Towards Automated Scheduling of NASA’s Deep Space Network: A Mixed Integer Linear Programming Approach
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Johnston, Mark↗
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Mixed-Integer Nonlinear Programming Applications: Pyomo Tools and Tailored Strategies.
Abstract not provided.
Laird, Carl Damon↗
Engineering calculations for communications satellite systems planning
Computer-based techniques for optimizing communications-satellite orbit and frequency assignments are discussed. A gradient-search code was tested against a BSS scenario derived from the RARC-83 data. Improvement was obtained, but each iteration requires about 50 minutes of IBM-3081 CPU time. Gradient-search experiments on a small FSS test problem, consisting of a single service area served by 8 satellites, showed quickest convergence when the satellites were all initially placed near the center of the available orbital arc with moderate spacing. A transformation technique is proposed for investigating the surface topography of the objective function used in the gradient-search method. A new synthesis approach is based on transforming single-entry interference constraints into corresponding constraints on satellite spacings. These constraints are used with linear objective functions to formulate the co-channel orbital assignment task as a linear-programming (LP) problem or mixed integer programming (MIP) problem. Globally optimal solutions are always found with the MIP problems, but not necessarily with the LP problems. The MIP solutions can be used to evaluate the quality of the LP solutions. The initial results are very encouraging.
Reilly, C. H.↗
A bilevel multistage stochastic self-scheduling model with indivisibilities for trading in the continuous intraday electricity market
In this paper, we study the profit maximization problem of a virtual power plant trading in the continuous intraday electricity market. Our virtual power plant model is compatible with renewable, and thermal assets, covering a range of virtual power plants currently participating in energy markets. We model the trading problem as a bilevel multistage stochastic program. The upper level of the problem accounts for the profit maximization of the virtual power plant with explicit modeling of the technical constraints of the operational status of the thermal power plant including minimum start-up and shut-down times, ramp-up and ramp-down rates, and minimum generation level. The upper level also decides which continuous and indivisible (fill-or-kill) orders are submitted to the market. The lower-level problem accounts for the clearing of the continuous intraday market, i.e., matching of buy and sell orders. Because of the presence of fill-or-kill orders, the lower-level problem is mixed-integer, which prevents its direct conversion to a single-level problem using duality. In order to solve this challenging problem, we develop a convex-hull extended formulation for the lower-level problem, apply duality theory to obtain a single-level stochastic equivalent formulation, and employ McCormick envelopes to turn the problem into a multistage stochastic mixed-integer linear problem, which we solve using the stochastic dual dynamic integer programming algorithm. We conduct numerical experiments and analyze the optimal trading behavior of a virtual power plant trading in an ideal continuous market without arbitrage.
Bilevel multistage stochastic programming problem↗
New approaches for efficient solution of hitting set problem
A new method for solving the hitting set problem is proposed. This method is based on the mapping of the problem onto an integer programming optimization problem. this new approach provides an algorithm with much better performance compare to the algorithms for the hitting set problem that currently are used for solving the diagnosis problem.
integer programming↗
Optimizing design and dispatch of a renewable energy system with combined heat and power
We embellish a mixed-integer program that prescribes a set of renewable energy, conventional generation, and storage technologies to procure, along with a corresponding dispatch strategy. Specifically, we add combined heat and power to this set. The model minimizes fixed and operational costs less incentives for the use of various technologies, subject to a series of component interoperability and system-wide constraints. The resulting mixed-integer linear program contains hundreds of thousands of variables and constraints. We demonstrate how to efficiently formulate and solve the corresponding instances such that we produce near-optimal solutions in minutes. A previous rendition of the model required hours of solution time for the same instances.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Optimal selection of space transportation fleet to meet multi-mission space program needs
A space program that spans several decades will be comprised of a collection of missions such as low earth orbital space station, a polar platform, geosynchronous space station, lunar base, Mars astronaut mission, and Mars base. The optimal selection of a fleet of several recoverable and expendable launch vehicles, upper stages, and interplanetary spacecraft necessary to logistically establish and support these space missions can be examined by means of a linear integer programming optimization model. Such a selection must be made because the economies of scale which comes from producing large quantities of a few standard vehicle types, rather than many, will be needed to provide learning curve effects to reduce the overall cost of space transportation if these future missions are to be affordable. Optimization model inputs come from data and from vehicle designs. Each launch vehicle currently in existence has a launch history, giving rise to statistical estimates of launch reliability. For future, not-yet-developed launch vehicles, theoretical reliabilities corresponding to the maturity of the launch vehicles' technology and the degree of design redundancy must be estimated. Also, each such launch vehicle has a certain historical or estimated development cost, tooling cost, and a variable cost. The cost of a launch used in this paper includes the variable cost plus an amortized portion of the fixed and development costs. The integer linear programming model will have several constraint equations based on assumptions of mission mass requirements, volume requirements, and number of astronauts needed. The model will minimize launch vehicle logistic support cost and will select the most desirable launch vehicle fleet.
Morgenthaler, George W.↗
Optimization-Driven Scenario Grouping
Scenario decomposition algorithms for stochastic programs compute bounds by dualizing all nonanticipativity constraints and solving individual scenario problems independently. Here, we develop an approach that improves on these bounds by reinforcing a carefully chosen subset of nonanticipativity constraints, effectively placing scenarios into groups. Specifically, we formulate an optimization problem for grouping scenarios that aims to improve the bound by optimizing a proxy metric based on information obtained from evaluating a subset of candidate feasible solutions. We show that the proposed grouping problem is NP-hard in general, identify a polynomially solvable case, and present two formulations for solving the problem: a matching formulation for a special case and a mixed-integer programming formulation for the general case. We use the proposed grouping scheme as a preprocessing step for a particular scenario decomposition algorithm and demonstrate its effectiveness in solving standard test instances of two-stage 0–1 stochastic programs. Using this approach, we are able to prove optimality for all previously unsolved instances of a standard test set. Additionally, we implement this scheme as a preprocessing step for PySP, a publicly available and widely used implementation of progressive hedging, and compare this grouping approach with standard grouping approaches on large-scale stochastic unit commitment instances. Finally, the idea is extended to propose a finitely convergent algorithm for two-stage stochastic programs with a finite feasible region.
97 MATHEMATICS AND COMPUTING↗
Hybrid Imitation Learning for Real-Time Service Restoration in Resilient Distribution Systems
Self-healing capability is a critical factor for a resilient distribution system, which requires intelligent agents to automatically perform service restoration online, including network reconfiguration and reactive power dispatch. Here, the article proposes the imitation learning framework for training such an agent, where the agent will interact with an expert built based on the mixed-integer program to learn its optimal policy, and therefore significantly improve the training efficiency compared with exploration-dominant reinforcement learning (RL) methods. This significantly improved training efficiency makes the training problem under N-k scenarios tractable. A hybrid policy network is proposed to handle tie-line operations and reactive power dispatch simultaneously to further improve the restoration performance. The 33-bus and 119-bus systems with N-k disturbances are employed to conduct the training. The results indicate that the proposed method outperforms traditional RL algorithms such as the deep-Q network.
42 ENGINEERING↗
New high performance algorithmic solution for diagnosis problem
In this paper we address the problem of generating the minimal diagnosis from the conflicts. This problem can be formulated as the well-known Hitting Set Problem. Our approach starts by mapping the Hitting Set problem into the Integer Programming Problem that enables us, for the first time, a priori determination of the lower and upper bounds on the size for the solution. Based on these bounds, we introduce a new concept of solution window for the problem. We also propose a new branch-and-bound technique that not only is faster than the current techniques in terms of number of operations (by exploiting the structure of the problem) but also, using the concept of window, allows a massive reduction (pruning) in the number of branches. Furthermore, as the branch-and-bound proceeds, the solution window is dynamically updated and narrowed to enable further pruning.
diagnosis problems↗
Real-time Ridesharing for Transportation Hubs with Demand and Supply Uncertainty
Transportation hubs in major cities generate a significant amount of trips by taxis and for-hail vehicles (FHV), with many of the trips sharing similar destinations. This suggests promising opportunities to leverage the collective travel needs with dedicated ridesharing solutions to reduce the externalities of excessive traffic at transportation hubs. In this study, we develop a novel dynamic ridesharing approach to serve trips from the transportation hub by considering (1) demand (new passengers) and supply (newly available vehicles) in the near future and (2) the uncertainty of future predictions. Our approach consists of two stages. In the first stage, we develop a data structure called hub mobility tree to generate potential combinations of shareable trips as candidate schedules efficiently. Then the generated schedules are used in the second stage to formulate the stochastic hub-based ridesharing problem (SHRP), which is a stochastic integer programming problem with the objective to maximize the total expected ridesharing profit over time. Due to the prohibitive number of shareable trips, we then approximately solve SHRP by the sample average approximate method (SAA), and a dual Lagrangian technique is implemented to further improve the scalability of the solution approach. We demonstrate the performances of the proposed method by simulating the ridesharing service at JFK airport using NYC taxi and FHV data. The results indicate that the proposed method outperforms the myopic ridesharing (maximize profit for a single time step) and the rolling horizon method with point estimation of future demand and supply.
dynamic ridesharing↗
An agent-based approach to study the diffusion rate and the effect of policies on joint placement of photovoltaic panels and green roof under climate change uncertainty
As two of the highest trending green technologies, photovoltaic panels and green roofs are proven to be effective practices for energy generation and energy saving. The achievable impact from the widespread installation of such technologies is, however, not clearly established. This is mainly because the degree of this impact highly depends on the inherently uncertain environmental and climate factors, as well as the unknown adoption rates of these technologies, which in turn depend on different characteristics of decision makers and interactions among them. To that end, this study aims to investigate the diffusion rate of these green technologies under uncertainties caused by climate change, characteristics of adopters, and their interactions. An integrated framework is developed to capture the interplay between financial and attitudinal aspects, as well as the uncertainties due to both the stochastic nature of system parameters and the interactions among agents involving human beings. Specifically, this framework consists of a integer programming model to optimize the green roof and/or photovoltaic panel installation settings for a given building under climate change uncertainty, and an agent-based model to factor in the role of human behavior and interactions. A case study for the city of Knoxville, TN, is presented to evaluate the effects of different policies on the diffusion rate of the green technologies of interest. The results show that the affordability of green technologies and public awareness are the key drivers of the adoption of these technologies, which highlight the important role of the decision makers in impacting the diffusion rate.
14 SOLAR ENERGY↗
Automated shaker placement and regularized input estimation for MIMO testing.
Multi-input, multi-output (MIMO) testing is used in component qualification to reproduce operational responses in the laboratory. It is often preferred to single-input and base-shake testing because of the potential for equivalent or better tests using smaller actuators and shorter test suites. Given a target response, two key steps in MIMO test design are selecting actuator locations and solving for input loads. Actuator locations are often manually selected using expert judgment. If an automatic method is used, locations are usually determined by simulating the vibration control problem and minimizing a combination of the input energy and control residuals. To select a configuration, the relative importance of input energy and residuals must be specified. Specifying relative weights is, in general, a manual and subjective process. This paper develops an objective function that compares actuator configurations based on control accuracy and required input energy without any manual parameter tuning. The objective function uses an optimally selected tradeoff parameter for each candidate configuration. To choose actuator locations using the new objective function, a pivoting algorithm for integer programming problems is developed. Starting with an initial configuration (such as the one generated by a greedy algorithm), the pivoting algorithm guarantees an objective function decrease in each iteration until convergence is reached. In a simulation featuring a structure excited by a diffuse acoustic field, electrodynamic shaker locations and regularized inputs are solved for without any analyst-specified parameters. Simulations are performed in MIMO configurations where the number of target responses is less than, equal to, and greater than the number of actuators.
Multi-input multi-output↗
Partner with a Third-Party Delivery Service or Not? A Prediction-and-Decision Tool for Restaurants Facing Takeout Demand Surges During a Pandemic
Amidst the COVID-19 pandemic, restaurants become more reliant on no-contact pick-up or delivery ways for serving customers. As a result, they need to make tactical planning decisions such as whether to partner with online platforms, to form their own delivery team, or both. In this paper, we develop an integrated prediction-decision model to analyze the profit of combining the two approaches and to decide the needed number of drivers under stochastic demand. We first use the susceptible-infected-recovered (SIR) model to forecast future infected cases in a given region and then construct an autoregressive-moving-average (ARMA) regression model to predict food-ordering demand. Using predicted demand samples, we formulate a stochastic integer program to optimize food delivery plans. We conduct numerical studies using COVID-19 data and food-ordering demand data collected from local restaurants in Nuevo Leon, Mexico, from April to October 2020, to show results for helping restaurants build contingency plans under rapid market changes. Our method can be used under unexpected demand surges, various infection/vaccination status, and demand patterns. Here, our results show that a restaurant can benefit from partnering with third-party delivery platforms when (i) the subscription fee is low, (ii) customers can flexibly decide whether to order from platforms or from restaurants directly, (iii) customers require more efficient delivery, (iv) average delivery distance is long, or (v) demand variance is high.
97 MATHEMATICS AND COMPUTING↗
Co-design optimization of combined heat and power-based microgrids
With the emergent need for clean and reliable energy resources, hybrid energy systems, such as the microgrid, are widely adopted in the United States. A microgrid can consist of various distributed energy resources, for instance, combined heat and power (CHP) systems. Here, the CHP module is a distributed cogeneration technology that produces electricity and recaptures heat generated as a by-product. It is an energy-efficient technology converting heat that would otherwise be wasted to valuable thermal energy. For an optimal system configuration, this study develops a novel co-design optimization framework for CHP-based cogeneration microgrids. The framework provides the stakeholder with a method to optimize investments and attain resilient operations. The proposed co-design framework has a mixed integer programming (MIP) model that outputs decisions for both plant designs and operating controls. The microgrid considered in this study contains six components: the CHP, boiler, heat recovery unit, thermal storage system, power storage system, and photovoltaic plant. After solving the MIP model, the optimal design parameters of each component can be found to minimize the total installation cost of all components in the microgrid. Furthermore, the online costs from energy production, operation, maintenance, machine startup, and disruption-induced unsatisfied loads are minimized by solving the optimal control decisions for operations. Case studies based on designing a CHP-based microgrid with empirical data are conducted. Moreover, we consider both nominal and disruptive operational scenarios to validate the performance of the proposed co-design framework in terms of a cost-effective, resilient system.
42 ENGINEERING↗
Enhancing Active Distribution Systems Resilience by Fully Distributed Self-Healing Strategy
Distributed restoration can exploit smart grid technologies to enhance the resilience of active distribution networks toward a self-healing smart grid. However, the large number of decision variables, especially the binary ones for reconfiguration, bring challenges to developing scalable distributed distribution service restoration (DDSR) strategies. This paper proposes a fully distributed solution procedure based on the alternating direction method of multipliers (ADMM) for mixed-integer programming problems and applies to develop the DDSR framework. The method consists of relax-drive-polish phases, 1) relaxing binary variables, and applying the convex ADMM as a warm start; 2) driving the solutions toward Boolean values through a proximal operator; 3) fixing the obtained binding binary variables and solving the rest of the problem to polish results and achieve a high-quality suboptimal solution. Then, an autonomous clustering strategy and consensus ADMM are integrated with the proposed method to realize the fully distributed cluster-based framework of DDSR. This framework can first determine DER scheduling and switch status for reconfiguration to energize the out-of-service areas from local faults, and then provide the load restoration solution in a distributed manner for total blackouts in large-scale distribution networks. Furthermore, the effectiveness and scalability of the proposed DDSR framework are demonstrated through testing on the IEEE 123-node, IEEE 8500-node, and synthetic 100k-node test feeders.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Optimization of a Mixed Fleet of Aerial Drones for Medical Supplies: A Case Study of Blood Delivery Logistics
Aerial drones have emerged as an innovative solution for faster transportation of time-sensitive items (e.g., emergency medical supplies), potentially reducing the transmission of contagious diseases and enhancing healthcare availability through contactless autonomous delivery. We study fleet sizing and efficient scheduling of a mixed fleet of drones for delivering time-sensitive medical items having distinct release and due times to minimize the required fleet size and fleet composition, the required number of additional batteries, and the total energy consumption. We continuously track the remaining battery energy of drones to determine the optimal timing for battery replacement, rather than replacing the battery at each node. Using actual drone flight test data, we employed a machine learning (ML) method to estimate the energy consumption of different drone types during flight segments for different operating parameters. We present a novel mixed-integer programming model to efficiently formulate the problem that integrates the estimated energy consumption functions from ML. We propose a new greedy heuristic (GH) algorithm and a customized genetic algorithm (GA) for solving large-scale instances of this problem faster. Results demonstrate that the GH algorithm is substantially faster than the accelerated CPLEX and the GA, while sacrificing the solution quality by a small amount. Results based on an actual blood sample delivery case study from Pendleton, Oregon, United States, show that using a mixed fleet of drones reduces the total cost and total energy consumption up to 18.18% and 28.7%, respectively, compared to using a homogeneous fleet.
29 - ENERGY PLANNING, POLICY AND ECONOMY↗