Static Optimization Model Research Articles

Implicit-integral dynamic optimization based on spatial partitioning and temporal segmentation for the power jumps of renewable energy sources

With the widespread development of renewable energy sources, the increasing short-term power volatility poses a significant challenge to the normal operation of power systems. This paper presents a two-timescale adaptive dynamic optimization (TADO) strategy based on implicit trapezoidal integral to address dynamic state fluctuations due to renewable power jumps. Firstly, a static optimization model is established utilizing the model predictive control (MPC) to obtain the optimal states on a longer temporal scale, considering the uncertain renewable power jumps. Next, provide a partitioning method based on modularity to divide the power system into several independent subsystems with constant tie-line power. Using an implicit trapezoidal integral algorithm, each subsystem's dynamic reactive power optimization model is constructed with an appropriate discrete time granularity, accounting for the electromechanical transient processes due to renewable power jumps. Then, to improve the solving efficiency of the dynamic optimization model, a new solution method is proposed based on temporal segmentation. The whole process's optimal state trajectory is achieved by splicing all sub-optimization results. Finally, case studies conducted on the IEEE 9-bus power system and IEEE 39-bus power system validate the feasibility of the proposed strategy.

Ship sailing speed optimization considering dynamic meteorological conditions

Sailing speed optimization is a cost-effective strategy to improve ship energy efficiency and a viable way to fulfill emission reduction requirements. This study develops a novel ship sailing speed optimization method that considers dynamic meteorological conditions. We first develop an artificial neural network model for vessel fuel consumption rate (FCR) prediction based on a fusion dataset of ship noon reports and public meteorological data. Then, based on the predicted FCRs, the method repeatedly formulates a multistage graph based on the most recent forecasts, and optimal speeds for the remaining voyage are obtained until the vessel reaches the destination port. The computational efficiency of the optimization process is enhanced by progressively removing nodes without connections to successor nodes, starting from the penultimate stage. We examine the proposed method on two 11-day voyages of a dry bulk carrier. Results show that the proposed method demonstrates significant reductions in fuel consumption by 5.35% compared with a constant sailing speed scheme and by 7.34% compared with a static speed optimization model. In addition, the proposed model achieves similar fuel savings to those achieved by speed optimization based on actual meteorological conditions, enabling shipping companies to optimize ship sailing speeds in the absence of actual meteorological conditions. The proposed method can be applied to various types of vessels due to its flexibility and adaptability, making it a valuable tool for the shipping industry to reduce greenhouse gas (GHG) emissions, thereby supporting the International Maritime Organization (IMO)’s goal of reaching net-zero GHG emissions by around 2050.

A static robust energy management approach for modelling low emission multi-vectored energy hub including emission markets and power-to-gas units

This paper develops a robust and sustainable energy management framework to model a multi-vectored energy hub (MVEH) system. A max-min-based static robust optimization model is developed to counter the uncertainties. Furthermore, a flexible energy demand management program, battery electric vehicles (BEVs), and compressed air battery storage (CABS) are integrated to enhance MVEH's flexibility. Hybrid power-to-X units (electrolyser, methanization reactor and fuel cells) are modelled to reduce green energy spillage and improve operational independence, including heat pumps. Moreover, the emission (carbon cap and trade) market along with carbon capture storage and utilization units (CCS–U), are incorporated to establish a low-emission multi-energy model. Simulation results demonstrate that with flexible resources and power-to-X units, MVEH reduces the operating energy cost by 46.4 % and improves the system independence by 19.06 %. Besides, CCS-U units produce 92 % less emission while increasing the energy cost by 5.1 %. However, MVEH gains the right to sell carbon credits under the emission market. Thus, the multi-vectored system's economical, reliable, and environmental viability are ensured. Finally, sensitivity analysis proves the robustness of the proposed framework against natural gas and carbon price fluctuations.

A simulation framework for optimizing bike rebalancing and maintenance in large-scale bike-sharing systems

Bike-sharing systems (BSSs) have rapidly attracted worldwide interest for their success in improving quality-of-life in metropolitan areas. One kind of BSS requires docking stations to avoid misplacements of bikes. Such a BSS is faced with challenges caused by imbalanced demands across stations and frequent failures of bikes and docks. To achieve a high level of customer satisfaction, timely bike rebalancing and system maintenance must be performed. In this work, a simulation framework is proposed for evaluating different rebalancing and maintenance strategies. The framework can be integrated with any multi-vehicle static or dynamic rebalancing optimization model. An optimization model solved by an enhanced k-means clustering method (EKM) and an Ant Colony Optimization (ACO) algorithm is provided as an example for demonstrating such integration. A case study based on the configuration and historical data of Citi Bike in New York City is conducted for simulation model validation and for illustrating the managerial impacts of different rebalancing and maintenance strategies on the investment, operation, and service levels of such a large-scale BSS. The application of the proposed simulation framework is not limited to BSSs but also can be extended to other types of shared transport systems with non-floating stations where rebalancing and maintenance optimization are critical for efficient and healthy operation.

Rainfall shocks and household welfare: Evidence from northern Ghana

CONTEXTRainfall shocks pose a threat to farmers in rural West Africa especially in the wake of the recurrent climate variability and its impacts on agricultural production. Despite the harm they pose, limited empirical studies exist on the welfare implications of rainfall shocks on farmers' welfare in West Africa. In addition, the potential impacts of rainfall induced commodity and labor market failures have not been given much attention in the empirical literature. OBJECTIVEOur study aimed to analyze the impact of negative rainfall shocks and commodity and labor market failures on farm households' welfare in northern Ghana. Examining the impact of commodity and labor market failures amidst the experience of a negative rainfall shock helps to identify the possible entry points through which the adverse impacts of rainfall deficits may be reduced. METHODSThe study is based on a household survey data from the Africa Rising program, historical daily climate data from the CCAFS-Climate data portal and random rainfall distributions from Monte Carlo simulation. A total of 1168 households were considered in the analysis. We analyze the impact of rainfall shocks and the above-mentioned entitlement failures using a static optimization model that incorporates a crop yield response function. RESULTS AND CONCLUSIONWe found that an increase in the frequency of negative rainfall shocks under a dry future with and without entitlement failures would impact negatively on the total income and consumption levels of both the asset non-poor and asset poor households in the study area. The asset poor households would however bear the brunt of the impact, and the anticipated impact would mostly be yielded through changes in agricultural incomes and expenditure on food purchases. With increasing risk of dry rainfall conditions, total incomes of farmers could decrease by 7.3% to 45.5%. It was found that ignoring potential failures in commodity and labor markets lead to over/underestimation of the impacts of major rainfall deficits on the different types of farmers. The impact of rainfall shocks on the welfare of farmers is scenario and cluster dependent. SIGNIFICANCEThe results have significance for policy formulation and future research. The findings from this study indicate a need for targeting and acknowledgement of the differential impacts of climate shocks on the different farmer groups. Efforts made in future research to incorporate entitlement failures in climate impact studies could produce more informative guide for effective policy formulation.

Model of an automated decision-making support system by a municipality in public transport management

The static optimization model of passenger’s transport structure of small town is described. The transport network was interpreted by an oriented graph, whose vertices correspond to stops, and the arcs - parts of highways between stops. The route of transport was supposed to be given. The passenger traffic on each arc at the current fee was considered to be know.

A new ride‐sharing model incorporating the passengers' efforts

AbstractWe address a novel ride‐sharing model aiming to improve the quality of carpool services, by means of incorporation of passengers' efforts. In densely populated areas, locating and picking up passengers are often time costly. These phenomena, which are rarely considered in literature, will hurdle the service efficiency of ride‐sharing businesses by a significant amount, and contribute to the performance gap between theoretical estimation and practical performance. We notice that major platforms, such as DiDi, Uber, and Lyft are all starting innovative ways to encourage passengers to take efforts to walk to the assigned stations. We present a static optimization model for the planning stage of the service and establish an estimation of the carpooling rate for each station together with robustness consideration. In addition, we provide simple and efficient optimization algorithms with theoretical performance guarantee. At the same time, we conduct simulation studies based on both random generated data and open accessible data from DiDi. By applying our model and algorithm to the data of DiDi, we can achieve carpooling rates of 90% while passengers are located within an average radius of 250 m spending an extra waiting time of less than 3 min for their shared rides during rush hour.

Modified Newton integration algorithm with noise suppression for online dynamic nonlinear optimization

The solution of nonlinear optimization is usually encountered in many fields of scientific researches and engineering applications, which spawns a large number of corresponding algorithms to cope with it. Besides, with developments of modern cybernetics technology, it imperatively requires some advanced numerical algorithms to solve online dynamic nonlinear optimization (ODNO). Nevertheless, the major existing algorithms are limited to the static nonlinear optimization models, few works considering the dynamic ones, let alone tolerating noise. For the abovementioned reasons, this paper proposes a modified Newton integration (MNI) algorithm for ODNO with strong robustness and high-accuracy computing solution, which can effectively suppress the influence caused by noise components. In addition, the correlative theoretical analyses and mathematical proofs on convergence and robustness of the MNI algorithm are carried out, which indicates that computing solutions of the proposed MNI algorithm can globally converge to relative small value in the presence of various noise or zero noise conditions. Finally, to illustrate the advantages and feasibilities of the proposed MNI algorithm for ODNO problems, four numerical simulation examples and an application to robot manipulator motion generation are performed.

EXPERIENCE OF THE INPUT-OUTPUT MODELS APPLICATION TO THE MOLDOVAN ECONOMY

The main goal of this article is to present an overview of the input-output models which have been applied to Moldovan economy development study. We examined: static input-output model, dynamic input-output model restricted by limited energy resources, and the Markov chain approach based on the input-output tables. All these models have been examined using statistic data referring to the input-output table, constructed on the base of aggregated branches of the Moldovan economy. Static and dynamic optimization models were formulated, simulation calculation was done and analysed. Input-output table balancing problem was solved using RAS method. For dynamic model matrix of the investment coefficients was constructed. The emphasis was putt on the problem of applying the theory of Markov chain for examination of the 19 and 16 branches in the framework of the input-output model for Republic of Moldova. A square exchange matrix of order has been constructed. Every branch was considered as one of the states of the Markov chain with states. We introduced a new -th absorption state so that the examined matrix became of the order . The obtained transition matrix – probabilities matrix has been used for forecasting

Towards the use of bond graphs for manufacturing control: Design of controllers

The integration of control theory methods with operations management techniques enables to treat the dynamic facet of production and supply chain problems. In this paper, we revisit a bond graph/mathematical model devoted to depict the dynamics of multi-workstation production systems, and propose closed-loop simulation models with state feedback controllers, designed according to the pole placement and LQR methods. A real case was explored and simulations with the introduction of a disturbance in the production system were carried out. The results revealed that the model can provide prescriptive capacity adjustments and can help to define appropriate reference levels for the work in process in the system. It presents a disturbance-oriented behaviour that has advantages over pure push or pull systems commonly used in Production Planning and Control (PPC). In contrast to previous publications referring to the model, where the emphasis is set on the modelling process itself, the contribution of this paper concerns the design of the controllers, an aspect that is still left open for this kind of model. This design of the controllers has some peculiarities, since the state model of the production system does not fit the standard form. The presented approach is also relevant to the readership of the operations management (OM) and operational research (OR) fields for two reasons: (1) the use of control theory in OM provides good prescriptive solutions for dynamic production environments and the quality of these solutions is directly related to the design of the controllers; (2) the models generated by the integration of control theory and optimization, in some scenarios, present advantages over purely static optimization models.

Bounds for two static optimization problems on routing and spectrum allocation of anycasting

Elastic optical networks with optical-orthogonal frequency division multiplexing have been addressed enthusiastically for communication networks in the last decade because they result in high bandwidth efficiency. Routing and spectrum allocation (RSA) problems need to be solved when we transmit demands in an elastic optical network. This research deals with static RSA models for anycast transmission, which is one-to-one-of-many transmission in inter-datacenter networks. Two static RSA optimization models are considered. One minimizes the maximum number of spectrum slots needed to allocate given demands. The other maximizes the traffic volume of demands served under a given spectrum slot number. For both models, lower and upper bounds are developed in order to obtain exact optimal solutions. One-side bounds of the problems are evaluated by relaxing spectrum continuity constraints. For the other side bounds, several greedy algorithms are investigated. We conducted computational experiments to confirm whether relaxation problems can give tight bounds and to determine greedy algorithmic behaviors by using each of route selection criterion and each of demand ordering policies. The results show that the solutions obtained by relaxing spectrum continuity constraints are almost optimal. They also indicate that exact optimal solutions are obtained efficiently by using these bounds.

Data-driven decision making under uncertainty integrating robust optimization with principal component analysis and kernel smoothing methods

This paper proposes a novel data-driven robust optimization framework that leverages the power of machine learning and big data analytics for decision-making under uncertainty. By applying principal component analysis to uncertainty data, correlations between uncertain parameters are effectively captured, and latent uncertainty sources are identified. These data are then projected onto each principal component to facilitate extracting distributional information of latent uncertainties using kernel density estimation techniques. To explicitly account for asymmetric distributions, we introduce forward and backward deviation vectors into the data-driven uncertainty set, which are further incorporated into novel data-driven static and adaptive robust optimization models. The proposed framework not only significantly ameliorates the conservatism of robust optimization, but also enjoys computational efficiency and wide-ranging applicability. Three applications on optimization under uncertainty, including model predictive control, batch production scheduling, and process network planning, are presented to demonstrate the applicability of the proposed framework.

Preface: Static and dynamic optimization models for network routing problems

Preface: Static and dynamic optimization models for network routing problems

Robust timing of markdowns

We propose an approach to the timing of markdowns in a continuous-time finite-horizon setting that does not require the precise knowledge of the underlying probabilities, instead relying on range forecasts for the arrival rates of the demand processes, and that captures the degree of the manager’s risk aversion through intuitive budget of uncertainty functions. These budget functions bound the cumulative deviation of the arrival rates from their nominal values over the lengths of time for which a product is offered at a given price. A key issue is that using lengths of time as decision variables introduces non-convexities when budget functions are concave. In the single-product case, we describe a tractable and intuitive framework to incorporate uncertainty on customers’ arrival rates, formulate the resulting robust optimization model, describe an efficient procedure to compute the optimal sale times, and provide theoretical insights. We then describe how to use the solution of the static robust optimization model to implement a dynamic markdown policy. We also extend the robust optimization approach to multiple products and suggest the idea of constraint aggregation to preserve performance for this type of problem structure.

Applying Bond Graphs for Modelling the Manufacturing Dynamics

Supply chain dynamics and execution control seem not to receive as much attention as the domain of supply chain planning by means of static optimization models. The dynamics of manufacturing systems also deserves attention, since they are the fundamental pieces of a supply chain. In this paper, a dynamic model for the production control of a multi-product manufacturing system is developed using the Bond Graph modeling methodology. The proposed model is applied to depict the dynamics of a real job shop production system of propylene bags, where the control objective is to adjust the processing frequency of the machines to attend the demands of the products, while keeping the work in process at the desired levels. Exploratory simulations were carried out, and the preliminary results showed that the system could be autonomously controlled. Some advantages of the Bond Graph methodology are also highlighted.

Integration of set point optimization techniques into nonlinear MPC for improving the operation of WWTPs

Optimization and control strategies are necessary to keep wastewater treatment plants (WWTPs) operating in the best possible conditions, maximizing effluent quality with the minimum consumption of energy. In this work, a benchmarking of different hierarchical control structures for WWTPs that combines static and dynamic real time optimization (RTO) and nonlinear model predictive control (NMPC) is presented. The objective is to evaluate the enhancement of the operation in terms of economics and effluent quality that can be achieved when introducing NMPC technologies in the distinct levels of the multilayer structure. Three multilayer hierarchical structures are evaluated and compared for the N-Removal process considering the short term and long term operation in a rain weather scenario. A reduction in the operation costs of approximately 20% with a satisfactory compromise to effluent quality is achieved with the application of these control schemes.

Critical Solutions of Maximum Loadability Via Direct Methods

This work proposes a direct method for determination of the saddle-node bifurcation point corresponding to the maximum loadability of the power system. This problem is stated as a static optimization model, whose solution is obtained through an extended version of Newton’s method. The power flow equations are expressed in rectangular coordinates, which allows both to use second-order information (tensor calculation) as well as to handle directly the generated reactive power constraints. Sensitivity relationships between the power system variables at the maximum loadability point are computed as a by-product of the optimization process. Numerical results obtained with power systems of different sizes are used to illustrate the main features of the proposed methodology.

Valuing fuel diversification in power generation capacity planning

Deterministic capacity planning problems in electricity systems can be solved by comparing technology specific long-term and short-term marginal costs. In an uncertain market environment, Mean-Variance Portfolio (MVP) theory provides a consistent framework to balance risk and return in power generation portfolios. Focusing on fuel price risks, MVP theory can be adopted to determine the welfare efficient system generation technology mix.Existing literature on MVP applications in electricity generation markets uses predominantly numerical methods to characterize portfolio risks. In contrast, this article presents a novel analytical approach combining conceptual elements of classical capacity planning models and MVP theory to derive the efficient portfolio structure consisting of an arbitrary number of plant technologies given uncertain fuel prices. For this purpose, we provide a static optimization model which allows to fully capture fuel price risks in a mean variance portfolio framework. The analytically derived optimality conditions contribute to a better understanding of the optimal investment policy and its risk characteristics compared to existing numerical methods. Furthermore, we demonstrate an application of the proposed framework and provide results for the German electricity market which has been hardly treated in MVP literature on electricity markets.This article provides easily interpretable analytical optimality conditions for efficient generation portfolios from a societal point of view and therewith contributes to a better understanding of MVP in electricity applications.

Static and dynamic collaborative optimization of ship hull structure

The goal of this effort was to provide a static and dynamic collaborative optimization (CO) model for the design of ship hull structure. The CO model integrated with static, mode and dynamic analyses. In the system-level optimization model, a new objective function was advised, integrating all the subsystem-levels’ objective functions, so as to eliminate the effects of dimensions and magnitude order. The proposed CO architecture enabled multi-objectives of the system and subsystem-level to be considered at both levels during optimization. A bi-level optimization strategy was advised, using the multi-island genetic algorithm. The proposed model was demonstrated with a deck optimization problem of container ship stern. The analysis progress and results of example show that the CO strategy is not only feasible and reliable, but also well suited for use in actual optimization problems of ship design.

Formalizing the Optimization Problem in Long-Term Capability Planning

In defining future force capabilities, decision makers need to balance objectives, strategy, force capabilities, and risk within a forecasted force development environment and resource levels. This is commonly a task in long-term defense and force planning. This paper presents a mathematical formalization of the planning problem that involves static and dynamic optimization. Several static and dynamic discrete optimization models illustrate the approach. The concluding section presents a short deliberation on applicability.