rather universal for different problem specifications. The approach will be illustrated on an artificial example dealing with accelerated lifetime after each maintenance action.展开更多
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 ...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.展开更多
Stochastic optimization offers a means of considering the objectives and constrains with stochastic parameters. However, it is generally difficult to solve the stochastic optimization problem by employing conventional...Stochastic optimization offers a means of considering the objectives and constrains with stochastic parameters. However, it is generally difficult to solve the stochastic optimization problem by employing conventional methods for nonlinear programming when the number of random variables involved is very large. Neural network models and algorithms were applied to solve the stochastic optimization problem on the basis of the stability theory. Stability for stochastic programs was discussed. If random vector sequence converges to the random vector in the original problem in distribution, the optimal value of the corresponding approximation problems converges to the optimal value of the original stochastic optimization problem.展开更多
A two-stage mixed integer linear programming model(MILP)incorporating a novel method of stochastic scenario generation was proposed in order to optimize the economic performance of the synergistic combination of midst...A two-stage mixed integer linear programming model(MILP)incorporating a novel method of stochastic scenario generation was proposed in order to optimize the economic performance of the synergistic combination of midstream and downstream petrochemical supply chain.The uncertainty nature of the problem intrigued the parameter estimation,which was conducted through discretizing the assumed probability distribution of the stochastic parameters.The modeling framework was adapted into a real-world scale of petrochemical enterprise and fed into optimization computations.Comparisons between the deterministic model and stochastic model were discussed,and the influences of the cost components on the overall profit were analyzed.The computational results demonstrated the rationality of using reasonable numbers of scenarios to approximate the stochastic optimization problem.展开更多
A stochastic control model is studied.The objective of the investor is to maximize expected utility from terminalconsumption.However,the investor possesses informa-tion about the terminal values of the components of t...A stochastic control model is studied.The objective of the investor is to maximize expected utility from terminalconsumption.However,the investor possesses informa-tion about the terminal values of the components of the Brownian motion which drives securities’prices.With the method of stochastic control being applied,investor’s optimal decision is obtained.Especially,the logarith-展开更多
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 optimiza...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.展开更多
We provide a new simple approach to stochastic dynamic optimization. In doing so, we derive the existing (standard) results using a far simpler technique than the duality and the variational methods.
In this paper, an adaptive estimation algorithm is proposed for non-linear dynamic systems with unknown static parameters based on combination of particle filtering and Simultaneous Perturbation Stochastic Approximati...In this paper, an adaptive estimation algorithm is proposed for non-linear dynamic systems with unknown static parameters based on combination of particle filtering and Simultaneous Perturbation Stochastic Approximation (SPSA) technique. The estimations of parameters are obtained by maximum-likelihood estimation and sampling within particle filtering framework, and the SPSA is used for stochastic optimization and to approximate the gradient of the cost function. The proposed algorithm achieves combined estimation of dynamic state and static parameters of nonlinear systems. Simulation result demonstrates the feasibility and efficiency of the proposed algorithm.展开更多
The last three decades ha</span><span style="font-family:"">ve</span><span style="font-family:""> witnessed development of optimization under fuzziness and randomn...The last three decades ha</span><span style="font-family:"">ve</span><span style="font-family:""> witnessed development of optimization under fuzziness and randomness also called Fuzzy Stochastic Optimization. The main objective </span><span style="font-family:"">of </span><span style="font-family:"">this new field is the need for basing many human decisions on information which is both fuzzily imprecise and probabilistically uncertain. Consistency indexes providing a union nexus between possibilities and probabilities of uncertain events exist in the literature. Nevertheless, there are no reliable transformations between them. This calls for new paradigms for coping with mathematical models involving both fuzziness and randomness. Fuzzy Stochastic Optimization (FSO) is an attempt to fulfill this need. In this paper, we present a panoramic view of Fuzzy Stochastic Optimization emphasizing the methodological aspects. The merits of existing methods are also briefly discussed along with some related theoretical aspects.展开更多
Many difficult engineering problems cannot be solved by the conventional optimization techniques in practice.Direct searches that need no recourse to explicit derivatives are revived and become popular since the new c...Many difficult engineering problems cannot be solved by the conventional optimization techniques in practice.Direct searches that need no recourse to explicit derivatives are revived and become popular since the new century.In order to get a deep insight into this field,some notes on the direct searches for non-smooth optimization problems are made.The global convergence vs.local convergence and their influences on expected solutions for simulation-based stochastic optimization are pointed out.The sufficient and simple decrease criteria for step acceptance are analyzed,and why simple decrease is enough for globalization in direct searches is identified. The reason to introduce the positive spanning set and its usage in direct searches is explained.Other topics such as the generalization of direct searches to bound,linear and non-linear constraints are also briefly discussed.展开更多
In this paper,we address matrix-valued distributed stochastic optimization with inequality and equality constraints,where the objective function is a sum of multiple matrix-valued functions with stochastic variables a...In this paper,we address matrix-valued distributed stochastic optimization with inequality and equality constraints,where the objective function is a sum of multiple matrix-valued functions with stochastic variables and the considered problems are solved in a distributed manner.A penalty method is derived to deal with the constraints,and a selection principle is proposed for choosing feasible penalty functions and penalty gains.A distributed optimization algorithm based on the gossip model is developed for solving the stochastic optimization problem,and its convergence to the optimal solution is analyzed rigorously.Two numerical examples are given to demonstrate the viability of the main results.展开更多
The use of topology optimization in structural design under dynamic excitation is becoming more prevalent in the literature.While many such applications utilize frequency or time domain formulations,relatively few con...The use of topology optimization in structural design under dynamic excitation is becoming more prevalent in the literature.While many such applications utilize frequency or time domain formulations,relatively few consider stochastic dynamic excitations.This paper presents an efficient and compact code called TopSTO for structural topology optimization considering stationary stochastic dynamic loading using a method derived from random vibration theory.The theory,described in conjunction with the implementation in the provided code,is illustrated for a seismically excited building.This work demonstrates the efficiency of the approach in terms of both the computational resources and minimal amount of code required.This code is intended to serve as a baseline for understanding the theory and implementation of this topology optimization approach and as a foundation for additional applications and developments.展开更多
Currently,energy conservation draws wide attention in industrial manufacturing systems.In recent years,many studies have aimed at saving energy consumption in the process of manufacturing and scheduling is regarded as...Currently,energy conservation draws wide attention in industrial manufacturing systems.In recent years,many studies have aimed at saving energy consumption in the process of manufacturing and scheduling is regarded as an effective approach.This paper puts forwards a multi-objective stochastic parallel machine scheduling problem with the consideration of deteriorating and learning effects.In it,the real processing time of jobs is calculated by using their processing speed and normal processing time.To describe this problem in a mathematical way,amultiobjective stochastic programming model aiming at realizing makespan and energy consumption minimization is formulated.Furthermore,we develop a multi-objective multi-verse optimization combined with a stochastic simulation method to deal with it.In this approach,the multi-verse optimization is adopted to find favorable solutions from the huge solution domain,while the stochastic simulation method is employed to assess them.By conducting comparison experiments on test problems,it can be verified that the developed approach has better performance in coping with the considered problem,compared to two classic multi-objective evolutionary algorithms.展开更多
The accurate prediction of energy consumption has effective role in decision making and risk management for individuals and governments.Meanwhile,the accurate prediction can be realized using the recent advances in ma...The accurate prediction of energy consumption has effective role in decision making and risk management for individuals and governments.Meanwhile,the accurate prediction can be realized using the recent advances in machine learning and predictive models.This research proposes a novel approach for energy consumption forecasting based on a new optimization algorithm and a new forecasting model consisting of a set of long short-term memory(LSTM)units.The proposed optimization algorithm is used to optimize the parameters of the LSTM-based model to boost its forecasting accuracy.This optimization algorithm is based on the recently emerged dipper-throated optimization(DTO)and stochastic fractal search(SFS)algo-rithm and is referred to as dynamic DTOSFS.To prove the effectiveness and superiority of the proposed approach,five standard benchmark algorithms,namely,stochastic fractal search(SFS),dipper throated optimization(DTO),whale optimization algorithm(WOA),particle swarm optimization(PSO),and grey wolf optimization(GWO),are used to optimize the parameters of the LSTM-based model,and the results are compared with that of the proposed approach.Experimental results show that the proposed DDTOSFS+LSTM can accurately forecast the energy consumption with root mean square error RMSE of 0.00013,which is the best among the recorded results of the other methods.In addition,statistical experiments are conducted to prove the statistical difference of the proposed model.The results of these tests confirmed the expected outcomes.展开更多
To maximize energy profit with the participation of electricity,natural gas,and district heating networks in the day-ahead market,stochastic scheduling of energy hubs taking into account the uncertainty of photovoltai...To maximize energy profit with the participation of electricity,natural gas,and district heating networks in the day-ahead market,stochastic scheduling of energy hubs taking into account the uncertainty of photovoltaic and wind resources,has been carried out.This has been done using a new meta-heuristic algorithm,improved artificial rabbits optimization(IARO).In this study,the uncertainty of solar and wind energy sources is modeled using Hang’s two-point estimating method(TPEM).The IARO algorithm is applied to calculate the best capacity of hub energy equipment,such as solar and wind renewable energy sources,combined heat and power(CHP)systems,steamboilers,energy storage,and electric cars in the day-aheadmarket.The standard ARO algorithmis developed to mimic the foraging behavior of rabbits,and in this work,the algorithm’s effectiveness in avoiding premature convergence is improved by using the dystudynamic inertia weight technique.The proposed IARO-based scheduling framework’s performance is evaluated against that of traditional ARO,particle swarm optimization(PSO),and salp swarm algorithm(SSA).The findings show that,in comparison to previous approaches,the suggested meta-heuristic scheduling framework based on the IARO has increased energy profit in day-ahead electricity,gas,and heating markets by satisfying the operational and energy hub limitations.Additionally,the results show that TPEM approach dependability consideration decreased hub energy’s profit by 8.995%as compared to deterministic planning.展开更多
We introduce a new algorithm,extended regularized dual averaging(XRDA),for solving regularized stochastic optimization problems,which generalizes the regularized dual averaging(RDA)method.The main novelty of the metho...We introduce a new algorithm,extended regularized dual averaging(XRDA),for solving regularized stochastic optimization problems,which generalizes the regularized dual averaging(RDA)method.The main novelty of the method is that it allows a flexible control of the backward step size.For instance,the backward step size used in RDA grows without bound,while for XRDA the backward step size can be kept bounded.We demonstrate experimentally that additional control over the backward step size can speed up the convergence of the algorithm while preserving desired properties of the iterates,such as sparsity.Theoretically,we show that the XRDA method achieves the same convergence rate as RDA for general convex objectives.展开更多
Alternating direction method of multipliers(ADMM)receives much attention in the recent years due to various demands from machine learning and big data related optimization.In 2013,Ouyang et al.extend the ADMM to the s...Alternating direction method of multipliers(ADMM)receives much attention in the recent years due to various demands from machine learning and big data related optimization.In 2013,Ouyang et al.extend the ADMM to the stochastic setting for solving some stochastic optimization problems,inspired by the structural risk minimization principle.In this paper,we consider a stochastic variant of symmetric ADMM,named symmetric stochastic linearized ADMM(SSL-ADMM).In particular,using the framework of variational inequality,we analyze the convergence properties of SSL-ADMM.Moreover,we show that,with high probability,SSL-ADMM has O((ln N)·N^(-1/2))constraint violation bound and objective error bound for convex problems,and has O((ln N)^(2)·N^(-1))constraint violation bound and objective error bound for strongly convex problems,where N is the iteration number.Symmetric ADMM can improve the algorithmic performance compared to classical ADMM,numerical experiments for statistical machine learning show that such an improvement is also present in the stochastic setting.展开更多
In this paper,given the shortcomings of jellyfish search algorithmwith low search ability in the early stage and easy to fall into local optimal solution,this paper introduces adaptive weight function and elite strate...In this paper,given the shortcomings of jellyfish search algorithmwith low search ability in the early stage and easy to fall into local optimal solution,this paper introduces adaptive weight function and elite strategy,improving the global search scope in the early stage and the ability to refine the local development in the later stage.In the numerical study,the benchmark problem of dimensional optimization with a 10-bar truss structure and simultaneous dimensional shape optimization with a 15-bar truss structure is adopted,and the corresponding penalty method is used for constraint treatment.The test results show that the improved jellyfish search algorithm can provide better truss sections as well as weights.Because when the steel main truss of the large-span covered bridge is lifted,the site is limited and the large lifting equipment cannot enter the site,and the original structure does not meet the problem of stress concentration and large deformation of the bolt group,so the spreader is used to lift,and the improved jellyfish search algorithm is introduced into the design optimization of the spreader.The results show that the improved jellyfish algorithm can efficiently and accurately find out the optimal shape and weight of the spreader,and throughMidas Civil simulation,the spreader used canmeet the requirements of weight and safety.展开更多
基金supported in part by the Shanghai Natural Science Foundation under the Grant 22ZR1407000.
文摘We are investigating the distributed optimization problem,where a network of nodes works together to minimize a global objective that is a finite sum of their stored local functions.Since nodes exchange optimization parameters through the wireless network,large-scale training models can create communication bottlenecks,resulting in slower training times.To address this issue,CHOCO-SGD was proposed,which allows compressing information with arbitrary precision without reducing the convergence rate for strongly convex objective functions.Nevertheless,most convex functions are not strongly convex(such as logistic regression or Lasso),which raises the question of whether this algorithm can be applied to non-strongly convex functions.In this paper,we provide the first theoretical analysis of the convergence rate of CHOCO-SGD on non-strongly convex objectives.We derive a sufficient condition,which limits the fidelity of compression,to guarantee convergence.Moreover,our analysis demonstrates that within the fidelity threshold,this algorithm can significantly reduce transmission burden while maintaining the same convergence rate order as its no-compression equivalent.Numerical experiments further validate the theoretical findings by demonstrating that CHOCO-SGD improves communication efficiency and keeps the same convergence rate order simultaneously.And experiments also show that the algorithm fails to converge with low compression fidelity and in time-varying topologies.Overall,our study offers valuable insights into the potential applicability of CHOCO-SGD for non-strongly convex objectives.Additionally,we provide practical guidelines for researchers seeking to utilize this algorithm in real-world scenarios.
基金supported in part by the National Key R&D Program of China(2021YFB1714800)the National Natural Science Foundation of China(62222303,62073035,62173034,61925303,62088101,61873033)+1 种基金the CAAI-Huawei MindSpore Open Fundthe Chongqing Natural Science Foundation(2021ZX4100027)。
文摘This paper considers distributed stochastic optimization,in which a number of agents cooperate to optimize a global objective function through local computations and information exchanges with neighbors over a network.Stochastic optimization problems are usually tackled by variants of projected stochastic gradient descent.However,projecting a point onto a feasible set is often expensive.The Frank-Wolfe(FW)method has well-documented merits in handling convex constraints,but existing stochastic FW algorithms are basically developed for centralized settings.In this context,the present work puts forth a distributed stochastic Frank-Wolfe solver,by judiciously combining Nesterov's momentum and gradient tracking techniques for stochastic convex and nonconvex optimization over networks.It is shown that the convergence rate of the proposed algorithm is O(k^(-1/2))for convex optimization,and O(1/log_(2)(k))for nonconvex optimization.The efficacy of the algorithm is demonstrated by numerical simulations against a number of competing alternatives.
文摘The contribution deals with the optimization of a sequential preventive maintenance schedule of a technical device. We are given an initial time-to-failure probability distribution, model of changes of this distribution after maintenance actions, as well as the costs of maintenance, of a device acquisition, and of the impact of failure. The maintenance timing and, eventually, its extent, are the matter of optimization. The objective of the contribution is two-fold: first, to formulate a proper (random) objective function evaluating the lifetime of the maintained device relatively to maintenance costs;second, to propose a numerical method searching for a maintenance policy optimizing selected characteristics of this objective function. The method is based on the MCMC random search combined with simulated annealing. It is also shown that such a method is rather universal for different problem specifications. The approach will be illustrated on an artificial example dealing with accelerated lifetime after each maintenance action.
基金The research was supported by the Excellence Project PrF UHK No.2208/2021-2022,University of Hradec Kralove,Czech Republic.
文摘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.
基金The National Natural Science Foundation of China(No70271039)
文摘Stochastic optimization offers a means of considering the objectives and constrains with stochastic parameters. However, it is generally difficult to solve the stochastic optimization problem by employing conventional methods for nonlinear programming when the number of random variables involved is very large. Neural network models and algorithms were applied to solve the stochastic optimization problem on the basis of the stability theory. Stability for stochastic programs was discussed. If random vector sequence converges to the random vector in the original problem in distribution, the optimal value of the corresponding approximation problems converges to the optimal value of the original stochastic optimization problem.
基金the support from the National Natural Science Foundation of China(No.21676183)State Key Laboratory of Chemical Engineering,Collaborative Innovation of Chemical Science and Engineering(Tianjin)。
文摘A two-stage mixed integer linear programming model(MILP)incorporating a novel method of stochastic scenario generation was proposed in order to optimize the economic performance of the synergistic combination of midstream and downstream petrochemical supply chain.The uncertainty nature of the problem intrigued the parameter estimation,which was conducted through discretizing the assumed probability distribution of the stochastic parameters.The modeling framework was adapted into a real-world scale of petrochemical enterprise and fed into optimization computations.Comparisons between the deterministic model and stochastic model were discussed,and the influences of the cost components on the overall profit were analyzed.The computational results demonstrated the rationality of using reasonable numbers of scenarios to approximate the stochastic optimization problem.
基金Projecta supported by the Education Commission of Anhui Provinee(No.2000jw049)
文摘A stochastic control model is studied.The objective of the investor is to maximize expected utility from terminalconsumption.However,the investor possesses informa-tion about the terminal values of the components of the Brownian motion which drives securities’prices.With the method of stochastic control being applied,investor’s optimal decision is obtained.Especially,the logarith-
基金funded from the National Science and Engineering Research Council of Canada,Collaborative R&D Grant CRDPJ 335696 with BHP Billiton and NSERC Discovery Grant 239019 to R. Dimitrakopoulos
文摘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.
文摘We provide a new simple approach to stochastic dynamic optimization. In doing so, we derive the existing (standard) results using a far simpler technique than the duality and the variational methods.
基金the National Natural Science Foundation of China (No. 60404011)
文摘In this paper, an adaptive estimation algorithm is proposed for non-linear dynamic systems with unknown static parameters based on combination of particle filtering and Simultaneous Perturbation Stochastic Approximation (SPSA) technique. The estimations of parameters are obtained by maximum-likelihood estimation and sampling within particle filtering framework, and the SPSA is used for stochastic optimization and to approximate the gradient of the cost function. The proposed algorithm achieves combined estimation of dynamic state and static parameters of nonlinear systems. Simulation result demonstrates the feasibility and efficiency of the proposed algorithm.
文摘The last three decades ha</span><span style="font-family:"">ve</span><span style="font-family:""> witnessed development of optimization under fuzziness and randomness also called Fuzzy Stochastic Optimization. The main objective </span><span style="font-family:"">of </span><span style="font-family:"">this new field is the need for basing many human decisions on information which is both fuzzily imprecise and probabilistically uncertain. Consistency indexes providing a union nexus between possibilities and probabilities of uncertain events exist in the literature. Nevertheless, there are no reliable transformations between them. This calls for new paradigms for coping with mathematical models involving both fuzziness and randomness. Fuzzy Stochastic Optimization (FSO) is an attempt to fulfill this need. In this paper, we present a panoramic view of Fuzzy Stochastic Optimization emphasizing the methodological aspects. The merits of existing methods are also briefly discussed along with some related theoretical aspects.
基金supported by the Key Foundation of Southwest University for Nationalities(09NZD001).
文摘Many difficult engineering problems cannot be solved by the conventional optimization techniques in practice.Direct searches that need no recourse to explicit derivatives are revived and become popular since the new century.In order to get a deep insight into this field,some notes on the direct searches for non-smooth optimization problems are made.The global convergence vs.local convergence and their influences on expected solutions for simulation-based stochastic optimization are pointed out.The sufficient and simple decrease criteria for step acceptance are analyzed,and why simple decrease is enough for globalization in direct searches is identified. The reason to introduce the positive spanning set and its usage in direct searches is explained.Other topics such as the generalization of direct searches to bound,linear and non-linear constraints are also briefly discussed.
基金Project supported by the National Natural Science Foundation of China(No.62173308)the Natural Science Foundation of Zhejiang Province,China(Nos.LR20F030001 and LD19A010001)the Jinhua Science and Technology Project,China(No.2022-1-042)。
文摘In this paper,we address matrix-valued distributed stochastic optimization with inequality and equality constraints,where the objective function is a sum of multiple matrix-valued functions with stochastic variables and the considered problems are solved in a distributed manner.A penalty method is derived to deal with the constraints,and a selection principle is proposed for choosing feasible penalty functions and penalty gains.A distributed optimization algorithm based on the gossip model is developed for solving the stochastic optimization problem,and its convergence to the optimal solution is analyzed rigorously.Two numerical examples are given to demonstrate the viability of the main results.
文摘The use of topology optimization in structural design under dynamic excitation is becoming more prevalent in the literature.While many such applications utilize frequency or time domain formulations,relatively few consider stochastic dynamic excitations.This paper presents an efficient and compact code called TopSTO for structural topology optimization considering stationary stochastic dynamic loading using a method derived from random vibration theory.The theory,described in conjunction with the implementation in the provided code,is illustrated for a seismically excited building.This work demonstrates the efficiency of the approach in terms of both the computational resources and minimal amount of code required.This code is intended to serve as a baseline for understanding the theory and implementation of this topology optimization approach and as a foundation for additional applications and developments.
文摘Currently,energy conservation draws wide attention in industrial manufacturing systems.In recent years,many studies have aimed at saving energy consumption in the process of manufacturing and scheduling is regarded as an effective approach.This paper puts forwards a multi-objective stochastic parallel machine scheduling problem with the consideration of deteriorating and learning effects.In it,the real processing time of jobs is calculated by using their processing speed and normal processing time.To describe this problem in a mathematical way,amultiobjective stochastic programming model aiming at realizing makespan and energy consumption minimization is formulated.Furthermore,we develop a multi-objective multi-verse optimization combined with a stochastic simulation method to deal with it.In this approach,the multi-verse optimization is adopted to find favorable solutions from the huge solution domain,while the stochastic simulation method is employed to assess them.By conducting comparison experiments on test problems,it can be verified that the developed approach has better performance in coping with the considered problem,compared to two classic multi-objective evolutionary algorithms.
基金funded by the Deanship of Scientific Research,Princess Nourah bint Abdulrahman University,through the Program of Research Project Funding After Publication,Grant No (43-PRFA-P-52).
文摘The accurate prediction of energy consumption has effective role in decision making and risk management for individuals and governments.Meanwhile,the accurate prediction can be realized using the recent advances in machine learning and predictive models.This research proposes a novel approach for energy consumption forecasting based on a new optimization algorithm and a new forecasting model consisting of a set of long short-term memory(LSTM)units.The proposed optimization algorithm is used to optimize the parameters of the LSTM-based model to boost its forecasting accuracy.This optimization algorithm is based on the recently emerged dipper-throated optimization(DTO)and stochastic fractal search(SFS)algo-rithm and is referred to as dynamic DTOSFS.To prove the effectiveness and superiority of the proposed approach,five standard benchmark algorithms,namely,stochastic fractal search(SFS),dipper throated optimization(DTO),whale optimization algorithm(WOA),particle swarm optimization(PSO),and grey wolf optimization(GWO),are used to optimize the parameters of the LSTM-based model,and the results are compared with that of the proposed approach.Experimental results show that the proposed DDTOSFS+LSTM can accurately forecast the energy consumption with root mean square error RMSE of 0.00013,which is the best among the recorded results of the other methods.In addition,statistical experiments are conducted to prove the statistical difference of the proposed model.The results of these tests confirmed the expected outcomes.
基金This research is supported by the Deputyship forResearch&Innovation,Ministry of Education in Saudi Arabia under Project Number(IFP-2022-35).
文摘To maximize energy profit with the participation of electricity,natural gas,and district heating networks in the day-ahead market,stochastic scheduling of energy hubs taking into account the uncertainty of photovoltaic and wind resources,has been carried out.This has been done using a new meta-heuristic algorithm,improved artificial rabbits optimization(IARO).In this study,the uncertainty of solar and wind energy sources is modeled using Hang’s two-point estimating method(TPEM).The IARO algorithm is applied to calculate the best capacity of hub energy equipment,such as solar and wind renewable energy sources,combined heat and power(CHP)systems,steamboilers,energy storage,and electric cars in the day-aheadmarket.The standard ARO algorithmis developed to mimic the foraging behavior of rabbits,and in this work,the algorithm’s effectiveness in avoiding premature convergence is improved by using the dystudynamic inertia weight technique.The proposed IARO-based scheduling framework’s performance is evaluated against that of traditional ARO,particle swarm optimization(PSO),and salp swarm algorithm(SSA).The findings show that,in comparison to previous approaches,the suggested meta-heuristic scheduling framework based on the IARO has increased energy profit in day-ahead electricity,gas,and heating markets by satisfying the operational and energy hub limitations.Additionally,the results show that TPEM approach dependability consideration decreased hub energy’s profit by 8.995%as compared to deterministic planning.
基金Verne M.Willaman Fund,the Center for Computational Mathematics and Applications(CCMA)at the Pennsylvania State University,and the National Science Foundation(Grant No.DMS-1819157).
文摘We introduce a new algorithm,extended regularized dual averaging(XRDA),for solving regularized stochastic optimization problems,which generalizes the regularized dual averaging(RDA)method.The main novelty of the method is that it allows a flexible control of the backward step size.For instance,the backward step size used in RDA grows without bound,while for XRDA the backward step size can be kept bounded.We demonstrate experimentally that additional control over the backward step size can speed up the convergence of the algorithm while preserving desired properties of the iterates,such as sparsity.Theoretically,we show that the XRDA method achieves the same convergence rate as RDA for general convex objectives.
基金Supported by National Natural Science Foundation of China (61662036)。
文摘Alternating direction method of multipliers(ADMM)receives much attention in the recent years due to various demands from machine learning and big data related optimization.In 2013,Ouyang et al.extend the ADMM to the stochastic setting for solving some stochastic optimization problems,inspired by the structural risk minimization principle.In this paper,we consider a stochastic variant of symmetric ADMM,named symmetric stochastic linearized ADMM(SSL-ADMM).In particular,using the framework of variational inequality,we analyze the convergence properties of SSL-ADMM.Moreover,we show that,with high probability,SSL-ADMM has O((ln N)·N^(-1/2))constraint violation bound and objective error bound for convex problems,and has O((ln N)^(2)·N^(-1))constraint violation bound and objective error bound for strongly convex problems,where N is the iteration number.Symmetric ADMM can improve the algorithmic performance compared to classical ADMM,numerical experiments for statistical machine learning show that such an improvement is also present in the stochastic setting.
基金the National Natural Science Foundation of China(Grant No.51305372)the Open Fund Project of the Transportation Infrastructure Intelligent Management and Maintenance Engineering Technology Center of Xiamen City(Grant No.TCIMI201803)the Project of the 2011 Collaborative Innovation Center of Fujian Province(Grant No.2016BJC019).
文摘In this paper,given the shortcomings of jellyfish search algorithmwith low search ability in the early stage and easy to fall into local optimal solution,this paper introduces adaptive weight function and elite strategy,improving the global search scope in the early stage and the ability to refine the local development in the later stage.In the numerical study,the benchmark problem of dimensional optimization with a 10-bar truss structure and simultaneous dimensional shape optimization with a 15-bar truss structure is adopted,and the corresponding penalty method is used for constraint treatment.The test results show that the improved jellyfish search algorithm can provide better truss sections as well as weights.Because when the steel main truss of the large-span covered bridge is lifted,the site is limited and the large lifting equipment cannot enter the site,and the original structure does not meet the problem of stress concentration and large deformation of the bolt group,so the spreader is used to lift,and the improved jellyfish search algorithm is introduced into the design optimization of the spreader.The results show that the improved jellyfish algorithm can efficiently and accurately find out the optimal shape and weight of the spreader,and throughMidas Civil simulation,the spreader used canmeet the requirements of weight and safety.
