Multi-level Optimization Model Research Articles

Scheduling optimization of electric energy meter distribution vehicles for intelligent batch rotation

As industrial technology continues to advance through integration, society's demand for electricity is rapidly increasing. To meet the requirements of refined grid management and address the elevated challenges arising from the increased electrical load, this paper delves into the investigation of distribution vehicle scheduling for the practical scenario of batch rotation of smart meters. Initially, based on the practical distribution task requirements of a provincial metrology verification center, a multi-level optimization model is constructed for the batch rotation and distribution vehicle scheduling of smart meters. The primary objective is to maximize the enhancement of smart meter distribution efficiency while minimizing the overall distribution cost. Moreover, this paper introduces a refined Grey Wolf Optimization algorithm (OLC-GWO) based on Opposition-based Learning, Levy flight strategy, and Cauchy mutation to solve the model. By generating an opposite population to improve the quality of initial feasible solutions and further harnessing the global search capabilities of Levy flight and Cauchy mutation operators, the algorithm's effectiveness is enhanced. The algorithm is subjected to testing using multiple benchmark functions and its performance is compared with variants of GWO, as well as several cutting-edge intelligent optimization algorithms including Particle Swarm Optimization (PSO), Harris Hawks Optimization (HHO), and Honey Bee Algorithm (HBA). The results indicate that OLC-GWO exhibits excellent performance in terms of convergence speed and optimization capability. Finally, the improved algorithm is subjected to simulation experiments by incorporating order data from the practical distribution operations of a provincial metrology verification center. The outcomes verify the efficiency of the proposed algorithm, reinforcing the practical significance of the established model in addressing the real-world challenge of batch rotation and distribution vehicle scheduling for smart meters.

Control Simulation of Flapping-Wing Micro Aerial Vehicle Based on Multi-Level Optimization Model Predictive Control

Control Simulation of Flapping-Wing Micro Aerial Vehicle Based on Multi-Level Optimization Model Predictive Control

An equilibrium approach for compensating public–private partnership concessionaires for reduced tolls during roadway maintenance

This study considers the possibility of exploiting excess capacity along concurrent tolled roadway facilities operating in a public–private partnership for the purpose of alleviating traffic congestion during improvement action execution on a public roadway facility. Increased access to the tolled facility is enabled by reducing or suspending tolls during periods of roadway improvement action and appropriately compensating the tolled facility concessionaire for expected losses. The problem of determining an optimal reduced toll pricing strategy and compensation level is referred to as the Maintenance Timing and Price Discovery (MTPD) problem. A multi-level optimization model and iterative solution method are proposed to solve this problem. As toll prices often depend on traffic levels, the model also determines the optimal timing and time-of-day and day-of-week for executing the set of required improvement actions over the planning horizon to ensure a lowest total cost. The multi-level model consists of two bilevel models. Solution of the greater model is attained at a Stackelberg equilibrium between these two bilevel models. An additional Stackelberg equilibrium is sought between upper and lower levels of each of these two bilevel models individually. The MTPD formulation and general solution methodology are applied on an illustrative example from which computational results are obtained. Insights from the results show that this strategy for alleviating traffic congestion during roadway maintenance or other improvement activities can lead to substantial savings in total agency and user costs.

Multi-level model predictive control based multi-objective optimal energy management of integrated energy systems considering uncertainty

Integrated energy systems (IES) with renewable energy systems (RES), carbon capture systems (CCS) and energy storage systems (ESS) are considered efficient in supporting the low-carbon energy supply with both economic and environmental benefits. Effective energy management is required to ensure the economical, environmental and reliable operation of the IES. However, the optimal IES operation is considered a non-trivial task due to the renewable generation uncertainty and the optimization of multiple contradictory objectives (e.g. economic, environmental and risk costs). This paper aims to provide a multi-level optimization model for the real-time optimal IES operation consisting of RES, ESS and CCS. This work quantifies the uncertainty by the Conditional Value at Risk (CVaR) theory in the optimization model. The uncertainty is further reduced by improving the operation strategy through a model predictive control (MPC)-based method. Also, the multi-objective optimization model is adopted to minimize the economic cost, carbon dioxide emissions (CDE) and primary energy consumption (PEC) for optimal energy scheduling in the intra-day stage. Based on the result of the intra-day stage, the feedback correction model is applied to adjust the schedule to balance the difference between the forecasting and actual values. Numerical results show that the proposed solution can provide the trade-off between economical and environmental performance. Through ablation experiments, the proposed method with feedback correction can carry out demand response with lower costs, CDE and PEC. The proposed solution is further confirmed with outperformed performance compared with single-objective optimization methods and other stochastic optimization methods. In addition, a robustness analysis is conducted to quantify the benefits of RES, ESS and CCS in IES.

Multilevel optimization framework to support self-sustainability of industrial processes for energy/material recovery using circular integration concept

Climate change, resource scarcity, waste reduction, and the lack of sustainability in process industries are vital concerns that civilization confronts. The process integration methodology may aid such sustainability. In this study, a novel chemical exergy resource recovery network is proposed for optimal energy and waste recovery in high-salinity-gradient chemical industries using a pressure-retarded osmosis membrane while indicating a self-sustainability and allocation in complex industrial networks. The mathematical programming paradigm is expressed as a multilevel optimization model to introduce novel ideas for explicitly modeling the trade-offs between waste and energy flows in circular integration while demonstrating industrial network’s environmental impact assessment. This problem is decomposed into two subproblems (SPs) that must be addressed sequentially. The first SP is designed to decrease the total cost of the network while reducing external resource use. The second SP formulates a mixed-integer nonlinear programming model with the objective of minimizing the environmental effects and exergy consumption rate of the network. A case study of a naphthalene-methaforming plant demonstrates the efficacy of the proposed methodology. The results showed that using a tri-level optimization technique, a considerable improvement in flowrate, total annualized cost, and energy recovery is obtained while limiting the network's environmental impact. The operating phase accounts for approximately 75% of the global warming potential output. The proposed tri-level approach based on Benders’ decomposition approach reduced the overall cost of the network by 19.29%, and 47.42 MW net power is recovered in the case study. In addition, the circular exergy use rate and environmental factor were reduced from 400 to 0.037 MW and from 2.569 to 1.481 kgCO2/year, respectively, using the tri-level decomposition approach.

A Multi-Level Optimization Model Based Integration Scheduling Method for Flexible Job Shop with Green Lot Splitting

A Multi-Level Optimization Model Based Integration Scheduling Method for Flexible Job Shop with Green Lot Splitting

Optimization of flight test tasks allocation and sequencing using genetic algorithm

Flight test tasks arrangement is one of the most significant problems in the development of new civil aircraft. Normally, there are many factors restraining flight test tasks arrangement, including characteristics of experimental aircraft, requirements of tasks themselves, and logical relationships among them, leading to increased development period and costs. Hence, flight test tasks arrangement is generally viewed as a multi-constraint nonlinear optimization problem. To improve flight test efficiency, a multi-level optimization model of flight test tasks allocation and sequencing is introduced in this paper, where flight test period is the main optimization objective, and a penalty function evaluating tasks testing dates is the minor optimization objective. A flight test tasks sequence oriented improved genetic algorithm (FTTSOIGA) is proposed to solve the model. Firstly, a tasks allocation algorithm is designed to establish the mapping between tasks sequence and tasks arrangement result, which is independent of feasible sequence. Then, the arrangement result is optimized by optimizing the tasks sequence using the genetic algorithm. Furthermore, a tasks sequence adjustment strategy is applied to accelerate algorithm convergence. Simulation cases of 3 experimental aircraft and 80 flight test tasks demonstrate the efficiency of FTTSOIGA.

A multi-level optimization model of infrastructure-dependent technology adoption: Overcoming the chicken-and-egg problem

Policymakers seeking to promote the diffusion of infrastructure-dependent technologies are often confronted with the “chicken-and-egg” problem: consumers are reluctant to adopt the technology without adequate infrastructure available, and firms are reluctant to invest in infrastructure without a sufficient number of adopters. This chicken-and-egg problem can hinder the diffusion of new technologies and prolong the timeframe over which existing technological systems remain locked-in. In this paper, we formulate a stylized model of technology policy decision-making from the perspective of a policymaker who seeks to stimulate the market penetration of an infrastructure-dependent technology. Our model is a multi-level optimization problem in which a policymaker (first level) maximizes net social benefits by setting the levels of two incentives: a subsidy for a profit-maximizing firm (in equilibrium with two other firms, the second level) to invest in infrastructure that raises the benefit of adoption to consumers, and a direct subsidy for consumers to adopt the technology (third level). Under certain assumptions about functional forms, we solve the full multi-level problem analytically through backward induction and derive closed-form expressions for the policymaker’s optimal subsidy levels. Then, we present a case study on policies to promote battery electric vehicle (BEV) diffusion. Our results reveal three main insights: (1) the optimal policy portfolio often subsidizes charging infrastructure more than BEV purchases, (2) infrastructure and adoption subsidies tend to be substitutes rather than complements, and (3) an increase in the marginal social benefit of BEV adoption shifts the optimal policy away from infrastructure subsidies and toward BEV subsidies.

A Technical and Economic Criteria Comparison on Demand Side Management with Multi-Level Optimization Model

One-level optimization methods have been proposed to optimize the load profile of a single user or a cluster of users in the smart grids. In this work, two two-level optimization methods are studied, one considering technical requirements and other considering economic criteria. In the upper level, the supplier optimizes it objective function. Meanwhile, at the lower level, users optimize their electrical costs. The proposed methods are based on genetic algorithm methods. In this sense, an indirect control is established in which users react to a price signal. Simulations results illustrate that both cases improve the demand profile and increase the retailer profit. However, when the supplier tries to maximize the profit, some users receive benefits in detriment of others, concluding that the technical approach is preferable than the economical one.

Robust design approach to the minimization of functional performance variations of products and systems

Functional performance variations of products and systems are often used to measure the qualities of products and systems considering the changes in the design parameter values caused by uncertainties. A robust design approach has been developed in this research to minimize the functional performance variations considering the design parameter uncertainties by identifying the boundaries of the functional performance variations through optimization. In this work, a mathematical model is developed to describe the relationships among functional performance, design configurations and parameters, and design parameter uncertainties. A multi-level optimization model is established to identify: (1) The optimal design configuration, (2) the optimal values of design parameters, and (3) the boundaries of functional performance variations. Sensitivity analysis considering the impact of parameter uncertainties on functional performance variation boundaries has also been conducted. A case study on the design of a truss system has been conducted. Case study results show that the sensitivities of functional performance variation boundaries to the design parameter uncertainties can be reduced significantly using the new robust design approach.

Sensitive integration of multilevel optimization model in human activity recognition for smartphone and smartwatch applications

This study proposes an intelligent data analysis model for finding optimal patterns in human activities on the basis of biometric features obtained from four sensors installed on smartphone and smartwatch devices. Theproposed model, referred to as Scheduling Activities of smartphone and smartwatch based on Optimal Pattern Model(SA-OPM), consists of four main stages. The first stage relates to the collection of data from four sensors in real time (i.e., two smartphone sensors called accelerometer and gyroscope and two smartwatch sensors of the same name). The second stage involves the preprocessing of the data by converting them into graphs. As graphs are difficult to deal with directly, a deterministic selection algorithm is proposed as a new method to find the optimal root to split the graphs into multiple subgraphs. The third stage entails determining the number of samples related to each subgraphby using the optimization technique called the lion optimization algorithm. The final stage involves the generation of patterns from the optimal subgraph by using the association pattern algorithm called gSpan. The pattern finder based on Forward-Backward Rules (FBR) generates the optimal patterns and thus aids humans in organizing their activities. Results indicate that the proposed SA-OPM model generates robust and authentic patterns of human activities.

Based on the multi-level optimization model of remanufacturing and pricing balance strategy research under TIFR subsidy in China

Remanufacturing is one of the most effective forms of the recycling economy, and the “Trade-in for Remanufacturing” (TIFR) program in China plays an important role in the development of remanufacturing. To understand this new business model of remanufacturing, the price and demand relationship of the NP and RP are examined in two periods, considering TIFR subsidy which is in practice in China. Comparing integrated optimization scheme and tiered optimization scheme, this paper then researches the pricing strategy with TIFR subsidy respectively, as multi-object optimization is employed in the latter scheme. Tiered optimization pricing is found to improve the old customer’s TIFR enthusiasm, balance the remanufacturing system and work better with TIFR subsidy through numerical experiments. This paper studies the impacts of subsidy rate, receptiveness to RP, and the mixture of them, then verifies the proposed model and gives an inspiration to the management of the new remanufacturing business model about TIFR subsidy.

Multi-level fleet size optimization for containers handling using double-cycling strategy

Every few years, larger containerized vessels are introduced to the market to accommodate the increase in global trade. Although increasing the capacity of vessels results in maximizing the amount of imported and exported goods per voyage, yet it is accompanied with new challenges to terminal planners. One of the primary challenges is minimizing the vessel turnaround time with the least possible cost. In this context, this paper presents the development of a multi-level optimization model using the elitist non-dominated sorting genetic algorithm (NSGA-II) to determine the optimal or near-optimal fleet size combination of the different container handling equipment used in the terminal. The model aims to minimize two conflicting objective functions, namely, vessel turnaround time and total handling cost. Furthermore, the model considers a double-cycling strategy for the container handling process to achieve increased productivity and eventually more reduction in the vessel turnaround time. The model was implemented on a real-life case study to demonstrate its efficiency and the benefit of employing the double-cycling strategy compared with the traditional single-cycling strategy. The results demonstrated the efficiency of employing the double-cycling strategy by providing a reduction of above 20% in both the vessel turnaround time and the total handling cost and an increase of above 25% in the productivity when compared to the traditional single-cycling strategy.

Optimal allocation of energy storage and solar photovoltaic systems with residential demand scheduling

Improvements to the current generation and distribution of electricity via demand side management (DSM) and storage systems are prevalent facing increasing energy demand and environmental implications of electricity generation. In this paper, a multi-level optimization model, which incorporates energy demand scheduler (DS), energy storage (ES) and solar photovoltaic (PV) panels amongst households, was developed so as to lower the peak-to-average ratio (PAR) of energy demand and reduce electricity bills. This model consists of three levels: (1) household consumption optimization (solo opt) using convex programming, (2) grid consumption optimization (base opt) via a game-theoretic framework, and (3) ES/PV allocation optimization using genetic algorithm (GA opt). This framework searches for the optimal allocation of ES/PV in a heterogeneous residential population subdivided into consumer groups by household sizes and income levels. A case study was performed with model parameters determined by referencing state-averaged electricity bills and electricity usage data from Texas, US. The results showed that GA opt can achieve bills savings of ~11% and a PAR reduction from 1.53 to 1.30 by allocating a non-trivial optimal combination of ES/PVs to the households. Another GA opt approach was adopted by minimizing PAR and found that PAR can be effectively reduced from 1.53 to 1.00 with bills savings of ~4%. Most significantly, it was observed that the optimal allocation differs from the free market equilibrium due to positive externalities and synergies when combining DSM together with ES/PVs.

Operational optimization of industrial steam systems under uncertainty using data‐Driven adaptive robust optimization

This article addresses the operational optimization of industrial steam systems under device efficiency uncertainty using a data‐driven adaptive robust optimization approach. A semiempirical model of steam turbine is first developed based on process mechanism and operational data. Uncertain parameters of the proposed steam turbine model are further derived from the historical process data. A robust kernel density estimation method is then used to construct the uncertainty sets for modeling these uncertain parameters. The data‐driven uncertainty sets are incorporated into a two‐stage adaptive robust mixed‐integer linear programming (MILP) framework for operational optimization of steam systems to minimize the total operating cost. Integer variables are introduced to model the on/off decisions of the steam turbines and electrical motors, which are the major energy consumers of the steam system. By applying the affine decision rule, the proposed multilevel optimization model is transformed into its robust counterpart, which is a single‐level MILP problem. The proposed framework is applied to the steam system of a real‐world ethylene plant to demonstrate its applicability. © 2018 American Institute of Chemical Engineers AIChE J, 65: e16500 2019

Self-balancing robust scheduling with flexible batch loads for energy intensive corporate microgrid

With the development of microgrid technology, for an energy intensive corporate such as an iron and steel plant energy consumptions and costs can be saved significantly by achieving the balance between self-generation and consumption. In this paper, we present a self-balancing and robust scheduling model with flexible batch loads for an energy intensive corporate. The model is a multi-level optimization model with the objective to minimize the unbalance cost in the worst case. Load following properties are given to determine whether the uncertain loads can be followed or not, and the self-balancing capability of an energy intensive corporate is analyzed. The problem is equivalently converted from the multi-level model to a single-level optimization model with a set of constraints. In this way, the iteration between the outer and inner level can be avoided. Case study based on an energy intensive corporate microgrid is tested and the results show that the unbalance cost can be significantly reduced by using the robust self-balancing model. In addition, compared the approach method with iterative solving method, computational efficiency can be improved and local optimum can be avoided.

Liner Ship Fleet Deployment with Uncertain Demand

This paper points out that the deployment problem of the liner ship fleet with uncertain demand is different from other logistics problems with uncertain demand (e.g., truck transport and airlines) because container ships operate 24 h a day and 7 days a week. This difference is largely ignored in the literature. To address this problem, a multilevel optimization model is developed. In addition to liner ship fleet deployment, the model is applicable to other liner shipping decision problems, such as network design with uncertain demand, and to port operations planning problems, such as berth planning with uncertain ship arrival times.

Multi‐level design model and genetic algorithm for structural control system optimization

AbstractThe integrated optimum problem of structures subjected to strong earthquakes and wind excitations, optimizing the number of actuators, the configuration of actuators and the control algorithms simultaneously, is studied. Two control algorithms, optimal control and acceleration feedback control, are used as the control algorithms. A multi‐level optimization model is proposed with respect to the solution procedure of the optimum problem. The characteristics of the model are analysed, and the formulation of each suboptimization problem at each level is presented. To solve the multi‐level optimization problem, a multi‐level genetic algorithm (MLGA) is proposed. The proposed model and MLGA are used to solve two multi‐level optimization problems in which the optimization of the number of actuators, the positions of actuators and the control algorithm are considered in different levels. In problem 1, an example structure is excited by strong wind, and in problem 2, an example structure is subjected to strong earthquake excitation. Copyright © 2001 John Wiley & Sons, Ltd.

Multi-level optimal design of buildings with active control under winds using genetic algorithms

The goal of this paper is to study the complicated optimal design problem of integrating the number of actuators, the configuration of the actuators and the active control algorithms in buildings excited by strong wind force. To do this, the following sequential studies are carried out: (1) Two control algorithms, linear quadratic regulator (LQR) and acceleration feedback control algorithm, are analyzed and used as the control algorithms. (2) The characteristics of the optimal design problem are analyzed in detail by a simulation study. (3) A multi-level optimization model is proposed, and the formulation of sub-optimization problems in each level is presented. (4) To solve the multi-level optimization problem, a multi-level genetic algorithm (MLGA) is proposed. The properties and implementation of MLGA are given and analyzed in detail. Finally, the optimal design model and the corresponding solving algorithm are tested by numerical simulation. The results show that: (1) in the design of actively controlled structures subjected to strong wind excitation, the problem of considering the number of actuators, the position of actuators and the control algorithm simultaneously is of a multi-level design optimization with the properties of non-linearity, discreteness and so on. (2) This kind of optimization problem should be described naturally by the multi-level design model. (3) The multi-level genetic algorithm can solve this complicated problem effectively. (4) The optimal locations of actuators depend on the control approaches.

Cost Effectiveness from Regional Optimization in the USDA Forest Service

Abstract This paper addresses the potential for improving cost effectiveness in the National Forest System through large-scale optimization. It is shown theoretically why allocations of output targets and budgets across National Forests should be expected to be inefficient in the absence of large-scale optimization analysis. And, conservative estimates of the potential for cost savings from large-scale optimization are developed using a multilevel optimization model. These estimates indicate that the output levels in the current "preferred alternatives" in Forest Service land management planning could be achieved for at least 1 to 11% less cost if outputs and budgets were allocated more efficiently across forests. For. Sci. 36(4):939-954.