Gradient-based algorithms for multi-objective bi-level optimization

Multi-objective bi-level optimization(MOBLO)addresses nested multi-objective optimization problems common in a range of applications.However,its multi-objective and hierarchical bi-level nature makes it notably complex.Gradient-based MOBLO algorithms have recently grown in popularity,as they effectively solve crucial machine learning problems like meta-learning,neural architecture search,and reinforcement learning.Unfortunately,these algorithms depend on solving a sequence of approximation subproblems with high accuracy,resulting in adverse time and memory complexity that lowers their numerical efficiency.To address this issue,we propose a gradient-based algorithm for MOBLO,called gMOBA,which has fewer hyperparameters to tune,making it both simple and efficient.Additionally,we demonstrate the theoretical validity by accomplishing the desirable Pareto stationarity.Numerical experiments confirm the practical efficiency of the proposed method and verify the theoretical results.To accelerate the convergence of gMOBA,we introduce a beneficial L2O(learning to optimize)neural network(called L2O-gMOBA)implemented as the initialization phase of our gMOBA algorithm.Comparative results of numerical experiments are presented to illustrate the performance of L2O-gMOBA.

Bi-level optimization based two-stage market clearing model considering guaranteed accommodation of renewable energy generation

The existing electricity market mechanisms designed to promote the consumption of renewable energy generation complicate network participation in market transactions owing to an unfair market competition environment,where the low cost renewable energy generation is not reflected in the high bidding price of high cost conventional energy generation.This study addresses this issue by proposing a bi-level optimization based two-stage market clearing model that considers the bidding strategies of market players,and guarantees the accommodation of renewable energy generation.The first stage implements a dual-market clearing mechanism that includes a unified market for trading the power generations of both renewable energy and conventional energy units,and a subsidy market reserved exclusively for conventional generation units.A re-adjustment clearing mechanism is then proposed in the second stage to accommodate the power generation of remaining renewable energy units after first stage energy allocations.Each stage of the proposed model is further described as a bi-level market equilibrium problem and is solved using a co-evolutionary algorithm.Finally,numerical results involving an improved IEEE 39-bus system dem-onstrate that the proposed two-stage model meets the basic requirements of incentive compatibility and individual rationality.It can facilitate the rational allocation of resources,promote the economical operation of electric power grids,and enhance social welfare.

Bi-level optimization model applications in managing air emissions from ships:A review

Ship air emissions are recognized as one of the key concerns of the maritime industry.Competent authorities have issued various regulations to manage air emissions from ships.Although the authorities are policy makers,the effectiveness of policies is up to the shipping industry who operates the vessels and terminals to fulfill maritime transportation works.Given this characteristic,bi-level optimization model has been widely adopted in studies that optimize policy design or evaluate its effectiveness.The framework of a typical bi-level optimization model for ship emission management problem is given to show the basic structure of similar issues.A series of applications of bi-level optimization model in managing ship emissions is reviewed,including cases of Energy Efficiency Design Index,Emissions Control Area,Market Based Measure,Carbon Intensity Indicator,and Vessel Speed Reduction Incentive Program.We hope this paper can enlighten scholars interested in this area and provide help for them.

Necessary Optimality Conditions for Semi-vectorial Bi-level Optimization with Convex Lower Level:Theoretical Results and Applications to the Quadratic Case

This paper explores related aspects to post-Pareto analysis arising from the multicriteria optimization problem.It consists of two main parts.In the first one,we give first-order necessary optimality conditions for a semi-vectorial bi-level optimization problem:the upper level is a scalar optimization problem to be solved by the leader,and the lower level is a multi-objective optimization problem to be solved by several followers acting in a cooperative way(greatest coalition multi-players game).For the lower level,we deal with weakly or properly Pareto(efficient)solutions and we consider the so-called optimistic problem,i.e.when followers choose amongst Pareto solutions one which is the most favourable for the leader.In order to handle reallife applications,in the second part of the paper,we consider the case where each follower objective is expressed in a quadratic form.In this setting,we give explicit first-order necessary optimality conditions.Finally,some computational results are given to illustrate the paper.

A bi-level optimization for a make-to-order manufacturing supply chain planning:a case in the steel industry Lanndon

This paper presents an actual case application of a newly developed gametheoretic model in analyzing a single manufacturer-many supplier,multi-period,make-to-order supply chain with fuzzy parameters.The supply chain under consideration comprises an exclusive supplier for every component required by the manufacturer in producing its product.In certain instances,some supply chains enable the manufacturer to opt for a third-party subcontractor to produce a portion of its demand.We assume that the supply chain faces a price and lead-time-sensitive demand,which is relevant in a make-to-order environment.The vertical interaction within the supply chain is played as a Stackelberg game,where the manufacturer is considered the leader and the suppliers as the followers.Results show some important managerial insights in supply chain planning under a make-to-order condition.

Optimization of the bioconversion of glycerol to ethanol using Escherichia coli by implementing a bi-level programming framework for proposing gene transcription control strategies based on genetic algorithms

In silico approaches for metabolites optimization have been derived from the flood of sequenced and annotated genomes. However, there exist still numerous degrees of freedom in terms of optimization algorithm approaches that can be exploited in order to enhance yield of processes which are based on biological reactions. Here, we propose an evolutionary approach aiming to suggest different mutant for augmenting ethanol yield using glycerol as substrate in Escherichia coli. We found that this algorithm, even though is far from providing the global optimum, is able to uncover genes that a global optimizer would be incapable of. By over-expressing accB, eno, dapE, and accA mutants in ethanol production was augmented up to 2 fold compared to its counterpart E. coli BW25113.

Multi-Strategy Assisted Multi-Objective Whale Optimization Algorithm for Feature Selection

In classification problems,datasets often contain a large amount of features,but not all of them are relevant for accurate classification.In fact,irrelevant features may even hinder classification accuracy.Feature selection aims to alleviate this issue by minimizing the number of features in the subset while simultaneously minimizing the classification error rate.Single-objective optimization approaches employ an evaluation function designed as an aggregate function with a parameter,but the results obtained depend on the value of the parameter.To eliminate this parameter’s influence,the problem can be reformulated as a multi-objective optimization problem.The Whale Optimization Algorithm(WOA)is widely used in optimization problems because of its simplicity and easy implementation.In this paper,we propose a multi-strategy assisted multi-objective WOA(MSMOWOA)to address feature selection.To enhance the algorithm’s search ability,we integrate multiple strategies such as Levy flight,Grey Wolf Optimizer,and adaptive mutation into it.Additionally,we utilize an external repository to store non-dominant solution sets and grid technology is used to maintain diversity.Results on fourteen University of California Irvine(UCI)datasets demonstrate that our proposed method effectively removes redundant features and improves classification performance.The source code can be accessed from the website:https://github.com/zc0315/MSMOWOA.

Multidisciplinary Design Optimization of A Human Occupied Vehicle Based on Bi-Level Integrated System Collaborative Optimization

The design of Human Occupied Vehicle （HOV） is a typical multidisciplinary problem, but heavily dependent on the experience of naval architects at present engineering design. In order to relieve the experience dependence and improve the design, a new Multidisciplinary Design Optimization （MDO） method ＂Bi-Level Integrated System Collaborative Optimization （BLISCO）＂ is applied to the conceptual design of an HOV, which consists of hull module, resistance module, energy module, structure module, weight module, and the stability module. This design problem is defined by 21 design variables and 23 constraints, and its objective is to maximize the ratio of payload to weight. The results show that the general performance of the HOV can be greatly improved by BLISCO.

MCWOA Scheduler:Modified Chimp-Whale Optimization Algorithm for Task Scheduling in Cloud Computing

Cloud computing provides a diverse and adaptable resource pool over the internet,allowing users to tap into various resources as needed.It has been seen as a robust solution to relevant challenges.A significant delay can hamper the performance of IoT-enabled cloud platforms.However,efficient task scheduling can lower the cloud infrastructure’s energy consumption,thus maximizing the service provider’s revenue by decreasing user job processing times.The proposed Modified Chimp-Whale Optimization Algorithm called Modified Chimp-Whale Optimization Algorithm(MCWOA),combines elements of the Chimp Optimization Algorithm(COA)and the Whale Optimization Algorithm(WOA).To enhance MCWOA’s identification precision,the Sobol sequence is used in the population initialization phase,ensuring an even distribution of the population across the solution space.Moreover,the traditional MCWOA’s local search capabilities are augmented by incorporating the whale optimization algorithm’s bubble-net hunting and random search mechanisms into MCWOA’s position-updating process.This study demonstrates the effectiveness of the proposed approach using a two-story rigid frame and a simply supported beam model.Simulated outcomes reveal that the new method outperforms the original MCWOA,especially in multi-damage detection scenarios.MCWOA excels in avoiding false positives and enhancing computational speed,making it an optimal choice for structural damage detection.The efficiency of the proposed MCWOA is assessed against metrics such as energy usage,computational expense,task duration,and delay.The simulated data indicates that the new MCWOA outpaces other methods across all metrics.The study also references the Whale Optimization Algorithm(WOA),Chimp Algorithm(CA),Ant Lion Optimizer(ALO),Genetic Algorithm(GA)and Grey Wolf Optimizer(GWO).

Accelerated design of high-performance Mg-Mn-based magnesium alloys based on novel bayesian optimization

Magnesium(Mg),being the lightest structural metal,holds immense potential for widespread applications in various fields.The development of high-performance and cost-effective Mg alloys is crucial to further advancing their commercial utilization.With the rapid advancement of machine learning(ML)technology in recent years,the“data-driven''approach for alloy design has provided new perspectives and opportunities for enhancing the performance of Mg alloys.This paper introduces a novel regression-based Bayesian optimization active learning model(RBOALM)for the development of high-performance Mg-Mn-based wrought alloys.RBOALM employs active learning to automatically explore optimal alloy compositions and process parameters within predefined ranges,facilitating the discovery of superior alloy combinations.This model further integrates pre-established regression models as surrogate functions in Bayesian optimization,significantly enhancing the precision of the design process.Leveraging RBOALM,several new high-performance alloys have been successfully designed and prepared.Notably,after mechanical property testing of the designed alloys,the Mg-2.1Zn-2.0Mn-0.5Sn-0.1Ca alloy demonstrates exceptional mechanical properties,including an ultimate tensile strength of 406 MPa,a yield strength of 287 MPa,and a 23%fracture elongation.Furthermore,the Mg-2.7Mn-0.5Al-0.1Ca alloy exhibits an ultimate tensile strength of 211 MPa,coupled with a remarkable 41%fracture elongation.

Optimization Design of the Multi-Layer Cross-Sectional Layout of An Umbilical Based on the GA-GLM

Marine umbilical is one of the key equipment for subsea oil and gas exploitation,which is usually integrated by a great number of different functional components with multi-layers.The layout of these components directly affects manufacturing,operation and storage performances of the umbilical.For the multi-layer cross-sectional layout design of the umbilical,a quantifiable multi-objective optimization model is established according to the operation and storage requirements.Considering the manufacturing factors,the multi-layering strategy based on contact point identification is introduced for a great number of functional components.Then,the GA-GLM global optimization algorithm is proposed combining the genetic algorithm and the generalized multiplier method,and the selection operator of the genetic algorithm is improved based on the steepest descent method.Genetic algorithm is used to find the optimal solution in the global space,which can converge from any initial layout to the feasible layout solution.The feasible layout solution is taken as the initial value of the generalized multiplier method for fast and accurate solution.Finally,taking umbilicals with a great number of components as examples,the results show that the cross-sectional performance of the umbilical obtained by optimization algorithm is better and the solution efficiency is higher.Meanwhile,the multi-layering strategy is effective and feasible.The design method proposed in this paper can quickly obtain the optimal multi-layer cross-sectional layout,which replaces the manual design,and provides useful reference and guidance for the umbilical industry.

Design and optimization of a greener sinomenine hydrochloride preparation process considering variations among different batches of the medicinal herb

The current methods used to industrially produce sinomenine hydrochloride involve several issues,including high solvent toxicity,long process flow,and low atomic utilization efficiency,and the greenness scores of the processes are below 65 points.To solve these problems,a new process using anisole as the extractant was proposed.Anisole exhibits high selectivity for sinomenine and can be connected to the subsequent water-washing steps.After alkalization of the medicinal material,heating extraction,water washing,and acidification crystallization were carried out.The process was modeled and optimized.The design space was constructed.The recommended operating ranges for the critical process parameters were 3.0–4.0 h for alkalization time,60.0–80.0℃ for extraction temperature,2.0–3.0(volume ratio)for washing solution amount,and 2.0–2.4 mol·L^(-1) for hydrochloric acid concentration.The new process shows good robustness because different batches of medicinal materials did not greatly impact crystal purity or sinomenine transfer rate.The sinomenine transfer rate was about 20%higher than that of industrial processes.The greenness score increased to 90 points since the novel process proposed in this research solves the problems of long process flow,high solvent toxicity,and poor atomic economy,better aligning with the concept of green chemistry.

Optimal planning of energy storage system in active distribution system based on fuzzy multi-objective bi-level optimization

A fuzzy multi-objective bi-level optimization problem is proposed to model the planning of energy storage system(ESS) in active distribution systems(ADS). The proposed model enables us to take into account how optimal operation strategy of ESS in the lower level can affect and be affected by the optimal allocation of ESS in the upper level. The power characteristic model of micro-grid(MG)and typical daily scenarios are established to take full consideration of time-variable nature of renewable energy generations(REGs) and load demand while easing the burden of computation. To solve the bi-level mixed integer problem, a multi-subgroup hierarchical chaos hybrid algorithm is introduced based on differential evolution(DE) and particle swarm optimization(PSO). The modified IEEE-33 bus benchmark distribution system is utilized to investigate the availability and effectiveness of the proposed model and the hybrid algorithm. Results indicate that the planningmodel gives an adequate consideration to the optimal operation and different roles of ESS, and has the advantages of objectiveness and reasonableness.

Frilled Lizard Optimization: A Novel Bio-Inspired Optimizer for Solving Engineering Applications

This research presents a novel nature-inspired metaheuristic algorithm called Frilled Lizard Optimization(FLO),which emulates the unique hunting behavior of frilled lizards in their natural habitat.FLO draws its inspiration from the sit-and-wait hunting strategy of these lizards.The algorithm’s core principles are meticulously detailed and mathematically structured into two distinct phases:(i)an exploration phase,which mimics the lizard’s sudden attack on its prey,and(ii)an exploitation phase,which simulates the lizard’s retreat to the treetops after feeding.To assess FLO’s efficacy in addressing optimization problems,its performance is rigorously tested on fifty-two standard benchmark functions.These functions include unimodal,high-dimensional multimodal,and fixed-dimensional multimodal functions,as well as the challenging CEC 2017 test suite.FLO’s performance is benchmarked against twelve established metaheuristic algorithms,providing a comprehensive comparative analysis.The simulation results demonstrate that FLO excels in both exploration and exploitation,effectively balancing these two critical aspects throughout the search process.This balanced approach enables FLO to outperform several competing algorithms in numerous test cases.Additionally,FLO is applied to twenty-two constrained optimization problems from the CEC 2011 test suite and four complex engineering design problems,further validating its robustness and versatility in solving real-world optimization challenges.Overall,the study highlights FLO’s superior performance and its potential as a powerful tool for tackling a wide range of optimization problems.

Towards the performance limit of catenary meta-optics via field-driven optimization

Catenary optics enables metasurfaces with higher efficiency and wider bandwidth,and is highly anticipated in the imaging system,super-resolution lithography,and broadband absorbers.However,the periodic boundary approximation without considering aperiodic electromagnetic crosstalk poses challenges for catenary optical devices to reach their performance limits.Here,perfect control of both local geometric and propagation phases is realized through field-driven optimization,in which the field distribution is calculated under real boundary conditions.Different from other optimization methods requiring a mass of iterations,the proposed design method requires less than ten iterations to get the efficiency close to the optimal value.Based on the library of shape-optimized catenary structures,centimeter-scale devices can be designed in ten seconds,with the performance improved by ~15%.Furthermore,this method has the ability to extend catenary-like continuous structures to arbitrary polarization,including both linear and elliptical polarizations,which is difficult to achieve with traditional design methods.It provides a way for the development of catenary optics and serves as a potent tool for constructing high-performance optical devices.

A FLEXIBLE OBJECTIVE-CONSTRAINT APPROACH AND A NEW ALGORITHM FOR CONSTRUCTING THE PARETO FRONT OF MULTIOBJECTIVE OPTIMIZATION PROBLEMS

In this article, a novel scalarization technique, called the improved objective-constraint approach, is introduced to find efficient solutions of a given multiobjective programming problem. The presented scalarized problem extends the objective-constraint problem. It is demonstrated that how adding variables to the scalarized problem, can lead to find conditions for (weakly, properly) Pareto optimal solutions. Applying the obtained necessary and sufficient conditions, two algorithms for generating the Pareto front approximation of bi-objective and three-objective programming problems are designed. These algorithms are easy to implement and can achieve an even approximation of (weakly, properly) Pareto optimal solutions. These algorithms can be generalized for optimization problems with more than three criterion functions, too. The effectiveness and capability of the algorithms are demonstrated in test problems.

Rao Algorithms-Based Structure Optimization for Heterogeneous Wireless Sensor Networks

The structural optimization of wireless sensor networks is a critical issue because it impacts energy consumption and hence the network’s lifetime.Many studies have been conducted for homogeneous networks,but few have been performed for heterogeneouswireless sensor networks.This paper utilizes Rao algorithms to optimize the structure of heterogeneous wireless sensor networks according to node locations and their initial energies.The proposed algorithms lack algorithm-specific parameters and metaphorical connotations.The proposed algorithms examine the search space based on the relations of the population with the best,worst,and randomly assigned solutions.The proposed algorithms can be evaluated using any routing protocol,however,we have chosen the well-known routing protocols in the literature:Low Energy Adaptive Clustering Hierarchy(LEACH),Power-Efficient Gathering in Sensor Information Systems(PEAGSIS),Partitioned-based Energy-efficient LEACH(PE-LEACH),and the Power-Efficient Gathering in Sensor Information Systems Neural Network(PEAGSIS-NN)recent routing protocol.We compare our optimized method with the Jaya,the Particle Swarm Optimization-based Energy Efficient Clustering(PSO-EEC)protocol,and the hybrid Harmony Search Algorithm and PSO(HSA-PSO)algorithms.The efficiencies of our proposed algorithms are evaluated by conducting experiments in terms of the network lifetime(first dead node,half dead nodes,and last dead node),energy consumption,packets to cluster head,and packets to the base station.The experimental results were compared with those obtained using the Jaya optimization algorithm.The proposed algorithms exhibited the best performance.The proposed approach successfully prolongs the network lifetime by 71% for the PEAGSIS protocol,51% for the LEACH protocol,10% for the PE-LEACH protocol,and 73% for the PEGSIS-NN protocol;Moreover,it enhances other criteria such as energy conservation,fitness convergence,packets to cluster head,and packets to the base station.

Quafu-Qcover:Explore combinatorial optimization problems on cloud-based quantum computers

We introduce Quafu-Qcover,an open-source cloud-based software package developed for solving combinatorial optimization problems using quantum simulators and hardware backends.Quafu-Qcover provides a standardized and comprehensive workflow that utilizes the quantum approximate optimization algorithm(QAOA).It facilitates the automatic conversion of the original problem into a quadratic unconstrained binary optimization(QUBO)model and its corresponding Ising model,which can be subsequently transformed into a weight graph.The core of Qcover relies on a graph decomposition-based classical algorithm,which efficiently derives the optimal parameters for the shallow QAOA circuit.Quafu-Qcover incorporates a dedicated compiler capable of translating QAOA circuits into physical quantum circuits that can be executed on Quafu cloud quantum computers.Compared to a general-purpose compiler,our compiler demonstrates the ability to generate shorter circuit depths,while also exhibiting superior speed performance.Additionally,the Qcover compiler has the capability to dynamically create a library of qubits coupling substructures in real-time,utilizing the most recent calibration data from the superconducting quantum devices.This ensures that computational tasks can be assigned to connected physical qubits with the highest fidelity.The Quafu-Qcover allows us to retrieve quantum computing sampling results using a task ID at any time,enabling asynchronous processing.Moreover,it incorporates modules for results preprocessing and visualization,facilitating an intuitive display of solutions for combinatorial optimization problems.We hope that Quafu-Qcover can serve as an instructive illustration for how to explore application problems on the Quafu cloud quantum computers.

Falcon Optimization Algorithm-Based Energy Efficient Communication Protocol for Cluster-Based Vehicular Networks

Rapid development in Information Technology(IT)has allowed several novel application regions like large outdoor vehicular networks for Vehicle-to-Vehicle(V2V)transmission.Vehicular networks give a safe and more effective driving experience by presenting time-sensitive and location-aware data.The communication occurs directly between V2V and Base Station(BS)units such as the Road Side Unit(RSU),named as a Vehicle to Infrastructure(V2I).However,the frequent topology alterations in VANETs generate several problems with data transmission as the vehicle velocity differs with time.Therefore,the scheme of an effectual routing protocol for reliable and stable communications is significant.Current research demonstrates that clustering is an intelligent method for effectual routing in a mobile environment.Therefore,this article presents a Falcon Optimization Algorithm-based Energy Efficient Communication Protocol for Cluster-based Routing(FOA-EECPCR)technique in VANETS.The FOA-EECPCR technique intends to group the vehicles and determine the shortest route in the VANET.To accomplish this,the FOA-EECPCR technique initially clusters the vehicles using FOA with fitness functions comprising energy,distance,and trust level.For the routing process,the Sparrow Search Algorithm(SSA)is derived with a fitness function that encompasses two variables,namely,energy and distance.A series of experiments have been conducted to exhibit the enhanced performance of the FOA-EECPCR method.The experimental outcomes demonstrate the enhanced performance of the FOA-EECPCR approach over other current methods.

Cooperative User-Scheduling and Resource Allocation Optimization for Intelligent Reflecting Surface Enhanced LEO Satellite Communication

Lower Earth Orbit(LEO) satellite becomes an important part of complementing terrestrial communication due to its lower orbital altitude and smaller propagation delay than Geostationary satellite. However, the LEO satellite communication system cannot meet the requirements of users when the satellite-terrestrial link is blocked by obstacles. To solve this problem, we introduce Intelligent reflect surface(IRS) for improving the achievable rate of terrestrial users in LEO satellite communication. We investigated joint IRS scheduling, user scheduling, power and bandwidth allocation(JIRPB) optimization algorithm for improving LEO satellite system throughput.The optimization problem of joint user scheduling and resource allocation is formulated as a non-convex optimization problem. To cope with this problem, the nonconvex optimization problem is divided into resource allocation optimization sub-problem and scheduling optimization sub-problem firstly. Second, we optimize the resource allocation sub-problem via alternating direction multiplier method(ADMM) and scheduling sub-problem via Lagrangian dual method repeatedly.Third, we prove that the proposed resource allocation algorithm based ADMM approaches sublinear convergence theoretically. Finally, we demonstrate that the proposed JIRPB optimization algorithm improves the LEO satellite communication system throughput.