Bi-level Optimization Technique Research Articles

Smoothness-oriented motion planning method for milling robot considering workpiece set-up optimization

Robots are attracing increasing attention in the machining field owing to their great flexibility, vast workspace and low cost. Functional redundancy exists when robots are engaged in milling tasks. Redundancy resolution be considered not only in milling robot motion planning, but also in workpiece layout. A two-step motion planning method is proposed to optimize the trajectory and the workpiece set-up simultaneously to improve planning efficiency with less computational burden. In the first stage, a bilevel optimization technique is proposed that can plan the motion from a global perspective and search the optimal workpiece layout. In the second step, based on a novel smoothness index, a modified whale optimization algorithm combined with the differential evolution algorithm (DE-WOA) is proposed to resolve redundancy under robot and machining error constraints. Experiments demonstrate that the proposed method can enhance the quality of surface machining while avoiding the impact of path length on computational complexity.

BiG-Fed: Bilevel Optimization Enhanced Graph-Aided Federated Learning

In federated learning (FL), due to the non-i.i.d. nature of distributedly owned local datasets, personalization is an important design goal. In this paper, we investigate FL scenarios in which data owners are related by a network topology (e.g., traffic prediction based on sensor networks). Existing personalized FL approaches cannot take this information into account. To address this limitation, we propose the Bilevel Optimization enhanced Graph-aided Federated Learning (BiG-Fed) approach. The inner weights enable local tasks to evolve towards personalization, and the outer shared weights on the server side target the non-i.i.d problem enabling individual tasks to evolve towards a global constraint space. To the best of our knowledge, BiG-Fed is the first bilevel optimization technique to enable FL approaches to cope with two nested optimization tasks at the FL server and FL clients simultaneously. Theoretical analysis shows that BiG-Fed is guaranteed to converge in an efficient manner. Extensive experiments on both synthetic and real-world data demonstrate significant superior performance of BiG-Fed over seven state-of-the-art methods.

Bilevel optimization for automated machine learning: a new perspective on framework and algorithm.

Formulating the methodology of machine learning by bilevel optimization techniques provides a new perspective to understand and solve automated machine learning problems.

Gaussian process-based bilevel optimization with critical load restoration for system resilience improvement through data centers-to-grid scheme

Bilevel optimization problems can be used to represent the collaborative interaction between a power system and grid-connected entities. Meanwhile, internet data centers (IDCs), the newly emerged loads, can largely improve power systems’ resiliency owing to their flexibility on computing loads migration. However, most existing bilevel optimization techniques, for system restoration after disasters, assume that the entities’ behaviors are available to power systems for the decision-making, which may be untenable due to the independence and autonomy of IDCs. Thus, this work proposes a novel two-layer optimization framework based on Gaussian Process Regression to enhance power systems’ restoration capability after disasters by exploiting the potential of IDCs. The proposed two-layer model respects the information barriers between power systems and IDCs through a regression function representing IDCs’ response to power system decisions, which contribute to the protection of IDCs’ privacy and the significant improvement on the computational efficiency of the optimization problem without compromising accuracy. Moreover, compared to the conventional methods, the proposed restoration model considers the load-side operations and the varying load marginal values, such that the interests and physical properties of the lower layer can be closer to real scenarios. Two case studies validate the advantages of the proposed approach.

Techno-economic multi-objective reactive power planning in integrated wind power system with improving voltage stability

• Suggesting a probabilistic multi-objective framework for the RPP problem. • Proposing a novel WT model that can dynamically control reactive power. • Exploring a modified operational cost formula for wind power generation. • Introducing a new bi-level multi-objective strategy to solve the RPP. Electrical power systems encounter a variety of challenges due to load growth and technological improvement; reactive power planning (RPP) and improvement of voltage stability (VS) are the two most significant ones. The integration of wind farms (WFs) into power networks has many advantages in terms of operation cost and emissions. But leads to voltage instability if it is not optimally sized, placed, and coordinated with VAR sources. In this study, a probabilistic multi-objective RPP framework is proposed for power systems with high penetration of WFs. A novel wind turbine model that can dynamically control reactive power is suggested based on the capability curve of a double-fed induction generator. A new bi-level optimization technique is introduced to address the problem considering the uncertainties of loads and wind power. Multi-objective genetic algorithm is employed at the upper level to optimally allocate VAR sources, and select the optimal locations of WFs to improve VS and decrease VAR sources’ costs. While at the lower level, the overall operation cost is minimized. A fuzzy min-max method is modified to find the optimum compromise solution. The results show that the proposed technique is effective in improving system VS and operation costs.

An optimal bilevel optimization model for the generalized total variation and anisotropic tensor parameters selection

This paper investigates a novel variational optimization model for image denoising. Within this work, a bilevel optimization technique with a suitable mathematical background is proposed to detect automatically three crucial parameters: α0, α1 and θ. The parameters α0, α1 control the Total Generalized Variation (TGV) regularization while the parameter θ is related to the anisotropic diffusive tensor. A proper selection of these parameters represents a challenging task. Since these parameters are always related to a better approximation of the image gradient and texture, their computation plays a major role in preserving the image features. Analytically, we include results on the approximation of these parameters as well as the resolution of the encountered bilevel problem in a suitable framework. In addition, to resolve the PDE-constrained minimization problem, a modified primal-dual algorithm is proposed. Finally, numerical results are provided to remove noise and simultaneously keep safe fine details and important features with numerous comparisons to show the performance of the proposed approach.

An improved bilevel optimization approach for image super-resolution based on a fractional diffusion tensor

Variational regularization techniques are widely used to improve the quality of the super-resolved image. However, the success of these methods depends on some sensitive parameters which have to be manually tuned. Recently, an improved strategy to avoid this illness is to learn these parameters from some available data. In this work we propose an improved super-resolution method with bilevel optimization technique to learn the spatially dependent parameter λ that controls the diffusivity of the fractional tensor of the Partial Differential Equation (PDE) to remove both Gaussian and speckle noises. Also, we elaborate a mathematical well-posedness of the optimal control problem and we introduce a projected quasi-Newton algorithm to compute the HR image X and the associated parameter λ. The numerical experiments cope with our theoretical part and show a significant improvement of the restored HR image compared to some state of art super-resolution.

Casting Light on the Hidden Bilevel Combinatorial Structure of the Capacitated Vertex Separator Problem

Exploiting Bilevel Optimization Techniques to Disconnect Graphs into Small Components In order to limit the spread of possible viral attacks in a communication or social network, it is necessary to identify critical nodes, the protection of which disconnects the remaining unprotected graph into a bounded number of shores (subsets of vertices) of limited cardinality. In the article “'Casting Light on the Hidden Bilevel Combinatorial Structure of the Capacitated Vertex Separator Problem”, Furini, Ljubic, Malaguti, and Paronuzzi provide a new bilevel interpretation of the associated capacitated vertex separator problem and model it as a two-player Stackelberg game in which the leader interdicts (protects) the vertices, and the follower solves a combinatorial optimization problem on the resulting graph. Thanks to this bilevel interpretation, the authors derive different families of strengthening inequalities and show that they can be separated in polynomial time. The ideas exploited in their framework can also be extended to other vertex/edge deletion/insertion problems or graph partitioning problems by modeling them as two-player Stackelberg games to be solved through bilevel optimization.

Stirling system optimization for series hybrid electric vehicles

There have been many studies conducted to replace the conventional internal combustion engine (ICE) with a more efficient engine, due to increasing regulations over vehicles’ emissions. Throughout the years, several external combustion engines were considered as alternatives to these traditional ICEs for their intrinsic benefits, among which are Stirling machines. These were formerly utilized in conventional powertrains; however, they were not implemented in hybrid vehicles. The purpose of this study is to investigate the possibility of implementing a Stirling engine in a series hybrid electric vehicle (SHEV) to substitute the ICE. Exergy analysis was conducted on a mathematical model, which was developed based on a real simple Stirling, to pinpoint the room for improvements. Then, based on this analysis, other configurations were retrieved to reduce exergy losses. Consequently, a Stirling-SHEV was modeled, to be integrated as auxiliary power unit (APU). Hereafter, through an exergo-technological detailed selection, the best configuration was found to be the Regenerative Reheat two stages serial Stirling (RRe-n2-S), offering the best efficiency and power combination. Then, this configuration was compared with the Regenerative Stirling (R-S) and the ICE in terms of fuel consumption, in the developed SHEV on the WLTC. This was performed using an Energy Management Strategy (EMS) consisting of a bi-level optimization technique, combining the Non-dominated Sorting Genetic Algorithm (NSGA) with the Dynamic Programming (DP). This arrangement is used to diminish the fuel consumption, while considering the reduction of the APU’s ON/OFF switching times, avoiding technical issues. Results prioritized the RRe-n2-S presenting 12.1% fuel savings compared to the ICE and 14.1% savings compared to the R-S.

Modeling operation problem of active distribution networks with retailers and microgrids: A multi-objective bi-level approach

Implementation of distributed energy resources (DERs) has led to a decrement in the cost of supplying demand in distribution networks. Integration of DERs in the forms of micro-grids (MGs) is a solution to enhance the operation of these resources in the low voltage networks. To meet the demand by MG operator, both technical and economic characteristics as well as the prices offered by retailers are considered to schedule DERs optimally. In these networks, the profit of retailers is maximized by power trading with MGs and optimally purchasing the energy from wholesale markets. Due to the existence of several retailers and MGs in active distribution networks (ADNs), hierarchical decision-making frameworks are needed to model their operation problem. For this purpose, a bi-level optimization technique is proposed in this paper to model the operation problem of retailers and MGs as decision-making variables in distribution networks in the upper and lower levels, respectively. To solve the proposed model, multi-objective particle swarm optimization (MOPSO) algorithm is used. The proposed model and its solution method are applied to a hypothetical distribution network with several retailers and MGs to validate the theories and discussions. Numerical results show that the maximum capacity of DG and the amount of demand have an important effect on this decision and the prices of purchased power from wholesale markets determine the amount of retailers’ offers to MGs.

Efficiency Improvement of a Series–Parallel Hybrid Electric Powertrain by Topology Modification

Among Series-Parallel Hybrid Electric Vehicle (SPHEV) powertrains, the Power-Split architecture with a planetary gear has an exemplary energetic efficiency in mixed driving conditions. Nevertheless, a simple SPHEV architecture can be realized without a planetary gear. It consists of 2 Electric Machines (EM) mounted on the engine shaft and separated by a clutch. With no power-split operation, this architecture allows the vehicle to operate in pure electric, or series hybrid, or parallel hybrid mode. It was proven to be less efficient than a reference Power-Split SPHEV: the Toyota Hybrid System (THS). The aim of this paper is to investigate the potential of efficiency improvement of the simple SPHEV powertrain by topology modification: the addition of gears for the components or a gearbox with few number of ratios. Two new variants of SPHEVs are proposed. The versions of SPHEVs and the reference THS are optimized by a bi-level optimization technique using Genetic Algorithm and Dynamic Programming. Compared to the simple SPHEV, results show an efficiency worsening in one variant and an efficiency improvement in another variant with a fuel consumption comparable to the one of THS. A global sensitivity study is then performed on the worsened variant. The sensitivities of the added gears are determined and an elimination of some is suggested. A new variant with fewer gears is therefore proposed and optimized. The efficiency is improved but remains less than the one of THS.

Valuation of distributed energy resources in active distribution networks

In concert with the transformation of conventional passive power distribution system, distributed energy resources (DERs) have progressively become participants in the provision of electricity services in active distribution networks (ADNs). In this paper, we propose a systematic valuation process to quantify the value of DERs in the ADN context. The paper first provides comprehensive insights into the impacts of DERs on ADN and the society as a whole. Given the technological, locational, and temporal diversity of DERs, a two-part scheme is developed to value and compensate DER portfolios proposed by customers and independent third parties. In particular, DERs are valued for their benefits and costs in both short and long terms. An integrated resource planning model is formulated to quantify the value of a given DER portfolio to be installed, where bi-level optimization techniques are applied to coordinate decisions on ADN planning and operations. In order to determine the short-term operation benefits of the DER portfolio on a continuous basis, a retail market operation model is developed based on peer-to-peer energy transactions among prosumers, when the impacts of DERs on ADN operations are monetized by distribution locational marginal prices. It is finally concluded in the paper that the proposed valuation scheme will not only contribute to the proactive investment of DERs in ADN but also help enhance the role of DERs in offering affordable, reliable, resilient and sustainable electricity services to customers.

Portfolio selection through Maslow’s need hierarchy theory

ABSTRACTInspired by Maslow’s need hierarchy theory, we construct a new portfolio selection framework using the bi-level optimization technique in which the lower-level need relates to safety (low risk) while the upper-level need is concerned with self-actualization (high payoff). Specially, we consider a bi-level portfolio selection model using variance and conditional value-at-risk associated with the lower-level need and upper-level need, respectively. Accordingly, we propose a procedure to solve this bi-level optimization problem without the normal distribution assumption. Empirical study on the American stock market and U.K. stock market shows that our new model can determine optimal portfolios with moderate diversification. Out of sample performance also confirms that in our framework investors can obtain higher returns in a safe way compared to models in the traditional framework.

Bi-level optimization of laminated composite structures using particle swarm optimization algorithm

This paper presents an efficient bi-level optimization technique to obtain the optimal stacking sequence for symmetric composite structures. The proposed approach involves two levels of modeling and optimization. The first level of the optimization procedure is used to minimize the weight of the composite structure. At this level, lamination parameters and the number of plies of specified angles (0, ±45 and 90 degree) are design variables, buckling load factor is treated as a constraint, and the weight of the structure is to be minimized using continuous-discrete particle swarm optimization algorithm. Next, at the second level the location of each ply orientation through the thickness (i.e. the layup of the panel) is found. At the second level, optimum stacking sequence is sought to maximize the load bearing capacity of the structure with respect to the buckling. The proposed methodology is applied to two test cases. Results show that the approach improves the buckling load factor of the structure without any weight penalty.

Subsidy rate decisions for the printer recycling industry by bi-level optimization techniques

This study attempts to optimize the operations of the Recycling Fund Management Board (RFMB), founded by the Environmental Protection Administration of the ROC Government (in Taiwan), by using a subsidy rate decision for domestic printer recyclers. The hierarchical and interactive relation between the two parties is modeled by bi-level programming, where the RFMB serves as the upper-level decision unit, recyclers are the lower-level counterpart, and the consumer’s action is embedded in the constraints of the lower level problem. The problem is solved by the Karush–Kuhn–Tucker transformation approach. Practical data including sales of printers per year, a survey of recycling intention, recycler cost structure, and resource recycling value are used to solve the problem. The resulting solution discovers the inefficiency of the current operations of RFMB, and suggests an appropriate recycling fee and subsidy rate that balance the interests of printer manufacturers, recyclers, and the RFMB.

Uncertainty-safe large scale support vector machines

The issue of large scale binary classification when data is subject to random perturbations is addressed. The proposed model integrates a learning framework that adjusts its robustness to noise during learning. The method avoids over-conservative situations that can be encountered with worst-case robust support vector machine formulations. The algorithm could be seen as a technique to learn the support-set of the noise distribution during the training process. This is achieved by introducing optimization variables that control the magnitude of the noise perturbations that should be taken into account. The magnitude is tuned by optimizing a generalization error. Only rough estimates of perturbations bounds are required. Additionally, a stochastic bi-level optimization technique is proposed to solve the resulting formulation. The algorithm performs very cheap stochastic subgradient moves and is therefore well suited to large datasets. Encouraging experimental results show that the technique outperforms robust second order cone programming formulations.

An Optimization Technique Based on Profit of Investment and Market Clearing in Wind Power Systems

Recently, renewable energies are widely used instead of the fuel energies due to their individual potentials such as its availability, low price and environmentally friendly. One of the most important renewable energies is wind power. As a result, investment in wind power is one of the most interesting research to maximize the profit of the investment and market clearing. In this paper, bi-level optimization technique is proposed to maximize the investment problem and market clearing for the wind power at the same time and in one single problem. Then, karush–kuhn–tucker (KKT) conditions and mathematical programming with equilibrium constraints (MPEC) are applied and tried to find one level optimization problem. Due to the nonlinearity of the optimization equation, the Fortuny-Amat & McCarl (FM) linearization technique is used to linearize the model. Finally, the proposed technique is applied to the IEEE 24 buses. The result proves that the optimization analysis is very easy, fast and accurate due to the linear characteristic of the system. All the simulation results are carried out in MATLAB and GAMS softwares.

Bilevel Optimization in the Context of Intermodal Pricing: State of Art

With the rising interest to stimulate intermodal transport, determining pricing strategies can be intrinsically challenging. We provide a review on the current state of research in intermodal pricing, through which we identify a peculiar gap in optimization approaches. A suggestion to exploit the bilevel optimization technique is presented, as well as an account of its widely successful application to price setting problems. The different approaches to express the network users’ behavior, regarded as the lower level problem, are highlighted together with the particular modeling aspects of intermodal networks.

Bilevel optimization techniques in computational strain design

Over the past decade a number of bilevel optimization techniques were introduced for computational strain design leading to the overproduction of biochemicals. In this paper, we provide an algorithm-centric description of the OptKnock and OptForce strain-design protocols, highlight their differences and demonstrate their application for a prototypical overproduction problem. The derivation of the equivalent MILP representation in both cases is described in detail along with provisions that lead to significantly improved performance. Comparison between the intervention strategies of OptKnock and OptForce for the overproduction of succinate in Escherichia coli reveal that while OptKnock couples succinate with biomass production, OptForce suggests interventions that improves the minimum production of succinate. Further, OptForce is more tractable as it identifies interventions from only the subset of reactions that must change in the overproducing strain. Overall, this paper highlights the computational challenges faced in strain design and the methodological choices explored by OptKnock and OptForce.

Pay-as-bid versus marginal pricing: The role of suppliers strategic behavior

This paper illustrates how a generator profit may be affected by the pricing method of an oligopoly market model. Through utilizing a bilevel optimization technique and game theory concepts, Supply Function Equilibria (SFE) of pay-as-bid pricing (PABP) and marginal pricing (MP) mechanisms are derived. Theoretically, it is demonstrated that in the presence of strategic interaction, the generator optimal bidding strategy and the market clearing price are higher under PABP as compared with MP. In addition, the probability distribution patterns of expected loss and profit of each generator are constructed by simulating a multiperiod market under PABP and MP rules. It is shown that a generator has a higher expected loss or profit under PABP in unconstrained networks. However, the generator may gain less expected loss or profit if its physical location or transmission limitations are considered.