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The water pump scheduling problem is an optimisation model that determines which water pumps will be turned on or off at each time period over a given time horizon for a given water supply system. This problem has received considerable attention in mining and desalination due to the high power consumption of water pumps and desalination plants and the complicated dynamics of water flows and the power market. Motivated by this, in this paper we solve the optimal operation of a desalinated water supply system consisting of interconnected tanks and pumps that transport water to high-altitude reservoirs. The optimisation of this process encounters several difficulties arising from (i) the nonlinearities of the equations for the frictional losses along the pipes and pumps, which makes the problem a nonlinear mixed-integer model, and (ii) many possible combinations of pressure head and flow rates, which quickly leads to high computational costs. These limitations prevent the problem from being solved in a reasonable computational time in high-altitude water supply systems with more than six pumps and reservoirs, as in many networks worldwide. Therefore, in this work we develop new exact methods for the optimal pump scheduling problem that use a binary expansion approach to efficiently account for the existing nonlinearities by reducing the computational difficulties of the original problem while keeping an excellent representation of the physical phenomena involved. We also extensively tested the proposed approach in different network topologies and a case study for a real-world copper mine water network, and we conclude that the binary expansion approach significantly reduces the computational time for solving the problem with high precision, which can be very relevant for the practical daily operation of real-world water supply systems. [ABSTRACT FROM AUTHOR]

With the increasing presence of renewable energy sources in the electrical power grid, demand response via thermostatic appliances such as electric water heaters is a promising way to compensate for the significant variability in renewable power generation. We propose a multistage stochastic optimization model that computes the optimal day-ahead target profile of the mean thermal energy contained in a large population of heaters, given various possible wind power production and uncontrollable load scenarios. This optimal profile is calculated to make the variable net demand as even as possible. [ABSTRACT FROM AUTHOR]

In this paper we introduce a new class of bounds for the maximum k -cut problem on undirected edge-weighted simple graphs. The bounds involve eigenvalues of the weighted adjacency matrix together with geometrical parameters. They generalize previous results on the maximum (2-)cut problem and we demonstrate that they can strictly improve over other eigenvalue bounds from the literature. We also report computational results illustrating the potential impact of the new bounds. [ABSTRACT FROM AUTHOR]

The optimal reactive power dispatch (ORPD) problem is an alternating current optimal power flow (ACOPF) problem where discrete control devices for regulating the reactive power, such as shunt elements and tap changers, are considered. The ORPD problem is modeled as a mixed-integer nonlinear optimization problem and its complexity is increased compared to the ACOPF problem, which is highly nonconvex and generally hard to solve. Recently, convex relaxations of the ACOPF problem have attracted a significant interest since they can lead to global optimality. We propose a tight conic relaxation of the ORPD problem and show that a round-off technique applied with this relaxation leads to near-global optimal solutions with very small guaranteed optimality gaps, unlike with the nonconvex continuous relaxation. We report computational results on selected MATPOWER test cases with up to 3375 buses. [ABSTRACT FROM AUTHOR]

Given an undirected edge weighted graph, the graph partitioning problem consists in determining a partition of the node set of the graph into subsets of prescribed sizes, so as to maximize the sum of the weights of the edges having both endpoints in the same subset. We introduce a new class of bounds for this problem relying on the full spectral information of the weighted adjacency matrix A. The expression of these bounds involves the eigenvalues and particular geometrical parameters defined using the eigenvectors of A. A connection is established between these parameters and the maximum cut problem. We report computational results showing that the new bounds compare favorably with previous bounds in the literature. [ABSTRACT FROM AUTHOR]

Summary: Smart homes have the potential to achieve optimal energy consumption with appropriate scheduling. The control of smart appliances can be based on optimization models, which should be realistic and efficient. However, increased realism also implies an increase in solution time. Many of the optimization models in the literature have limitations on the types of appliances considered and/or their reliability. This paper proposes a home energy management scheduling model that is more realistic and efficient. We develop a mixed integer linear optimization model that minimizes the energy cost while maintaining a given level of user comfort. Our main contribution is the variety of specific appliance models considered and their integration into a single model. We consider the use of energy in appliances and electric vehicles (EVs) and take into account renewable local generation, batteries, and demand response. Our models of a shower, a fridge, and a hybrid EV consider both the electricity consumption and the conventional fuel cost. We present computational results to validate the model and indicate how it overcomes the limitations of other models. Our results, compared with the best competitors, provide cost savings ranging from 8% to 389% over a horizon of 24 hours. [ABSTRACT FROM AUTHOR]

This paper proposes a framework to determine capacity profiles in smart buildings. In this scheme the users choose a level of power capacity to account for their stochastic demand while paying the corresponding electricity prices through a flexible time-and-level-of-use pricing policy. We formulate a two-stage stochastic optimization model that minimizes the total cost of booking a power capacity level and meeting the energy demand for the planning horizon. We present two approaches to select the scenarios for the stochastic optimization. In the first approach, we assume that the probability distributions of the start times of the loads are known, and the scenarios are generated using those distributions. In the second approach, we assume that only historical consumption data is available and we propose a new algorithm to build the scenarios using this data. Our simulation experiments validate the performance of both approaches and report cost savings of up to 16%. [ABSTRACT FROM AUTHOR]

Demand-response aggregators are faced with the challenge of how to best manage numerous and heterogeneous distributed energy resources (DERs). This paper proposes a decentralized methodology for optimal coordination of DERs. The proposed approach is based on Dantzig–Wolfe decomposition and column generation, thus allowing to integrate any type of resource whose operation can be formulated within a mixed-integer linear program. We show that the proposed framework offers the same guarantees of optimality as a centralized formulation, with the added benefits of distributed computation, enhanced privacy, and higher robustness to changes in the problem data. The practical efficiency of the algorithm is demonstrated through extensive computational experiments, on a set of instances generated using data from Ontario energy markets. The proposed approach was able to solve all test instances to proven optimality, while achieving significant speed-ups over a centralized formulation solved by state-of-the-art optimization software. [ABSTRACT FROM AUTHOR]

The classical alternating current optimal power flow problem is highly nonconvex and generally hard to solve. Convex relaxations, in particular semidefinite, second-order cone, convex quadratic, and linear relaxations, have recently attracted significant interest. The semidefinite relaxation is the strongest among them and is exact for many cases. However, the computational efficiency for solving large-scale semidefinite optimization is lower than for second-order cone optimization. We propose a conic relaxation obtained by combining semidefinite optimization with the reformulation-linearization technique, commonly known as RLT. The proposed relaxation is stronger than the second-order cone relaxation and nearly as tight as the standard semidefinite relaxation. Computational experiments using standard test cases with up to 6515 buses show that the time to solve the new conic relaxation is up to one order of magnitude lower than for the chordal relaxation, a semidefinite relaxation technique that exploits the sparsity of power networks. [ABSTRACT FROM AUTHOR]

Maintenance activities help prevent costly generator breakdowns but because generators under maintenance are typically unavailable, the impact of maintenance schedules is significant and their cost must be accounted for when planning maintenance. In this paper, we address the generator maintenance scheduling problem in hydropower systems. We propose a mixed-integer programing model that considers the time windows of the maintenance activities, as well as the nonlinearities and disjunctions of the hydroelectric production functions. Because the resulting model is hard to solve, we also propose an extended formulation, a set reduction approach that uses logical conditions for excluding unnecessary set elements from the model, and valid inequalities. We performed computational experiments using a variety of instances adapted from a real hydropower system in Canada, and the extended formulation with set reduction achieved the best results in terms of computational time and optimality gap. [ABSTRACT FROM AUTHOR]

Abstract This work presents a collaborative scheme for the end-users in a smart building with multiple housing units. This approach determines a day-ahead operational plan that provides demand-response services by taking into account the amount of energy consumed per household, the use of shared storage and solar panels, and the amount of shifted load. We use a biobjective optimization model to trade off total user satisfaction versus total cost of energy consumption. The optimization works in combination with a price structure based on time and level of use that encourages load shifting and benefits the participants. Computational experiments and an extensive sensitivity analysis validate the performance of the proposed approach and help to clarify its strengths, its limits, and the requirements for ensuring the desired outcome. Highlights • We present a collaborative scheme for end-users in a multi-unit smart building. • We use compromise programming to trade off user satisfaction and cost of energy. • Our approach achieves demand response through a combination of different resources. • We introduce a new cost structure that encourages load shifting. • We give insights into the boundary and basic conditions for the building operation. [ABSTRACT FROM AUTHOR]

An introduction is presented in which the editor discusses articles in the issue on topics including global optimization, mathematical optimization, and linear optimization.

We consider the maximum k-cut problem that consists in partitioning the vertex set of a graph into k subsets such that the sum of the weights of edges joining vertices in different subsets is maximized. We focus on identifying effective classes of inequalities to tighten the semidefinite programming relaxation. We carry out an experimental study of four classes of inequalities from the literature: clique, general clique, wheel and bicycle wheel. We considered 10 combinations of these classes and tested them on both dense and sparse instances for k∈{3,4,5,7}. Our computational results suggest that the bicycle wheel and wheel are the strongest inequalities for k=3, and that for k∈{4,5,7} the wheel inequalities are the strongest by far. Furthermore, we observe an improvement in the performance for all choices of k when both bicycle wheel and wheel are used, at the cost of 72% more CPU time on average when compared with using only one of them. [ABSTRACT FROM AUTHOR]

This paper presents the convergence proof and complexity analysis of an interior-point framework that solves linear programming problems by dynamically selecting and adding relevant inequalities. First, we formulate a new primal–dual interior-point algorithm for solving linear programmes in non-standard form with equality and inequality constraints. The algorithm uses a primal–dual path-following predictor–corrector short-step interior-point method that starts with a reduced problem without any inequalities and selectively adds a given inequality only if it becomes active on the way to optimality. Second, we prove convergence of this algorithm to an optimal solution at which all inequalities are satisfied regardless of whether they have been added by the algorithm or not. We thus provide a theoretical foundation for similar schemes already used in practice. We also establish conditions under which the complexity of such algorithm is polynomial in the problem dimension and address remaining limitations without these conditions for possible further research. [ABSTRACT FROM AUTHOR]

This paper presents a new methodology for the estimation of power capacity profiles for smart buildings. The capacity profile can be used within a demand-side management system in order to guide the building temperature operation. It provides a trade-off between the quality of service perceived by the end user and the requirements from the grid in a demand-response context. We use a data-fitting approach and a multiclass classifier to compute the required profile to run a set of electric heating and cooling units via an admission control module. Simulation results validate the performance of the proposed methodology under various conditions, and we compare our approach with neural networks in a real-world-based scenario. [ABSTRACT FROM AUTHOR]

This paper provides new results on the application of semidefinite optimization to satisfiability by studying the connection between semidefinite optimization and minimal unsatisfiability. We use a semidefinite least squares problem to assign weights to the clauses of a propositional formula in conjunctive normal form. We then show that these weights are a measure of the necessity of each clause in rendering the formula unsatisfiable, the weight of a necessary clause is strictly greater than the weight of any unnecessary clause. In particular, we show the following results: first, if a formula is minimal unsatisfiable, then all of its clauses have the same weight; second, if a clause does not belong to any minimal unsatisfiable subformula, then its weight is zero. An additional contribution of this paper is a demonstration of how the infeasibility of a semidefinite optimization problem can be tested using a semidefinite least squares problem by extending an earlier result for linear optimization. The connection between the semidefinite least squares problem and Farkas’ Lemma for semidefinite optimization is also discussed. [ABSTRACT FROM AUTHOR]

We study the potential role and advantages of a multinational carbon-credit (CC) market allowing a set of countries to procure CCs for their domestic producers. We study the interaction of such a market with renewable portfolio standards, specifically regarding whether a country's government or its energy producers are responsible for upholding the renewable portfolio standards (RPS), and how this impacts total emissions and energy mix. Implementing uniform carbon tax policies or cross-border emission trading systems hinders individual countries' autonomy while strictly segregated carbon markets suffer from the tragedy of the commons. We develop a model where countries can have their own policies to allocate the CCs, which may include taxes or subsidies depending upon the country's choices. We use a special form of equilibrium programs with equilibrium constraints (EPEC) game – Nash Among Stackelberg Players (NASP) – and recent algorithmic advances to identify equilibria for these games to identify the effect of such a common CC market, and the regional governments' individualized interests on the resulting energy production patterns and emissions. We observe that countries could retain their autonomy and have reasonable freedom to set national policy by acting as intermediaries between the CC market and the producers. We carry out a case study using historical data and projections of energy production for the US and Canada, and observe the varying effects of such a common CC market on government policy and the behavior of energy producers. Establishing a common CC market could significantly reduce global emissions without infringing on national autonomy. Such a market helps governments to motivate producers to uphold renewable standards because if the producers do not voluntarily reduce emissions, then the government could enforce the obligation through its national policies, generally leading to a revenue loss for producers. • A Nash Among Stackelberg Players for multinational carbon-credit markets. • Effects of ownership of renewable portfolio standards goals under carbon markets. • Common carbon markets could reduce global emissions without infringing on national autonomy. • Governments impose domestic policies to enforce producer's behavior for emissions reductions. [ABSTRACT FROM AUTHOR]

A Generation Expansion Planning problem with load uncertainty is formulated based on joint chance-constrained programming (CCP) and is solved by incorporating sensitivity into iterative algorithms. These algorithms exploit the characteristics of the system and its response to load variations. Sensitivities help to classify buses according to stress level, and sensitivity-based iterative algorithms distinguish each bus based on its contribution to the overall system reliability. The use of sensitivity overcomes some of the mathematical obstacles to solving joint CCP problems and, in addition, leads to optimal expansion solutions because uncertain loads are correctly estimated. The IEEE 30- and 118-bus test systems are used to demonstrate the proposed algorithms, and the results of these algorithms are compared with those of other algorithms for solving the joint CCP problem. [ABSTRACT FROM AUTHOR]

Abstract: This paper explores new connections between the satisfiability problem and semidefinite programming. We show how the process of resolution in satisfiability is equivalent to a linear transformation between the feasible sets of the relevant semidefinite programming problems. We call this transformation semidefinite programming resolution, and we demonstrate the potential of this novel concept by using it to obtain a direct proof of the exactness of the semidefinite formulation of satisfiability without applying Lasserre’s general theory for semidefinite relaxations of 0/1 problems. In particular, our proof explicitly shows how the exactness of the semidefinite formulation for any satisfiability formula can be interpreted as the implicit application of a finite sequence of resolution steps to verify whether the empty clause can be derived from the given formula. [Copyright &y& Elsevier]

This paper examines the polytope of feasible power generation schedules in the unit commitment (UC) problem. We provide computational results comparing formulations for the UC problem commonly found in the literature. We introduce a new class of inequalities, giving a tighter description of feasible operating schedules for generators. Computational results show that these inequalities can significantly reduce overall solution times. [ABSTRACT FROM PUBLISHER]

The minimum k-partition (M kP) problem is the problem of partitioning the set of vertices of a graph into k disjoint subsets so as to minimize the total weight of the edges joining vertices in the same partition. The main contribution of this paper is the design and implementation of a branch-and-cut algorithm based on semidefinite programming (SBC) for the M kP problem. The two key ingredients for this algorithm are: the combination of semidefinite programming with polyhedral results; and a novel iterative clustering heuristic (ICH) that finds feasible solutions for the M kP problem. We compare ICH to the hyperplane rounding techniques of Goemans and Williamson and of Frieze and Jerrum, and the computational results support the conclusion that ICH consistently provides better feasible solutions for the M kP problem. ICH is used in our SBC algorithm to provide feasible solutions at each node of the branch-and-bound tree. The SBC algorithm computes globally optimal solutions for dense graphs with up to 60 vertices, for grid graphs with up to 100 vertices, and for different values of k, providing a fast exact approach for k≥3. [ABSTRACT FROM AUTHOR]

Despite the many advantages of interior-point algorithms over active-set methods for linear optimization, one of the remaining practical challenges is their current limitation to efficiently solve series of related problems by an effective warmstarting strategy. As a remedy, in this paper we present a new infeasible-interior-point approach to quickly reoptimize an initial problem instance after data perturbations, or a new linear programming relaxation after adding cutting planes for discrete or combinatorial problems. Based on the detailed complexity analysis of the underlying algorithm, we perform a comparative analysis to coldstart initialization schemes and present encouraging computational results with iteration savings of around 50% on average for perturbations of the Netlib linear programs (LPs) and successive linear programming relaxations of max-cut and the traveling salesman problem. [ABSTRACT FROM AUTHOR]

This paper is concerned with the single-row facility layout problem (SRFLP). A globally optimal solution to the SRFLP is a linear placement of rectangular facilities with varying lengths that achieves the minimum total cost associated with the (known or projected) interactions between them. We demonstrate that the combination of a semidefinite programming relaxation with cutting planes is able to compute globally optimal layouts for large SRFLPs with up to 30 facilities. In particular, we report the globally optimal solutions for two sets of SRFLPs previously studied in the literature, some of which have remained unsolved since 1988. [ABSTRACT FROM AUTHOR]

We revisit a regularization technique of Mészáros for handling free variables within interior-point methods for conic linear optimization. We propose a simple computational strategy, supported by a global convergence analysis, for handling the regularization. Using test problems from benchmark suites and recent applications, we demonstrate that the modern code SDPT3 modified to incorporate the proposed regularization is able to achieve the same or significantly better accuracy over standard options of splitting variables, using a quadratic cone, and solving indefinite systems. [ABSTRACT FROM AUTHOR]

An affine supply function equilibrium (SFE) approach is used to discuss voltage constraints and reactive power issues in the modeling of strategic behavior. Generation companies (GenCos) can choose their bid parameters with no restrictions for both energy and spinning reserves. The strategic behavior of generators is formulated as a multi-leader single-follower game. Each GenCo is modeled as a leader, while the central market operator running a cost minimization process is the sole follower. An ac model is considered to represent the transmission system. A three-node system is used to illustrate several cases, and study the implications of the incentives of the strategic players to exploit active and reactive power, and spinning reserves in order to maximize profits. Results for a 14-node system are also presented. [ABSTRACT FROM AUTHOR]

In this paper, oligopolistic competition in a centralized power market is characterized by a multi-leader single-follower game, and formulated as a nonlinear programming (NLP) problem. An ac network is used to represent the transmission system and is modeled using rectangular coordinates. The follower is composed of a set of competitive suppliers, demands, and the system operator, while the leaders are the dominant suppliers. The ac approach allows one to capture the strategic behavior of suppliers regarding not only active but also reactive power. In addition, the impact of voltage and apparent power flow constraints can be analyzed. Different case studies are presented using a three-node system to highlight the features of the formulation. Results on a 14-node system are also presented. [ABSTRACT FROM AUTHOR]

Basic approximations of the transmission system are ubiquitous in the literature on modeling competition in electricity markets. Because the main concern of market power is with active power, reactive power and voltage-related issues are commonly neglected, even though they are inherent features of an electrical power system. However, the usefulness of stylized formulations that do not comprise these system elements may be severely limited. [Copyright &y& Elsevier]

We present a new framework for efficiently finding competitive solutions for the facility-layout problem. This framework is based on the combination of two new mathematical-programming models. The first model is a relaxation of the layout problem and is intended to find good starting points for the iterative algorithm used to solve the second model. The second model is an exact formulation of the facility-layout problem as a nonconvex mathematical program with equilibrium constraints (MPEC). Aspect ratio constraints, which are frequently used in facility-layout methods to restrict the occurrence of overly long and narrow departments in the computed layouts, are easily incorporated into this new framework. Finally, we present computational results showing that the complete framework can be solved efficiently using widely available optimization software, and the resulting layouts improve on those obtained using previous approaches in the literature. Moreover, the framework can be used to find different competitive layouts with relatively little computational effort, which is advantageous for a user who wishes to consider several competitive layouts rather than simply using a mathematically optimal layout. [ABSTRACT FROM AUTHOR]

The satisfiability (SAT) problem is a central problem in mathematical logic, computing theory, and artificial intelligence. An instance of SAT is specified by a set of boolean variables and a propositional formula in conjunctive normal form. Given such an instance, the SAT problem asks whether there is a truth assignment to the variables such that the formula is satisfied. It is well known that SAT is in general NP-complete, although several important special cases can be solved in polynomial time. Semidefinite programming (SDP) refers to the class of optimization problems where a linear function of a matrix variableXis maximized (or minimized) subject to linear constraints on the elements ofXand the additional constraint thatXbe positive semidefinite. We are interested in the application of SDP to satisfiability problems, and in particular in how SDP can be used to detect unsatisfiability. In this paper we introduce a new SDP relaxation for the satisfiability problem. This SDP relaxation arises from the recently introduced paradigm of “higher liftings” for constructing semidefinite programming relaxations of discrete optimization problems. To derive the SDP relaxation, we first formulate SAT as an optimization problem involving matrices. Relaxing this formulation yields an SDP which significantly improves on the previous relaxations in the literature. The important characteristics of the SDP relaxation are its ability to prove that a given SAT formula is unsatisfiable independently of the lengths of the clauses in the formula, its potential to yield truth assignments satisfying the SAT instance if a feasible matrix of sufficiently low rank is computed, and the fact that it is more amenable to practical computation than previous SDPs arising from higher liftings. We present theoretical and computational results that support these claims. [ABSTRACT FROM AUTHOR]

In this paper we study two strengthened semidefinite programming relaxations for the Max-Cut problem. Our results hold for every instance of Max-Cut; in particular, we make no assumptions about the edge weights. We prove that the first relaxation provides a strengthening of the Goemans–Williamson relaxation. The second relaxation is a further tightening of the first one and we prove that its feasible set corresponds to a convex set that is larger than the cut polytope but nonetheless is strictly contained in the intersection of the elliptope and the metric polytope. Both relaxations are obtained using Lagrangian relaxation. Hence, our results also exemplify the strength and flexibility of Lagrangian relaxation for obtaining a variety of SDP relaxations with different properties.We also address some practical issues in the solution of these SDP relaxations. Because Slater''s constraint qualification fails for both of them, we project their feasible sets onto a lower dimensional space in a way that does not affect the sparsity of these relaxations but guarantees Slater''s condition. Some preliminary numerical results are included. [Copyright &y& Elsevier]

We consider the complex cut polytope: the convex hull of Hermitian rank 1 matrices xxH\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$xx^\textrm{H}$$\end{document}, where the elements of x∈Cn\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$x \in \mathbb {C}^n$$\end{document} are mth unit roots. These polytopes have applications in MAX-3-CUT, digital communication technology, angular synchronization and more generally, complex quadratic programming. For m=2\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$m=2$$\end{document}, the complex cut polytope corresponds to the well-known cut polytope. We generalize valid cuts for this polytope to cuts for any complex cut polytope with finite m>2\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$m>2$$\end{document} and provide a framework to compare them. Further, we consider a second semidefinite lifting of the complex cut polytope for m=∞\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$m=\infty $$\end{document}. This lifting is proven to be equivalent to other complex Lasserre-type liftings of the same order proposed in the literature, while being of smaller size. Our theoretical findings are supported by numerical experiments on various optimization problems. [ABSTRACT FROM AUTHOR]

This paper presents a novel price setting optimization problem for an electricity supplier in the smart grid. In this framework the supplier provides electricity to a residential load aggregator using Time-and-Level-of-Use prices (TLOU). TLOU is an energy pricing structure recently introduced in the literature, where the prices vary depending on the time and the level of consumption. This problem is formulated as a bilevel optimization problem, in which the supplier sets the prices that maximize the profit in a demand response context, anticipating the reaction of a residential load aggregator that minimizes total cost. These decisions are made in a competitive environment, while explicitly considering the aggregator's load shifting preferences and the level of consumption, and ensuring a user-friendly price structure. The optimization problem is reformulated as a single-level problem to be solved using off-the-shelf solvers. We present computational experiments to validate the performance of TLOU, and provide insights on the relationship between the user's demand flexibility, the capacity profile and the resulting structure of prices. We show that the supplier's economical benefit is increased up to 10% through the implementation of this type of demand response program, while providing savings of up to 6% for the consumers. • We present a framework to determine TLOU energy prices for an electricity retailer. • We formulate the problem as a bilevel optimization problem to set optimal prices. • We explicitly consider user preferences in the in the price setting problem. • Our model can be reformulated and solve by of-the-shelf solvers. • We provide evidence of the effect of TLOU on retailer's and end-users' performance. [ABSTRACT FROM AUTHOR]

• We define a new flexibility product for residential heat loads on energy markets. • We consider aggregating electric water heaters as an example of such a product. • We use a mean field game approach to quantify the flexibility with recovery limits. • Our approach allows explicit constraints on the post control recovery dynamics. • We assess the economic viability of our approach with Net Present Value estimates. Electric thermal loads, such as those for space heaters, water heaters and air conditioners, due to their association with energy storage, are deferrable. Thus, they can become an effective tool to compensate for the mismatches between power generation and power demand induced by renewable sources. Load reduction and load increase may appear to be equivalent to generation increase and generation withdrawal, but there is a significant difference in the associated post-load-control energy rebound phenomena. These phenomena can provoke undesirable post-load-control changes in the demand dynamics. The contribution of this paper is twofold. First, we define a flexibility product that load aggregators could propose that would involve a mean energy increase or decrease offer for a price and also guarantee bounds on the post-load-control deviations from normal. Second, we provide aggregators with the mathematical tools to specify the maximum load relief or increase possible under specific constraints on post-control recovery dynamics. The analysis rests on successive solutions of a linear program and exploits recent results on load control based on mean field game theory. We consider the case of aggregate electric water heater loads. [ABSTRACT FROM AUTHOR]

Smart homes have the potential to achieve efficient energy consumption: households can profit from appropriately scheduled consumption. By 2020, 35% of all households in North America and 20% in Europe are expected to become smart homes. Developing a smart home requires considerable investment, and the householders expect a positive return. In this context, this work addresses the following question: what and/or when equipment should be bought for a specific site to gain a positive return on the investment? This work proposes a framework to guide the smart-home transition considering customized electricity usage. The framework is based on linear models and gives a simple payback analysis of each combination of equipment acquisition for any specific user taking into account geographical location and local conditions. It also possible to use the framework for equipment sizing. The results quantify the dependence of the simple payback on the site and the application. • Modeling and optimization of the integration of smart home components. • General framework for the optimal set of smart appliances and investment timing. • Maximization of the return on investment. • Economic feasibility shown for three case studies in different countries using real data. • Quantification of the payback for each site and application. [ABSTRACT FROM AUTHOR]

Semidefinite Programming (SDP) is a powerful technique to compute tight lower bounds for Optimal Power Flow (OPF) problems. Even using clique decomposition techniques, semidefinite relaxations are still computationally demanding. However, there are many different clique decompositions for the same SDP problem and they are not equivalent in terms of computation time. In this paper, we propose a new strategy to compute efficient clique decompositions with a clique merging heuristic. This heuristic is based on two different estimates of the computational burden of an SDP problem: the size of the problem and an estimation of a per-iteration cost for a state-of-the-art interior-point algorithm. We compare our strategy with other algorithms on MATPOWER instances and we show a significant decrease in solver time. [ABSTRACT FROM AUTHOR]

We present a new model for finding the optimal placement of electric vehicle charging stations across a multiperiod time frame so as to maximise electric vehicle adoption. Via the use of stochastic discrete choice models and user classes, this work allows for a granular modelling of user attributes and their preferences in regard to charging station characteristics. We adopt a simulation approach and precompute error terms for each option available to users for a given number of scenarios. This results in a bilevel optimisation model that is, however, intractable for all but the simplest instances. Our major contribution is a reformulation into a maximum covering model, which uses the precomputed error terms to calculate the users covered by each charging station. This allows solutions to be found more efficiently than for the bilevel formulation. The maximum covering formulation remains intractable in some instances, so we propose rolling horizon, greedy, and greedy randomised adaptive search procedure heuristics to obtain good-quality solutions more efficiently. Extensive computational results are provided, and they compare the maximum covering formulation with the current state of the art for both exact solutions and the heuristic methods. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms–Discrete. Funding: This work was supported by Hydro-Québec and the Natural Sciences and Engineering Research Council of Canada [Discovery Grant 2017-06054; Collaborative Research and Development Grant CRDPJ 536757–19]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/ijoc.2022.0185. [ABSTRACT FROM AUTHOR]

The evolving landscape of electrical grids has presented formidable challenges to energy systems, which need adaptable solutions for reliability, supply adequacy, and demand balance, where demand flexibility arises as a pivotal operational asset for these needs. In recent decades, desalination technology, particularly reverse osmosis, has been employed to purify seawater and brackish water by removing salt and impurities, effectively addressing water scarcity in some regions of the world. However, its energy-intensive nature, driven by high-pressure pump usage, leads to significant operational expenses and places additional strain on the power grid. Our study introduces a novel holistic model for the Chilean electricity system, incorporating reverse osmosis desalination facilities to comprehensively confront water scarcity through strategies that leverage the flexibility of high-pressure pumps. The model considers dispatch coordination, unveiling the synergy's value given mainly by the desalination system and the energy generation infrastructure. The study underscores the influence of desalination on power system dynamics, transmission, and generation expansion throughout the time horizon of 2025 to 2040. The principal findings underscore the advantages derived from co-optimizing desalination and the electrical system, the enhanced system performance from flexible desalination plant operations, and the synergistic potential of solar, battery energy storage, and the desalinated water system. These insights help to inform investment decisions, decarbonization policies, and the water–energy nexus interplay, charting a course towards comprehensive sustainability. • Co-optimization of electricity and desalinated water systems reach a more efficient power system transition. • Flexibility of desalination plants operation can be used as a tool to obtain more efficient power systems. • Synergies are observed when solar photovoltaic and battery storage are joined with desalination plants. • Levelised cost of water is smaller when flexible operation of RO desalination plants is used. • Investing in water storage allows to shift water production to lower electricity cost hours. [ABSTRACT FROM AUTHOR]

In VLSI layout, floorplanning refers to the task of placing macrocells on a chip without overlap while minimizing design objectives such as timing, congestion, and wire length. Experienced VLSI designers have traditionally been able to produce more efficient floorplans than automated methods. However, with the increasing complexity of modern circuits, manual design flows have become infeasible. An efficient top-down strategy for overlap removal which repairs overlaps in floorplans produced by placement algorithms or rough floorplanning methodologies is presented in this article. The algorithmic framework proposed incorporates a novel geometric shifting technique coupled with topological constraint graphs and linear programming within a top-down flow. The effectiveness of this framework is quantified across a broad range of floorplans produced by multiple tools. The method succeeds in producing valid placements in almost all cases; moreover, compared with leading methods, it requires only one-fifth of the run-time and produces placements with 4-13% less wire length and up to 43% less cell movement. [ABSTRACT FROM AUTHOR]

• Hydro-Québec can provide annual storage ranging from 3 to 6 TW h for high VRE markets. • Price arbitraging with high VRE markets leads to sustainable changes for hydropower. • Hydropower maintenance flexibility will gain more value with VRE growth. • Revenues from price arbitraging with high VRE markets remain low. Northeastern North America is transitioning rapidly from fossil fuel generation to variable renewable energy (VRE) sources such as wind and solar. Their integration into electricity grids poses challenges in terms of matching supply with demand. Once VRE represent a large share of installed capacity, intermittency and variability of their production will become a major issue. Hydro-Québec, the public electric utility in the Canadian province of Québec, has a large hydropower generation fleet. Its storage capacity enables adjusting hydro production, when the system needs it, to support VRE integration. In this paper, potential impacts of VRE growth within neighbouring grids are simulated through operational production management models. The results show that Hydro-Québec has the potential to facilitate this energy transition but that the current electricity market structure does not provide incentives for an optimal contribution. [ABSTRACT FROM AUTHOR]

This paper proposes a two-level framework for the operation of a competitive market for reactive power ancillary services. It is argued that the first-level, i.e., reactive power procurement, be on a seasonal basis while the second-level, i.e., reactive power dispatch, be close to real-time operation. To this effect, a reactive power procurement market model is proposed here taking into consideration system security aspects. This procurement procedure is based on a two-step optimization model. First, the marginal benefits of reactive power supply from each provider with respect to system security are obtained by solving an optimal power flow (OPF) that maximizes system loadability subject to transmission security constraints imposed by voltage limits, thermal limits, and stability limits. Second, the selected set of generators is then determined by solving an OPF-based auction to maximize a societal advantage function comprising generators' offers and their corresponding marginal benefits with respect to system security, considering all transmission system constraints. The proposed procedure yields the selected set of generators and zonal price components, which would form the basis for seasonal contracts between the system operator and the selected reactive power service providers. [ABSTRACT FROM AUTHOR]

• A novel optimization model to maximize energy for short-term hydropower unit commitment is proposed. • A MILP formulation based on the efficiency curves is established. • The optimized solutions can be directly implemented in practice. • A real case study in Canada shows benefits of optimal solutions compared to historical decisions. This paper presents a linear mixed-integer formulation to solve the short-term hydropower unit commitment problem. It uses the pair of maximum efficiency points of water discharge and the power produced at the maximum storage for all possible combinations of turbines. The goal is to maximize total energy production for all periods. The objective function is calculated using the correction between the power produced at the current volume and the maximum storage and penalizes unit start-ups. Constraints on the maximum number of turbine changes are imposed to find a viable solution. Computational results are reported for 65 instances with two powerhouses of five turbines each located in the Saguenay-Lac-St-Jean region of the province of Quebec in Canada. [ABSTRACT FROM AUTHOR]