Bilevel Optimization Problem Research Articles

Learning Individual Treatment Effects under Heterogeneous Interference in Networks

Estimating individual treatment effects in networked observational data is a crucial and increasingly recognized problem. One major challenge of this problem is violating the Stable Unit Treatment Value Assumption (SUTVA), which posits that a unit’s outcome is independent of others’ treatment assignments. However, in network data, a unit’s outcome is influenced not only by its treatment (i.e., direct effect) but also by the treatments of others (i.e., spillover effect) since the presence of interference. Moreover, the interference from other units is always heterogeneous (e.g., friends with similar interests have a different influence than those with different interests). In this paper, we focus on the problem of estimating individual treatment effects (including direct effect and spillover effect) under heterogeneous interference in networks. To address this problem, we propose a novel Dual Weighting Regression (DWR) algorithm by simultaneously learning attention weights to capture the heterogeneous interference from neighbors and sample weights to eliminate the complex confounding bias in networks. We formulate the learning process as a bi-level optimization problem. Theoretically, we give a generalization error bound for the expected estimation error of the individual treatment effects. Extensive experiments on four benchmark datasets demonstrate that the proposed DWR algorithm outperforms the state-of-the-art methods in estimating individual treatment effects under heterogeneous network interference.

Bi-level game theoretic approach for robust design: A case study of path-generating four-bar

This study addresses the bi-level multi-objective optimization problems (MOP) that raise in robust design and optimization of engineering systems through establishing a state-of-the-art game theoretic scenario. A novel leader-follower decentralized decision-making scenario is proposed, leveraging the synergy of game theory, Robust Design Optimization (RDO), Monte Carlo Simulation (MCS), and Artificial Intelligence (AI). The proposed algorithm can be employed for optimum robust Pareto design of a wide range of dynamical systems. In order to achieve a robust design, both the mean and variance of each objective function are considered as players in a multi-agent game setting. In this approach, both Stackelberg and cooperative games are utilized to model the behaviors of the players. Genetic Programming (GP) meta-models are employed to capture the Stackelberg protocol between two levels specifically for constructing the follower's rational reaction set (RRS). Additionally, the Nash bargaining function is -utilize to model the cooperative behaviors among players in each level. The proposed approach is applied and demonstrated through a case study involving multi-objective robust design of planar four-bar linkages. In this manner, four objective functions are assigned to four players within the system. Each player is responsible for optimizing a specific objective criterion, namely the mean of tracking error (TE), variance of tracking error, mean of transmission angle and variance of transmission angle (TA) of the linkage. As a result, the four-objective optimization problem of mechanism is transformed into a single-objective robust synthesis problem. The comparisons of the results show a significant enhancement in the robust behavior of the linkage, while ensuring that deterministic criteria such as quality of motion and precision are preserved.

A Psycholinguistics-inspired Method to Counter IP Theft Using Fake Documents

Intellectual property (IP) theft is a growing problem. We build on prior work to deter IP theft by generating n fake versions of a technical document so a thief has to expend time and effort in identifying the correct document. Our new SbFAKE framework proposes, for the first time, a novel combination of language processing, optimization, and the psycholinguistic concept of surprisal to generate a set of such fakes. We start by combining psycholinguistic-based surprisal scores and optimization to generate two bilevel surprisal optimization problems (an Explicit one and a simpler Implicit one) whose solutions correspond directly to the desired set of fakes. As bilevel problems are usually hard to solve, we then show that these two bilevel surprisal optimization problems can each be reduced to equivalent surprisal-based linear programs. We performed detailed parameter tuning experiments and identified the best parameters for each of these algorithms. We then tested these two variants of SbFAKE (with their best parameter settings) against the best performing prior work in the field. Our experiments show that SbFAKE is able to more effectively generate convincing fakes than past work. In addition, we show that replacing words in an original document with words having similar surprisal scores generates greater levels of deception.

Demand response mechanisms: A new debate on internalizing power generation sector negative technical spillovers

The presence of technical and operational constraints within the power generation sector gives rise to negative externalities, resulting in spillover effects that can significantly impact the economic efficiency of power markets. This article endeavors to address these challenges by focusing on the demand side of power systems. Within the article, a demand response-based approach is presented as a means to internalize the negative technical externalities spillovers originating from power plants in day-ahead power markets. This approach involves the responsive demand generating a new service that opens up opportunities for energy interchange within the power market. To effectively internalize these spillovers, the introduced service incorporates both quantity and price adjustments. A discriminatory pricing mechanism for this service is proposed, accompanied by a bi-level optimization problem aimed at determining the elastic responsive demand fraction necessary to deliver the service. Utilizing the proposed scheme facilitates attaining the first-best optimal market solution by alleviating negative spillovers inherent in sub-optimal second-best solutions arising from operational constraints in power plants. Numerical results presented in the article serve to underscore the efficacy of the proposed method, demonstrating its ability to function seamlessly and contribute to the optimization of power market outcomes.

Co-evolutionary traffic signal control using reinforcement learning for road networks under stochastic capacity

A co-evolutionary traffic signal control using reinforcement learning approach (CORLA) is proposed for time-varying road networks under stochastic capacity. Classic reinforcement learning based traffic signal control cannot effectively reduce traffic congestion for large-scale road networks while standard evolutionary metaheuristics often suffer from significantly high computational cost. A co-evolutionary decomposition algorithm (CODA) is proposed to improve traffic mobility for urban road networks with time-varying traffic flow. To capture time-varying spatial evolution of traffic flow inside road links, a stochastic traffic model is presented. To fully consider road users’ response, a stochastic bi-level optimization problem (SBOP) is given where road users’ route choice can be fully taken into account. To efficiently implement CORLA in a large-scale road network against high-consequence realization for stochastic capacity, a coordinated co-evolutionary two phase control (CCTPC) is proposed. Numerical experiments are performed at a real-data city road network and various sizable traffic grids. As compared to state-of-the-art traffic signal control for various traffic conditions, obtained results showed that CCTPC exhibits sufficient gain of achieving road network performance and suffers from the least computational cost in all cases.

Analysis of Grid Performance with Diversified Distributed Resources and Storage Integration: A Bilevel Approach with Network-Oriented PSO

The growing deployment of distributed resources significantly affects the distribution grid performance in most countries. The optimal sizing and placement of these resources have become increasingly crucial to mitigating grid issues and reducing costs. Particle Swarm Optimization (PSO) is widely used to address such problems but faces computational inefficiency due to its numerical convergence behavior. This limits its effectiveness, especially for power system problems, because the numerical distance between two nodes in power systems might be different from the actual electrical distance. In this paper, a scalable bilevel optimization problem with two novel algorithms enhances PSO’s computational efficiency. While the resistivity-driven algorithm strategically targets low-resistivity regions and guides PSO toward areas with lower losses, the connectivity-driven algorithm aligns solution spaces with the grid’s physical topology. It prioritizes actual physical neighbors during the search to prevent local optima traps. The tests of the algorithms on the IEEE 33-bus and the 69-bus and Norwegian networks show significant reductions in power losses (up to 74% for PV, wind, and storage) and improved voltage stability (a 21% reduction in mean voltage deviation index) with respect to the results of classical PSO. The proposed network-oriented PSO outperforms classical PSO by achieving a 2.84% reduction in the average fitness value for the IEEE 69-bus case with PV, wind, and storage deployment. The Norwegian case study affirms the effectiveness of the proposed approach in real-world applications through significant improvements in loss reduction and voltage stability.

Optimal pricing of integrated community energy system for building prosumers with P2P multi-energy trading

Buildings are typically integrated with multiple distributed energy resources (DERs), enabling them to act as building prosumers engaged in both energy production and consumption. Peer-to-peer (P2P) energy trading among building prosumers is crucial to improve their benefits. However, further exploration is required to balance the benefits between building prosumers and the system operator (e.g., the integrated community energy system (ICES) operator) since they are different entities. In this context, this paper proposes a comprehensive network charge and energy sale pricing scheme for the ICES operator on heterogeneous building prosumers with P2P multi-energy trading. The interaction between the ICES operator and building prosumers is modelled as a bi-level optimization problem that belongs to the hierarchical structure, while considering the heterogeneity of thermal insulation performance of buildings. At the upper level, the ICES operator optimizes the electricity/heat network charge prices and electricity/heat sale prices to maximize its revenue. At the lower level, building prosumers with a parallel structure optimize the schedules including P2P multi-energy trading and buildings' heating loads to minimize their costs. Furthermore, to address the bi-level optimization problem with parallel and hierarchical coupling structures, an accelerated asynchronous distributed algorithm based on alternating direction method of multipliers (ADMM) is developed, integrating a warm start strategy and a dual update accelerated iteration strategy for further improving computational efficiency. Finally, case studies demonstrate that the proposed scheme can effectively benefit both the ICES operator and building prosumers in P2P multi-energy trading at the same time. Meanwhile, the feasibility and effectiveness of the proposed algorithm are validated.

Energy Storage Capacity Configuration Planning Considering Dual Scenarios of Peak Shaving and Emergency Frequency Regulation

New energy storage methods based on electrochemistry can not only participate in peak shaving of the power grid but also provide inertia and emergency power support. It is necessary to analyze the planning problem of energy storage from multiple application scenarios, such as peak shaving and emergency frequency regulation. This article proposes an energy storage capacity configuration planning method that considers both peak shaving and emergency frequency regulation scenarios. A frequency response model based on emergency frequency regulation combined with low-frequency load shedding is established, taking into account the frequency safety constraints of the system and the principle of idle time reuse, to establish a bi-level programming model. In the upper-level model, the optimization objective is to minimize the annual operating cost of the system during the planning period, combined with the constraints of power grid operation to plan the energy storage capacity. The lower-level model embeds frequency safety constraints with the optimization objective of minimizing the cost of fault losses. To solve the bi-level optimization problem, the Karush–Kuhn–Tucher (KKT) condition and Big-M method were used to transform the bi-level model into a single-layer linear model. Finally, an improved IEEE RTS-24 system was used for numerical verification. The results show that the method proposed in this article can reasonably plan the capacity of energy storage, improve frequency safety during system operation, and reduce the operating cost of the power grid.

Multi-Objective BiLevel Optimization by Bayesian Optimization

In a multi-objective optimization problem, a decision maker has more than one objective to optimize. In a bilevel optimization problem, there are the following two decision-makers in a hierarchy: a leader who makes the first decision and a follower who reacts, each aiming to optimize their own objective. Many real-world decision-making processes have various objectives to optimize at the same time while considering how the decision-makers affect each other. When both features are combined, we have a multi-objective bilevel optimization problem, which arises in manufacturing, logistics, environmental economics, defence applications and many other areas. Many exact and approximation-based techniques have been proposed, but because of the intrinsic nonconvexity and conflicting multiple objectives, their computational cost is high. We propose a hybrid algorithm based on batch Bayesian optimization to approximate the upper-level Pareto-optimal solution set. We also extend our approach to handle uncertainty in the leader’s objectives via a hypervolume improvement-based acquisition function. Experiments show that our algorithm is more efficient than other current methods while successfully approximating Pareto-fronts.

Path-Based Formulations for the Design of On-demand Multimodal Transit Systems with Adoption Awareness

This paper reconsiders the On-Demand Multimodal Transit Systems (ODMTS) Design with Adoptions problem (ODMTS-DA) to capture the latent demand in on-demand multimodal transit systems. The ODMTS-DA is a bilevel optimization problem, for which Basciftci and Van Hentenryck proposed an exact combinatorial Benders decomposition. Unfortunately, their proposed algorithm only finds high-quality solutions for medium-sized cities and is not practical for large metropolitan areas. The main contribution of this paper is to propose a new path-based optimization model, called P-Path, to address these computational difficulties. The key idea underlying P-Path is to enumerate two specific sets of paths which capture the essence of the choice model associated with the adoption behavior of riders. With the help of these path sets, the ODMTS-DA can be formulated as a single-level mixed-integer programming model. In addition, the paper presents preprocessing techniques that can reduce the size of the model significantly. P-Path is evaluated on two comprehensive case studies: the midsize transit system of the Ann Arbor – Ypsilanti region in Michigan (which was studied by Basciftci and Van Hentenryck) and the large-scale transit system for the city of Atlanta. The experimental results show that P-Path solves the Michigan ODMTS-DA instances in a few minutes, bringing more than two orders of magnitude improvements compared with the existing approach. For Atlanta, the results show that P-Path can solve large-scale ODMTS-DA instances (about 17 millions variables and 37 millions constraints) optimally in a few hours or in a few days. These results show the tremendous computational benefits of P-Path which provides a scalable approach to the design of on-demand multimodal transit systems with latent demand. History: Accepted by Andrea Lodi, Design & Analysis of Algorithms—Discrete. Funding: This work was partially supported by National Science Foundation Leap-HI [Grant 1854684] and the Tier 1 University Transportation Center (UTC): Transit - Serving Communities Optimally, Responsively, and Efficiently (T-SCORE) from the U.S. Department of Transportation [69A3552047141]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.0014 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2023.0014 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Non-exemplar Online Class-Incremental Continual Learning via Dual-Prototype Self-Augment and Refinement

This paper investigates a new, practical, but challenging problem named Non-exemplar Online Class-incremental continual Learning (NO-CL), which aims to preserve the discernibility of base classes without buffering data examples and efficiently learn novel classes continuously in a single-pass (i.e., online) data stream. The challenges of this task are mainly two-fold: (1) Both base and novel classes suffer from severe catastrophic forgetting as no previous samples are available for replay. (2) As the online data can only be observed once, there is no way to fully re-train the whole model, e.g., re-calibrate the decision boundaries via prototype alignment or feature distillation. In this paper, we propose a novel Dual-prototype Self-augment and Refinement method (DSR) for NO-CL problem, which consists of two strategies: 1) Dual class prototypes: vanilla and high-dimensional prototypes are exploited to utilize the pre-trained information and obtain robust quasi-orthogonal representations rather than example buffers for both privacy preservation and memory reduction. 2) Self-augment and refinement: Instead of updating the whole network, we optimize high-dimensional prototypes alternatively with the extra projection module based on self-augment vanilla prototypes, through a bi-level optimization problem. Extensive experiments demonstrate the effectiveness and superiority of the proposed DSR in NO-CL.

RedCore: Relative Advantage Aware Cross-Modal Representation Learning for Missing Modalities with Imbalanced Missing Rates

Multimodal learning is susceptible to modality missing, which poses a major obstacle for its practical applications and, thus, invigorates increasing research interest. In this paper, we investigate two challenging problems: 1) when modality missing exists in the training data, how to exploit the incomplete samples while guaranteeing that they are properly supervised? 2) when the missing rates of different modalities vary, causing or exacerbating the imbalance among modalities, how to address the imbalance and ensure all modalities are well-trained. To tackle these two challenges, we first introduce the variational information bottleneck (VIB) method for the cross-modal representation learning of missing modalities, which capitalizes on the available modalities and the labels as supervision. Then, accounting for the imbalanced missing rates, we define relative advantage to quantify the advantage of each modality over others. Accordingly, a bi-level optimization problem is formulated to adaptively regulate the supervision of all modalities during training. As a whole, the proposed approach features Relative advantage aware Cross-modal representation learning (abbreviated as RedCore) for missing modalities with imbalanced missing rates. Extensive empirical results demonstrate that RedCore outperforms competing models in that it exhibits superior robustness against either large or imbalanced missing rates. The code is available at: https://github.com/sunjunaimer/RedCore.

Game-Theoretic Unlearnable Example Generator

Unlearnable example attacks are data poisoning attacks aiming to degrade the clean test accuracy of deep learning by adding imperceptible perturbations to the training samples, which can be formulated as a bi-level optimization problem. However, directly solving this optimization problem is intractable for deep neural networks. In this paper, we investigate unlearnable example attacks from a game-theoretic perspective, by formulating the attack as a nonzero sum Stackelberg game. First, the existence of game equilibria is proved under the normal setting and the adversarial training setting. It is shown that the game equilibrium gives the most powerful poison attack in that the victim has the lowest test accuracy among all networks within the same hypothesis space when certain loss functions are used. Second, we propose a novel attack method, called the Game Unlearnable Example (GUE), which has three main gradients. (1) The poisons are obtained by directly solving the equilibrium of the Stackelberg game with a first-order algorithm. (2) We employ an autoencoder-like generative network model as the poison attacker. (3) A novel payoff function is introduced to evaluate the performance of the poison. Comprehensive experiments demonstrate that GUE can effectively poison the model in various scenarios. Furthermore, the GUE still works by using a relatively small percentage of the training data to train the generator, and the poison generator can generalize to unseen data well. Our implementation code can be found at https://github.com/hong-xian/gue.

Robust Beamforming for Downlink Multi-Cell Systems: A Bilevel Optimization Perspective

Utilization of inter-base station cooperation for information processing has shown great potential in enhancing the overall quality of communication services (QoS) in wireless communication networks. Nevertheless, such cooperations require the knowledge of channel state information (CSI) at base stations (BSs), which is assumed to be perfectly known. However, CSI errors are inevitable in practice which necessitates beamforming technique that can achieve robust performance in the presence of channel estimation errors. Existing approaches relax the robust beamforming design problems into semidefinite programming (SDP), which can only achieve a solution that is far from being optimal. To this end, this paper views robust beamforming design problems from a bilevel optimization perspective. In particular, we focus on maximizing the worst-case weighted sum-rate (WSR) in the downlink multi-cell multi-user multiple-input single-output (MISO) system considering bounded CSI errors. We first reformulate this problem into a bilevel optimization problem and then develop an efficient algorithm based on the cutting plane method. A distributed optimization algorithm has also been developed to facilitate the parallel processing in practical settings. Numerical results are provided to confirm the effectiveness of the proposed algorithm in terms of performance and complexity, particularly in the presence of CSI uncertainties.

Value at Adversarial Risk: A Graph Defense Strategy against Cost-Aware Attacks

Deep learning methods on graph data have achieved remarkable efficacy across a variety of real-world applications, such as social network analysis and transaction risk detection. Nevertheless, recent studies have illuminated a concerning fact: even the most expressive Graph Neural Networks (GNNs) are vulnerable to graph adversarial attacks. While several methods have been proposed to enhance the robustness of GNN models against adversarial attacks, few have focused on a simple yet realistic approach: valuing the adversarial risks and focused safeguards at the node level. This empowers defenders to allocate heightened security level to vulnerable nodes, while lower to robust nodes. With this new perspective, we propose a novel graph defense strategy RisKeeper, such that the adversarial risk can be directly kept in the input graph. We start at valuing the adversarial risk, by introducing a cost-aware projected gradient descent attack that takes into account both cost avoidance and compliance with costs budgets. Subsequently, we present a learnable approach to ascertain the ideal security level for each individual node by solving a bi-level optimization problem. Through extensive experiments on four real-world datasets, we demonstrate that our method achieves superior performance surpassing state-of-the-art methods. Our in-depth case studies provide further insights into vulnerable and robust structural patterns, serving as inspiration for practitioners to exercise heightened vigilance.

Automated Design of Affine Maximizer Mechanisms in Dynamic Settings

Dynamic mechanism design is a challenging extension to ordinary mechanism design in which the mechanism designer must make a sequence of decisions over time in the face of possibly untruthful reports of participating agents. Optimizing dynamic mechanisms for welfare is relatively well understood. However, there has been less work on optimizing for other goals (e.g., revenue), and without restrictive assumptions on valuations, it is remarkably challenging to characterize good mechanisms. Instead, we turn to automated mechanism design to find mechanisms with good performance in specific problem instances. We extend the class of affine maximizer mechanisms to MDPs where agents may untruthfully report their rewards. This extension results in a challenging bilevel optimization problem in which the upper problem involves choosing optimal mechanism parameters, and the lower problem involves solving the resulting MDP. Our approach can find truthful dynamic mechanisms that achieve strong performance on goals other than welfare, and can be applied to essentially any problem setting---without restrictions on valuations---for which RL can learn optimal policies.

Inexact direct-search methods for bilevel optimization problems

In this work, we introduce new direct-search schemes for the solution of bilevel optimization (BO) problems. Our methods rely on a fixed accuracy blackbox oracle for the lower-level problem, and deal both with smooth and potentially nonsmooth true objectives. We thus analyze for the first time in the literature direct-search schemes in these settings, giving convergence guarantees to approximate stationary points, as well as complexity bounds in the smooth case. We also propose the first adaptation of mesh adaptive direct-search schemes for BO. Some preliminary numerical results on a standard set of bilevel optimization problems show the effectiveness of our new approaches.

The impact of congestion and dedicated lanes on on-demand multimodal transit systems

Traffic congestion can have a detrimental effect on public transit systems, and understanding and mitigating these effects is of critical importance for effective public transportation. Implementing Dedicated Bus Lanes (DBLs) is a well-known intervention to achieve this goal. A DBL is a designated lane for bus transit, which avoids congestion and substantially lowers the travel time. This makes transit more attractive, encouraging more travelers to adopt public transportation. This paper studies the impact of congestion and DBLs on novel On-Demand Multimodal Transit Systems (ODMTS). ODMTS combine traditional rail and bus networks with on-demand shuttles. Previous case studies have shown that ODMTS may simultaneously improve travel time, reduce system cost, and attract new passengers. Those benefits were shown for an ideal world without traffic congestion, and this paper hypothesizes that the advantages of ODMTS can be even more pronounced in the real world. This paper explores this hypothesis by creating realistic congestion scenarios and solving bilevel optimization problems to design ODMTS under these scenarios. The impact of DBLs on ODMTS is evaluated with a comprehensive case study in the Metro Atlanta Area. The results show that DBLs can significantly improve travel times and are effective at increasing adoption of the system.

Market design for ancillary service provisions of inertia and frequency response via virtual power plants: A non-convex bi-level optimisation approach

The Great Britain (GB) government is paving the path to decarbonisation by actively promoting the integration of wind power into its generation mix. This sharp transition to renewable energy, however, introduces specific challenges. The characteristics of non-synchronous wind turbines have the potential to impact grid stability and frequency security due to the reduction in system inertia. In response to these challenges, the deployment of virtual power plants (VPPs) is envisioned in deregulated power systems, which allow for the aggregation and coordinated control of diverse distributed energy resources, enhancing grid flexibility, reliability, and efficiency. Moreover, VPPs offer the provision of system inertia and frequency response services at the national level. This study drops this assumption and leverages the localised flexibility inherent in VPPs to meet the ancillary service requirements of the low-carbon power system. The formulated problem is constructed as a non-convex bi-level optimisation problem, where the upper-level problem represents the operation of a frequency-constrained unit commitment model, and the lower-level problem embodies the energy dispatches and frequency responses of a group of VPPs, guided by the dual price signals of cleared energy and ancillary services. To address the non-convex nature of the unit commitment problem, a two-fold approach is employed. First, binary commitment status decision variables are relaxed to continuous versions. Subsequently, the duality gap between the original non-convex unit commitment problem and its relaxed dual form is minimised, yielding a solution closely approximating the optimal solution of the original problem. Second, the relaxed bi-level optimisation problem is transformed into a single-level mathematical programs with equilibrium constraints by replacing the lower-level VPP problems with their equivalent Karush-Kuhn–Tucker optimality conditions. The case studies conducted in this work encompass a comprehensive scope. Initially, the study evaluates the effectiveness of VPPs in delivering ancillary services within the projected context of the GB power system for 2030. The findings reveal a substantial 28.28% decrease in system operation costs when compared to the benchmark case lacking VPP flexibility. Additionally, the integration of VPPs leads to significantly lower price signals for inertia, primary frequency response, and enhanced frequency response, reduced by 81.21%, 79.13%, and 86.27%, respectively, in contrast to the benchmark case. The analysis then delves into a sensitivity exploration, investigating the inherent flexibility of VPPs. The profit of local VPPs is expected to increase with VPP flexibility. Finally, the study illustrates how VPPs can adapt to and derive benefits from an increasing level of wind power penetration by providing a higher amount of frequency response.

An Optimization Control Method of IEH Considering User Thermal Comfort

In this paper, a user thermal comfort criterion based on predicted mean vote (PMV) values is introduced to realize the optimal operation of an improved energy hub (IEH) while considering thermal inertia and user thermal behavior. A three-layer optimization model based on user thermal comfort is constructed which fully considers user thermal comfort demand, IEH operating costs, and energy network constraints. Moreover, since IEH optimization considering user thermal comfort is a multi-objective bilevel optimization (MNBO) problem, this paper proposes an improved multilayer nested quantum genetic algorithm (IMNQGA) to solve it. Finally, the effectiveness of the proposed optimization model and algorithm is verified through the analysis of the four modes. The examples show that the proposed optimal control method can reduce the system’s operating costs and improve energy efficiency while satisfying user thermal comfort demand.