A distributionally robust optimization model for batch nonlinear switched time-delay system considering uncertain output measurements

In this paper, we consider a nonlinear switched time-delay (NSTD) system with unknown switching times and unknown system parameters, where the output measurement is uncertain. This system is the underling dynamical system for the batch process of glycerol bioconversion to 1,3-propanediol induced by Klebsiella pneumoniae. The uncertain output measurement is regarded as a stochastic vector (whose components are stochastic variables) and the only information about its distribution is the first-order moment. The objective of this paper is to identify the unknown quantities of the NSTD system. For this, a distributionally robust optimization problem (a bi-level optimization problem) governed by the NSTD system is proposed, where the relative error under the environment of uncertain output measurements is involved in the cost functional. The bi-level optimization problem is transformed into a single-level optimization problem with non-smooth term through the application of duality theory in probability space. By applying the smoothing technique, the non-smooth term is approximated by a smooth term and the convergence of the approximation is established. Then, the gradients of the cost functional with respect to switching times and system parameters are derived. A hybrid optimization algorithm is developed to solve the transformed problem. Finally, we verify the obtained switching times and system parameters, as well as the effectiveness of the proposed algorithm, by solving this distributionally robust optimization problem.     

A comprehensive extension of optimal ordering policy for stock-dependent demand under progressive payment scheme

In a recent paper, Soni and Shah (2008) presented an inventory model with a stock-dependent demand under progressive payment scheme, assuming zero ending-inventory and adopting a cost-minimization objective. However, with a stock-dependent demand a non-zero ending stock may increase profits resulting from the increased demand. This work is motivated by Soni and Shah’s (2008) paper extending their model to allow for: (1) a non-zero ending-inventory, (2) a profit-maximization objective, (3) a limited inventory capacity and (4) deteriorating items with a constant deterioration rate. For the resulted model sufficient conditions for the existence and uniqueness of the optimal solution are provided. Finally, several economic interpretations of the theoretical results are also given.     

Improved time varying inertia weight PSO for solved economic load dispatch with subsidies and wind power effects

This article presents a new approach to economic load dispatch (ELD) problems by the considering the cost functions, impact renewable energy as wind turbin and subsidies. Economic dispatch is the short‐term determination of the optimal output of a number of electricity generation facilities, to meet the system load, at the lowest possible cost, subject to transmission and operational constraints. The main goal in the deregulated system is subsidies and analysis performance on government to minimize the total fuel cost while satisfying the load demand and operational constraints. The practical ELD problems have nonsmooth cost functions with equality and inequality constraints, which make the problem of finding the global optimum difficult when using any mathematical approaches. Accordingly, particle swarm optimization with time‐varying inertia weight (PSO‐TVIW) used for solving this problem. The effectiveness of the proposed strategy is applied over real‐world engineering problem and highly constrained. Obtained results indicate that PSO‐TVIW can successfully solve this problem. © 2014 Wiley Periodicals, Inc. Complexity 21: 40–49, 2016     

Reliability and cost analysis of series system models using fuzzy parametric geometric programming

In this paper, we have discussed series system models with system reliability and cost. We have considered two types of the model; the former focuses on a problem of optimal reliability for series system with cost constraint and the latter is a center system cost model with reliability goal. It is necessary to improve the reliability of the system under limited available cost of system and also to minimize the systems cost subject to target goal of the reliability. Practically, cost of components has always been imprecise with vague in nature. So they are taken as fuzzy in nature and the reliability models are formulated as a fuzzy parametric geometric programming problem. Numerical examples are given to illustrate the model through fuzzy parametric geometric programming technique.     

Optimal engineering design via Benders’ decomposition

The optimal engineering design problem consists in minimizing the expected total cost of an infrastructure or equipment, including construction and expected repair costs, the latter depending on the failure probabilities of each failure mode. The solution becomes complex because the evaluation of failure probabilities using First-Order Reliability Methods (FORM) involves one optimization problem per failure mode. This paper formulates the optimal engineering design problem as a bi-level problem, i.e., an optimization problem constrained by a collection of other interrelated optimization problems. The structure of this bi-level problem is advantageously exploited using Benders’ decomposition to develop and report an efficient algorithm to solve it. An advantage of the proposed approach is that the design optimization and the reliability calculations are decoupled, resulting in a structurally simple algorithm that exhibits high computational efficiency. Bi-level problems are non-convex by nature and Benders algorithm is intended for convex optimization. However, possible non-convexities can be detected and tackled using simple heuristics. Its practical interest is illustrated through a realistic but simple case study, a breakwater design example with two failure modes: overtopping and armor instability.     

带随机启动时间与双阈值(m,N)-策略的M/G/1可修排队系统的最优控制策略

本文研究带随机启动时间与双阈值(m,N)-策略的M/G/1可修排队系统,首先讨论系统有关的排队指标,接着研究因为故障而产生的系统的下列可靠性指标,如:服务台首次失效前的寿命分布、不可用度和(0,t]时间内的平均故障次数。最后,在建立费用模型的基础上,结合实际中检测公司检测样品的这一现实情况,研究了双阈值最优控制策略(m^*,N^*),并在同一组参数下与服务台不发生故障时系统的双阈值最优控制策略进行了比较。     

Cold vs. hot standby mission operation cost minimization for 1-out-of-N systems

It is well recognized that using the hot standby redundancy provides fast restoration in the case of failures. However the redundant elements are exposed to working stresses before they are used, which reduces the overall system reliability. Moreover, the cost of maintaining the hot redundant elements in the operational state is usually much greater than the cost of keeping them in the cold standby mode. Therefore, there exists a tradeoff between the cost of losses associated with the restoration delays and the operation cost of standby elements. Such a trade-off can be obtained by designing both hot and cold redundancy types into the same system. Thus a new optimization problem arises for the standby system design. The problem, referred to in this work as optimal standby element distributing and sequencing problem (SE-DSP) is to distribute a fixed set of elements between cold and hot standby groups and select the element initiation sequence so as to minimize the expected mission operation cost of the system while providing a desired level of system reliability. This paper first formulates and solves the SE-DSP problem for 1-out-of-N: G heterogeneous non-repairable standby systems. A numerical method is proposed for evaluating the system reliability and expected mission cost simultaneously. This method is based on discrete approximation of time-to-failure distributions of the system elements. A genetic algorithm is used as an optimization tool for solving the formulated optimization problem. Examples are given to illustrate the considered problem and the proposed solution methodology.     

The explicit solution of the profit maximization problem with box-constrained inputs

In this paper we study the profit-maximization problem, considering maximum constraints for the general case of m-inputs and using the Cobb-Douglas model for the production function. To do so, we previously study the firm’s cost minimization problem, proposing an equivalent infimal convolution problem for exponential-type functions. This study provides an analytical expression of the production cost function, which is found to be a piece-wise potential. Moreover, we prove that this solution belongs to class C¹. Using this cost function, we obtain the explicit expression of maximum profit. Finally, we illustrate the results obtained in this paper with an example.     

A modified active set algorithm for transportation discrete network design bi-level problem

Transportation discrete network design problem (DNDP) is about how to modify an existing network of roads and highways in order to improve its total system travel time, and the candidate road building or expansion plan can only be added as a whole. DNDP can be formulated into a bi-level problem with binary variables. An active set algorithm has been proposed to solve the bi-level discrete network design problem, while it made an assumption that the capacity increase and construction cost of each road are based on the number of lanes. This paper considers a more general case when the capacity increase and construction cost are specified for each candidate plan. This paper also uses numerical methods instead of solvers to solve each step, so it provides a more direct understanding and control of the algorithm and running procedure. By analyzing the differences and getting corresponding solving methods, a modified active set algorithm is proposed in the paper. In the implementation of the algorithm and the validation, we use binary numeral system and ternary numeral system to avoid too many layers of loop and save storage space. Numerical experiments show the correctness and efficiency of the proposed modified active set algorithm.     

Scalability and Communication in Parallel Low-Complexity Lossless Compression

Approximation schemes for optimal compression with static and sliding dictionaries which can run on a simple array of processors with distributed memory and no interconnections are presented. These approximation algorithms can be implemented on both small and large scale parallel systems. The sliding dictionary method requires large size files on large scale systems. As far as lossless image compression is concerned, arithmetic encoders enable the best lossless compressors but they are often ruled out because they are too complex. Storer extended dictionary text compression to bi-level images to avoid arithmetic encoders (BLOCK MATCHING). We were able to partition an image into up to a hundred areas and to apply the BLOCK MATCHING heuristic independently to each area with no loss of compression effectiveness. Therefore, the approach is suitable for a small scale parallel system at no communication cost. On the other hand, bi-level image compression seems to require communication on large scale systems. With regard to grey scale and color images, parallelizable lossless image compression (PALIC) is a highly parallelizable and scalable lossless compressor since it is applied independently to blocks of 8 × 8 pixels. We experimented the BLOCK MATCHING and PALIC heuristics with up to 32 processors of a 256 Intel Xeon 3.06 GHz processors machine () on a test set of large topographic bi-level images and color images in RGB format. We obtained the expected speed-up of the compression and decompression times, achieving parallel running times about 25 times faster than the sequential ones. Finally, scalable algorithms computing static and sliding dictionary optimal text compression on an exclusive read, exclusive write shared memory parallel machine are presented. On the same model, compression by block matching of bi-level images is shown which can be implemented on a full binary tree architecture under some realistic assumptions with no scalability issues.     

Two-stage network constrained robust unit commitment problem

For a current deregulated power system, a large amount of operating reserve is often required to maintain the reliability of the power system using traditional approaches. In this paper, we propose a two-stage robust optimization model to address the network constrained unit commitment problem under uncertainty. In our approach, uncertain problem parameters are assumed to be within a given uncertainty set. We study cases with and without transmission capacity and ramp-rate limits (The latter case was described in Zhang and Guan (2009), for which the analysis part is included in Section 3 in this paper). We also analyze solution schemes to solve each problem that include an exact solution approach and an efficient heuristic approach that provides tight lower and upper bounds for the general network constrained robust unit commitment problem. The final computational experiments on an IEEE 118-bus system verify the effectiveness of our approaches, as compared to the nominal model without considering the uncertainty.     

基于两阶段启发式算法的物流配送选址-路径问题研究

为了解决配送中心选址与带时间窗的多中心车辆路径优化组合决策问题,利用双层规划法建立了配送中心选址与车辆路径安排的多目标整数规划模型,针对该模型的特点,采用两阶段启发式算法进行了求解。首先,通过基于聚集度的启发式算法对客户进行分类,确定了备选配送中心的服务范围;然后,基于双层规划法,以配送中心选址成本最小作为上层规划目标,以车辆配送成本最小作为下层规划目标,建立了多目标整数规划模型;最后,利用改进的蚁群算法进行了求解。通过分析实例数据和Barreto Benchmark算例的实验结果,验证了该模型的有效性和可行性。     

A fuzzy shortest path with the highest reliability

This paper concentrates on a shortest path problem on a network where arc lengths (costs) are not deterministic numbers, but imprecise ones. Here, costs of the shortest path problem are fuzzy intervals with increasing membership functions, whereas the membership function of the total cost of the shortest path is a fuzzy interval with a decreasing linear membership function. By the max–min criterion suggested in [R.E. Bellman, L.A. Zade, Decision-making in a fuzzy environment, Management Science 17B (1970) 141–164], the fuzzy shortest path problem can be treated as a mixed integer nonlinear programming problem. We show that this problem can be simplified into a bi-level programming problem that is very solvable. Here, we propose an efficient algorithm, based on the parametric shortest path problem for solving the bi-level programming problem. An illustrative example is given to demonstrate our proposed algorithm.     

Robust placement and tuning of UPFC via a new multiobjective scheme‐based fuzzy theory

This article addresses a new modified honey bee mating optimization namely multiobjective honey bee mating optimization (MOIHBMO) based fuzzy multiobjective methodology for optimal locating and parameter setting of unified power flow controller (UPFC) in a power system for a long‐term period. One of the profits obtained by UPFC placement in a transmission network is the reduction in total generation cost due to its ability to change the power flow pattern in the network. Considering this potential, UPFC can be also used to remove or at least mitigate the congestion in transmission networks. The other issue in a power system is voltage violation which could even render the optimal power flow problem infeasible to be solved. Voltage violation could be also mitigated by proper application of UPFC in a transmission system. These objectives are considered simultaneously in a unified objective function for the proposed optimization algorithm. At first, these objectives are fuzzified and designed to be comparable against each other and then they are integrated and introduced to a MOIHBMO method to find the solution which maximizes the value of integrated objective function in a 3‐year planning horizon, considering the load growth. A power injection model is adopted for UPFC. Unlike, the most previous works in this field the parameters of UPFC are set for each load level to avoid inconvenient rejection of more optimal solutions. IEEE reliability test system is used as an illustrative example to show the effectiveness of the proposed method. © 2014 Wiley Periodicals, Inc. Complexity 21: 126–137, 2015     

交通网络建设序列的动态规划方法

交通网络建设序列优化是交通规划中一个重要问题。文章对交通网络设计及其建设序列问题的研究现状进行了分析。按照网络建设中规划者和用户间的关系,以交通网络建设序列下的各阶段系统总费用作为上层规划,以各阶段的交通流用户平衡模型作为下层规划,建立了双层规划模型。并依照问题的特点,采用动态规划的求解方法进行探讨,而下层模型则采用了基于路径搜索的GP算法进行求解。并针对网络规划算例进行了计算,针对固定和变动客流OD两种情况下的结果进行了分析。计算的结果表明,问题的双层规划模型和动态规划求解算法能够为路网规划决策提供支持。     

Cost analysis on renewable full-service warranties for multi-component systems

This paper presents a novel warranty policy named ‘full-service warranty’ (FSW) for repairable multi-component systems under which the failed component(s) or subsystem(s) will be replaced, in addition, a (perfect) maintenance action will be performed to reduce the chance of future system failure, both free of charge to consumers. Such a policy is desirable for both consumers and manufacturers since consumers receive better warranty service compared to the traditional free repair policy, at the same time, manufacturers may enjoy increase in sale as well as cost-saving due to improved product reliability by the maintenance action. Under the renewable FSW policy, from manufacturers’ point of view, cost models for complex systems with series, parallel, series–parallel (s–p) and parallel–series (p–s) structure are developed. Exact expressions for the first and second centered moments of warranty cost per product sold are obtained. Sensitivity analysis is performed based on a numerical example.     

Transportation policies for single and multi-objective transportation problem using fuzzy logic

In this paper, single and multi-objective transportation models are formulated with fuzzy relations under the fuzzy logic. In the single-objective model, objective is to minimize the transportation cost. In this case, the amount of quantities transported from an origin to a destination depends on the corresponding transportation cost and this relation is verbally expressed in an imprecise sense i.e., by the words ‘low’, ‘medium’, ‘high’. For the multi-objective model, objectives are minimization of (i) total transportation cost and (ii) total time for transportation required for the system. Here, also the transported quantity from a source to a destination is determined on the basis of minimum total transportation cost as well as minimum transportation time. These relations are imprecise and stated by verbal words such as ‘very high’, ‘high’, ‘medium’, ‘low’ and ‘very low’. Both single objective and multi-objective problems using Real coded Genetic Algorithms (GA and MOGA) are developed and used to solve the single level and bi-level logical relations respectively. The models are illustrated with numerical data and optimum results are presented.     

Robust bi-level optimization of relief logistics operations

In this paper, a robust bi-level optimization model is developed for a supply–distribution relief network under uncertainty in demand and supply parameters. It optimizes the relief operating costs as well as considering a penalty term for unsatisfied victims’ demands. Moreover, the proposed framework optimizes the relief commodity flow in a relief chain along with the supply risk minimization by identifying the suppliers with a lower risk. This paper proposes an integrated optimization method in which the supply risk value for each supplier is obtained via the TOPSIS method. Next, these values are utilized in a robust bi-level model to select appropriate suppliers and allocate orders. Finally, the robustness and effectiveness of the proposed model are demonstrated by a case of flood disaster.     

Pavement rehabilitation scheduling and toll pricing under different regulatory regimes

This paper addresses the highway pavement rehabilitation scheduling and toll pricing issues over a planning horizon. In the highway system concerned, two types of agents are considered, namely highway operator and road users. Two models, which account for different highway regulatory regimes (i.e. public and private), are proposed. In the public regulatory model, the government aims to maximize total discounted social welfare of the transportation system over the planning horizon by determining the optimal pavement rehabilitation schedule and toll level. In the private regulatory regime, a profit-driven private operator seeks to optimize the pavement rehabilitation schedule and toll level to maximize its own discounted net profit over the planning horizon. The proposed models treat the interactions between the highway operator and the road users in the system as a bi-level hierarchical problem in which the upper level is a multi-period pavement rehabilitation scheduling and toll pricing problem, while the lower level is a multi-period route choice equilibrium problem. A heuristic solution algorithm that combines a greedy approach and a sensitivity analysis based approach is developed to solve the proposed bi-level multi-period optimization models. An illustrative example is used to show the applications of the proposed models. The findings show that the highway regulatory regime, pavement deterioration parameter and the roughness-induced vehicle operating cost can significantly affect the pavement rehabilitation schedules and the toll level as well as the performance of transportation system in terms of total life-cycle travel demand, net profit and social welfare.