General Cost Functions Research Articles

Scheduling Flexible Nonpreemptive Loads in Smart-Grid Networks

A market consisting of a generator with thermal and renewable generation capability, a set of <i>nonpreemptive</i> loads (i.e., loads which cannot be interrupted once started), and an independent system operator (ISO) is considered. Loads are characterized by durations, power demand rates, and utility for receiving service, as well as disutility functions giving preferences for time slots in which service is preferred. Given this information, along with the generator&#x2019;s thermal generation cost function and forecast renewable generation, the social planner solves a mixed-integer program to determine a load activation schedule which maximizes social welfare. Assuming price-taking behavior, we develop a competitive equilibrium concept based on a relaxed version of the social planner&#x2019;s problem, which includes prices for consumption and incentives for flexibility, and allows for probabilistic allocation of power to loads. Considering each load as representative of a population of identical loads with scaled characteristics, we demonstrate that the relaxed social planner&#x2019;s problem gives an exact solution to the original mixed integer problem in the large population limit, and give a market mechanism for implementing the competitive equilibrium. Finally, we evaluate via case study the benefit of incorporating load flexibility information into power consumption and generation scheduling in terms of proportion of loads served and overall social welfare.

Probabilistic clearing of the reactive power market in the presence of solar power plants and considering the solar irradiance variations

With the advent of renewable energy plants, new sources have been created to provide reactive power. This paper first explores the importance of renewable energy sources growth, especially solar power plants, then it examined the participation of solar power plants in the reactive power market. Various cost components of the solar power plant have been investigated and a general cost function model has been proposed for all reactive power suppliers that help the independent system operator (ISO) to better manage the system. Considering the probabilistic nature of energy generation from solar power plants, solar irradiance variations are considered in the reactive market and a probabilistic structure is proposed. To simulate and to consider the probabilistic nature of solar irradiance, the Monte Carlo method is used in simulations. The proposed method has been tested on the IEEE 24 buses system and two definitive and probabilistic markets are compared. As stated in the results, the proposed algorithm has satisfactory results.

Dynamic Optimization of Bus Line Schedule in Commuter Corridor Based on Bus IC Card Data

The aim of this study was to explore the bus operating state of the city bus passenger corridor, taking the minimum bus operating cost and passenger travel cost as the objective function, taking passenger flow demand and operating income as the constraint, and considering the average speed change of the bus line in the bus corridor at different times. This paper proposes a dynamic optimization model of bus route schedule based on bus Integrated Circuit Card (IC Card) data. The optimization variable is the departure frequency of the candidate lines. To solve the model, a dynamic departure interval optimization method based on improved Genetic Algorithm (GA) was designed under different decision preferences. The method includes the calibration of generalized cost functions for passengers and bus companies and grasps the characteristics of bus operating speed changes and the design of departure strategies under different decision preferences. The validity and applicability of the proposed method are verified by a numerical example. We mainly carried out the following work: (1) Dynamic analysis of the time dimension of the bus departure interval takes into account the changes in passenger time characteristics during peak periods. (2) Seven schemes of weight ratio of passenger waiting time cost and bus operation cost were designed, and the departure intervals with different benefit orientations of passengers and operators were discussed, respectively, so as to select the corresponding departure schemes for decision makers under different decision preferences. The results show that (1) the total cost of the 7 different weighting schemes is lower than the actual value by 6.90% to 18.20%; (2) when decision makers need to bias the weight to the bus company, the weight ratio α : β between passengers and bus company is 0.25 : 0.75 which works best. The frequency of departures has been reduced by 6, and at the same time, the total optimized cost is reduced by 18.2%; (3) when decision makers need to bias the weight to the passengers, the weight ratio α : β between the passengers and bus company is 0.75 : 0.25 which works best. The frequency of departures has been increased by 19, and at the same time, the total optimized cost is reduced by 17.7%; and (4) when decision makers consider passengers and bus companies equally, the weight ratio α : β between passengers and bus companies is 0.5 : 0.5, the optimization cost is the closest to the actual cost, the optimization cost is reduced by 6.9%, and the frequency of departures has been increased by 5. The results show that the model in this paper provides a new idea for the information mining of bus routes in the research based on the bus IC Card data and provides an effective tool for the management of different operation decision preferences.

Online Convex Optimization for Data-Driven Control of Dynamical Systems

We propose an algorithm based on online convex optimization for controlling discrete-time linear dynamical systems. The algorithm is data-driven, i.e., does not require a model of the system, and is able to handle a priori unknown and time-varying cost functions. To this end, we make use of a single persistently exciting input-output sequence of the system and results from behavioral systems theory which enable it to handle unknown linear time-invariant systems. Moreover, we consider noisy output feedback instead of full state measurements and allow general economic cost functions. Our analysis of the closed loop reveals that the algorithm is able to achieve sublinear regret, where the measurement noise only adds an additional constant term to the regret upper bound. In order to do so, we derive a data-driven characterization of the steady-state manifold of an unknown system. Moreover, our algorithm is able to asymptotically exactly estimate the measurement noise. The effectiveness and applicational aspects of the proposed method are illustrated by means of a detailed simulation example in thermal control.

A Class of Pareto Optimal Binaural Beamformers

The objective of binaural multi-microphone speech enhancement algorithms can be viewed as a multi-criteria design problem as there are several requirements to be met. The objective is not only to extract the target speaker without distortion, but also to suppress interfering sources (e.g., competing speakers) and ambient background noise, while preserving the auditory impression of the complete acoustic scene. Such a multi-objective problem (MOP) can be solved using a Pareto frontier, which provides a useful trade-off between the different criteria. In this paper, we propose a unified Pareto optimization framework, which is achieved by defining a generalized mean squared error (MSE) cost function, derived from a MOP. The solution to the multi-criteria problem is grounded on a solid mathematical foundation. The MSE cost function consists of a weighted sum of speech distortion (SD), partial interference reduction (IR), and partial noise reduction (NR) terms with scaling parameters that control the amount of IR and NR. The filter minimizing this generalized cost function, denoted Pareto optimal binaural multichannel Wiener filter (Pareto-BMWF), constitutes a generalization of various binaural MWF-based and binaural MVDR-based beamformers. This solution is optimal for any set of parameters. The improved speech enhancement capabilities are experimentally demonstrated using real-signal recordings when estimation errors are present and the binaural cue preservation capabilities are analyzed.

General attraction analysis on high-speed rail and aviation between Beijing and Shanghai, China

High-speed rail and aviation are the two most popular modes of transportation between Beijing and Shanghai. Based on the existing literature, this paper summarized seven key influencing factors of the high-speed rail and civil aviation comprehensive attraction from the Beijing-Shanghai corridor. Furthermore, we constructed five single index models to quantify them. By analysing the logical relationships among various indicators, the generalized travel cost function with different modes of transportation and different user types under different seasons is finally obtained. To ensure the reliability of the analysis results, the collected data were used to calibrate most of the parameters of the generalized cost function model. After that, a series of sensitivity analysis are conducted. The results show that the attractiveness ranking of these two transportation modes is influenced by the purpose of the trip, the characteristics of the passengers, and changes in the season. This paper may offer some valuable references for aviation and railway transport companies.

A Distributed Approach to Economic Dispatch in Power Systems

This paper proposes a distributed dynamics to solve the economic dispatch problem in electric power systems. The approach can be implemented in a fully decentralized manner and it does not require any central control unit. It is assumed that the participating entities can exchange information over a potentially asymmetric communication network. In particular, when the local generation cost functions are quadratic and the communication network is strongly connected, we establish the exponential convergence of the proposed dynamics to the optimal solution of the dispatch problem. We also provide simulation studies on an IEEE benchmark to demonstrate the performance of the proposed dynamics.

Impact of parameter control on the performance of APSO and PSO algorithms for the CSTHTS problem: An improvement in algorithmic structure and results.

Cascaded Short Term Hydro-Thermal Scheduling problem (CSTHTS) is a single objective, non-linear multi-modal or convex (depending upon the cost function of thermal generation) type of Short Term Hydro-Thermal Scheduling (STHTS), having complex hydel constraints. It has been solved by many metaheuristic optimization algorithms, as found in the literature. Recently, the authors have published the best-achieved results of the CSTHTS problem having quadratic fuel cost function of thermal generation using an improved variant of the Accelerated PSO (APSO) algorithm, as compared to the other previously implemented algorithms. This article discusses and presents further improvement in the results obtained by both improved variants of APSO and PSO algorithms, implemented on the CSTHTS problem.

Variational quantum algorithm for molecular geometry optimization

Classical algorithms for predicting the equilibrium geometry of strongly correlated molecules require expensive wave function methods that become impractical already for few-atom systems. In this work, we introduce a variational quantum algorithm for finding the most stable structure of a molecule by explicitly considering the parametric dependence of the electronic Hamiltonian on the nuclear coordinates. The equilibrium geometry of the molecule is obtained by minimizing a more general cost function that depends on both the quantum circuit and the Hamiltonian parameters, which are simultaneously optimized at each step. The algorithm is applied to find the equilibrium geometries of the ${\mathrm{H}}_{2},$ ${\mathrm{H}}_{3}{}^{+},$ ${\mathrm{BeH}}_{2},$ and ${\mathrm{H}}_{2}\mathrm{O}$ molecules. The quantum circuits used to prepare the electronic ground state for each molecule were designed using an adaptive algorithm where excitation gates in the form of Givens rotations are selected according to the norm of their gradient. All quantum simulations are performed using the PennyLane library for quantum differentiable programming. The optimized geometrical parameters for the simulated molecules show an excellent agreement with their counterparts computed using classical quantum chemistry methods.

Recursive Constraint Manifold Subsearch for Multirobot Path Planning with Cooperative Tasks

The Cooperative Path Planning (CPP) problem seeks to determine a path for a group of robots which form temporary teams to perform tasks. The multi-scale effects of simultaneously coordinating many robots distributed across the workspace while also tightly coordinating the members of teams increases the difficulty of planning. Previous research produced the Constraint Manifold Subsearch (CMS) algorithm that can find minimal length paths to the CPP problem. However, CMS as currently formulated cannot handle more general cost functions, such as minimizing energy expenditure, and cannot handle task schedules that require multiple input teams to merge to form a set of multiple output teams. Furthermore, as CMS must couple planning for all interacting teams, it does not scale well to very large environments. In this paper, we rederive the CMS algorithm using a task graph to reason about inter-team dependencies, allowing the use of more general cost functions and task schedules. We then introduce the recursive CMS (rCMS) algorithm that exploits the reformulation to split the CPP into independent subproblems, significantly reducing computational complexity. Simulation studies show that rCMS can solve substantially larger problems than CMS.

Dynamic analysis of R&amp;D in an oligopoly under general demand and cost functions

Dynamic analysis of R&amp;D in an oligopoly under general demand and cost functions

Advertising in an oligopoly with differentiated goods under general demand and cost functions: A differential game approach

AbstractWe present an analysis of advertising activities in a dynamic oligopoly with differentiated goods using a differential game approach under general demand and cost functions. The main conclusion is that the memoryless closed‐loop solution and the feedback solution are equivalent when there is no spillover effect of advertising activities. We also show that the comparison of the open‐loop solution and the memoryless closed‐loop solution depends on whether the firms’ outputs are strategic substitutes or strategic complements.

Cost- and Risk-Based Seismic Design Optimization of Nuclear Power Plant Safety Systems

Seismic analysis, design, and qualification of systems, structures, and components (SSCs) is a significant contributor to the capital cost of a nuclear power plant. To reduce capital costs of advanced nuclear power plants and make commercial nuclear energy more competitive, innovations are needed in their structural design and construction, and not just in the reactor core and associated systems. Seismic isolation has been identified as an important cost-cutting technology that enables standardization of equipment across various sites. This paper develops and demonstrates a cost- and risk-based seismic design optimization of a representative safety system in a nuclear power plant with the dual goals of minimizing overnight capital cost and meeting safety goals. The design optimization can also include component seismic isolation, in which case, the optimized design includes a set of equipment that needs to be seismically isolated to minimize capital cost. The open-source codes MASTODON and Dakota are used for seismic probabilistic risk assessment and design optimization, respectively. A generic nuclear facility with a safety system comprising SSCs that are common to nuclear power plants is considered for the demonstration of the design optimization and is assumed to be located at the Idaho National Laboratory site. Generic costs and seismic design cost functions are assumed for the SSCs of the safety system. The sum of the costs of the SSCs is minimized in the optimization process, while the risk of failure of the safety system is provided as a constraint. Results show that the optimization process reduces capital costs significantly while automatically prioritizing the safety of SSCs that contribute most to the risk of the safety system.

Variational Approach to Regularity of Optimal Transport Maps: General Cost Functions

We extend the variational approach to regularity for optimal transport maps initiated by Goldman and the first author to the case of general cost functions. Our main result is an epsilon -regularity result for optimal transport maps between Hölder continuous densities slightly more quantitative than the result by De Philippis–Figalli. One of the new contributions is the use of almost-minimality: if the cost is quantitatively close to the Euclidean cost function, a minimizer for the optimal transport problem with general cost is an almost-minimizer for the one with quadratic cost. This further highlights the connection between our variational approach and De Giorgi’s strategy for epsilon -regularity of minimal surfaces.

Social welfare maximization based optimal energy and reactive power dispatch using ant lion optimization algorithm

In this paper an optimal energy and reactive power dispatch problem is solved by using the ant lion optimization (ALO) algorithm by considering the total cost minimization and social welfare maximization (SWM) objectives. Two different market models are proposed in this work, i.e., conventional/sequential market clearing and the proposed/simultaneous market clearing. In each market model, two objectives, i.e., total cost minimization and SWM are considered. The conventional social welfare (SW) consists the benefit function of consumers and the cost function of active power generation. In this paper, the conventional SW is modified by including the reactive power cost function. The reactive power cost calculation is exactly same as that in the conventional practice. The most important difference is that instead of doing cost calculation in post-facto manner as in conventional practice, simultaneous approach is proposed in this work. The scientificity and suitability of the proposed simultaneous active and reactive power methodology has been examined on standard IEEE 30 bus test system.

A cordon-based reservation system for urban traffic management

This paper builds a novel framework for the cordon-based road reservation system to manage road traffic in urban areas, and the rules of reserving the right of way are established. Both the simulation experiment and the analytical modeling approaches offer evidence that the reservation system performs better than the basic system and some types of pricing systems. Considering two different types of vehicles (i.e., reserved and unreserved vehicles) and a general link cost function, we conduct three types of experiment simulations, including the basic system, the reservation system, and the pricing system. Although the severity of traffic congestion is mitigated inside the cordon both in the reservation and pricing systems, the reservation system shows the best network performance from the traffic indicators provided by the simulation software. In the analytical modeling approach, the Frank–Wolfe​ algorithm with a modified Bureau of Public Road function is used to analyze the road reservation scheme, and results agree with the expected effectiveness of the reservation both in the aspect of the total system travel time and the equilibrium of the traffic flow in the road network. Finally, practical issues about the application of the road reservation system are discussed.

Convergence analysis of a distributed gradient algorithm for economic dispatch in smart grids

The increasingly complex modern energy network arouses the need of flexible and dependable approaches to solve the economic dispatch problem (EDP) in the smart grids. Toward this end, this paper develops a fresh distributed algorithm with constant step-size, which aims to schedule the power generation among generators by complying with individual generation capacity limits to satisfy the total load demand at the minimized cost. The convergence of the proposed algorithm is analyzed through utilizing the Lyapunov method and the spectral decomposition technique. When the selected constant step-size is smaller than a specifically provided upper bound, the theoretical analysis demonstrates that the proposed algorithm can linearly achieve the optimal solution of the EDP under the smooth and strongly convex assumption on generation cost functions. In particular, the linear convergence rate of the proposed algorithm is tunable, and a relationship among the linear convergence rate, generation cost functions, network topology, weight matrix and constant step-size is established. The availability of the proposed algorithm is verified through simulation experiments.

A Game-Theoretic Framework for the Virtual Machines Migration Timing Problem

In a multi-tenant cloud, a number of Virtual Machines (VMs) are collocated on the same physical machine to optimize performance, power consumption and maximize profit. This, however, increases the risk of a malicious VM performing side-channel attacks and leaking sensitive information from neighboring VMs. As such, this paper develops and analyzes a game-theoretic framework for the VM migration timing problem in which the cloud provider decides when to migrate a VM to a different physical machine to reduce the risk of being compromised by a collocated malicious VM. The adversary decides the rate at which she launches new VMs to collocate with the victim VMs. Our formulation captures a data leakage model in which the cost incurred by the cloud provider depends on the duration of collocation with malicious VMs. It also captures costs incurred by the adversary in launching new VMs and by the defender in migrating VMs. We establish sufficient conditions for the existence of Nash equilibria for general cost functions, as well as for specific instantiations, and characterize the best response for both players. Furthermore, we extend our model to characterize its impact on the attacker’s payoff when the cloud utilizes intrusion detection systems that detect side-channel attacks. Our theoretical findings are corroborated with extensive numerical results in various settings as well as a proof-of-concept implementation in a realistic cloud setting.

The impacts of convex piecewise linear cost formulations on AC optimal power flow

Despite strong connections through shared application areas, research efforts on power market optimization (e.g., unit commitment) and power network optimization (e.g., optimal power flow) remain largely independent. A notable illustration of this is the treatment of power generation cost functions, where nonlinear network optimization has largely used polynomial representations and market optimization has adopted piecewise linear encodings. This work combines state-of-the-art results from both lines of research to understand the best mathematical formulations of the nonlinear AC optimal power flow problem with piecewise linear generation cost functions. An extensive numerical analysis of non-convex models, linear approximations, and convex relaxations across fifty-four realistic test cases illustrates that nonlinear optimization methods are surprisingly sensitive to the mathematical formulation of piecewise linear functions. The results indicate that a poor formulation choice can slow down algorithm performance by a factor of ten, increasing the runtime from seconds to minutes. These results provide valuable insights into the best formulations of nonlinear optimal power flow problems with piecewise linear cost functions, an important step towards building a new generation of energy markets that incorporate the nonlinear AC power flow model.

Dynamic Pricing and Matching for Two-Sided Markets with Strategic Servers

Motivated by applications in online marketplaces such as ridesharing, we study dynamic pricing and matching in two-sided queues with strategic servers. We consider a discrete-time process in which, heterogeneous customers and servers arrive. Each customer joins their type's queue, while servers might join a different type's queue depending on the prices posted by the system operator and an inconvenience cost. Then the system operator, constrained by a compatibility graph, decides the matching. The objective is to maximize the profit minus the expected waiting times. We develop a general framework that enables us to analyze a broad range of strategic behaviors. In particular, we encode servers' behavior in a properly defined cost function that can be tailored to various settings. Using this general cost function, we introduce a novel probabilistic fluid problem as an infinite dimensional optimization program. The probabilistic fluid model provides an upper bound on the achievable profit. We then study the system under a large market regime in which the arrival rates are scaled by η and present a probabilistic two-price policy and a max-weight matching policy which results in $O(η^1/3 )$ profit-loss. In addition, under a broad class of customer pricing policies, we show that any matching policy has profit-loss Ω(η1/3). Conditional on a given expected waiting time, we also establish scale-free lower and upper bounds for the profit. Our asymptotic analysis provides insight into near-optimal pricing and matching decisions, and our scale-free bounds provide insights into how different service levels impact the firm's profit.