Hierarchical Optimization Problem Research Articles

RETRACTED ARTICLE: Cooperative Virtual Connectivity Control in Uplink Small Cell Network: Towards Optimal Resource Allocation

Nowadays, the application of soft computational techniques in power systems has been increasing with good acceptance under the machine learning umbrella. In this paper, first we presented a deep reinforcement learning approach to find the optimal configuration for HetNet systems. We used a huge quantity of radial configurations from a test system for training purposes. We also studied the joint carrier/power allocation problem in a multi-layer hierarchical networks to achieve the optimal power efficiency in addition to ensure the quality-of-experience for all subscribers. The proposed approach utilizes an adaptive Load Balancing model that aims to obtain “almost optimal” fairness among all servers from the key performance indicator viewpoints. Contrary to current model-based energy efficiency methods, we proposed a Joint Resource Allocation, Energy Efficiency and Flow Control algorithm to solve conventional non-convex and hierarchical optimization problems. Also, referred to SLA-based continuous resource allocation, we generalized the proposed algorithm to Joint Flow/Power Control, and Throughput Optimization algorithm to achieve the optimal energy efficiency beside of guaranteeing user throughput constraints. The simulation results exhibit that the proposed flow-controlled power optimization approach using the capability of network topology adjustment, is able to considerably enhance the energy efficiency compared to the conventional schemes.

Multidisciplinary Lightweight Optimization for Front Impact Structure of Body Frame Based on Active and Passive Safety

The Analytic Target Cascading (ATC) is an effective method for solving hierarchical Multidisciplinary Design Optimization (MDO) problems. At the same time, this method suffers from poor convergence and low accuracy, which is caused by the inconsistency of system constraints. In this paper, a novel ATC method based on dynamic relaxation factor is proposed. The dynamic relaxation factor of consistency constraint is added in the system level and is adjusted by the deviation of the linking variables between the levels to ensure the feasible region of the design space. The effectiveness and accuracy of this method are verified by a mathematical example. This method is used to solve the lightweight problem of the trussed front part of the vehicle body frame based on active and passive safety to achieve the collaborative optimization of lightweight trussed frame, crash safety, and aerodynamic characteristics. The important value of the novel ATC method based on dynamic relaxation factor in engineering applications is proven.

Hierarchical Optimal Synchronization for Linear Systems via Reinforcement Learning: A Stackelberg-Nash Game Perspective.

Considering the fact that in the real world, a certain agent may have some sort of advantage to act before others, a novel hierarchical optimal synchronization problem for linear systems, composed of one major agent and multiple minor agents, is formulated and studied in this article from a Stackelberg-Nash game perspective. The major agent herein makes its decision prior to others, and then, all the minor agents determine their actions simultaneously. To seek the optimal controllers, the Hamilton-Jacobi-Bellman (HJB) equations in coupled forms are established, whose solutions are further proven to be stable and constitute the Stackelberg-Nash equilibrium. Due to the introduction of the asymmetric roles for agents, the established HJB equations are more strongly coupled and more difficult to solve than that given in most existing works. Therefore, we propose a new reinforcement learning (RL) algorithm, i.e., a two-level value iteration (VI) algorithm, which does not rely on complete system matrices. Furthermore, the proposed algorithm is shown to be convergent, and the converged values are exactly the optimal ones. To implement this VI algorithm, neural networks (NNs) are employed to approximate the value functions, and the gradient descent method is used to update the weights of NNs. Finally, an illustrative example is provided to verify the effectiveness of the proposed algorithm.

Automated parameter tuning as a bilevel optimization problem solved by a surrogate-assisted population-based approach

This work presents a proposal for the automated parameter tuning problem (APTP) modeled as a bilevel optimization problem. Different definitions and theoretical results are given in order to formalize the APTP in the context of this hierarchical optimization problem. The obtained bilevel optimization problem is solved via a population-based algorithm added with surrogate models to identify promising regions in the parameter search space. The approach is tested by configuring four representative metaheuristics for numerical optimization on a set of well-known and recent test problems; also a competitive algorithm for a popular combinatorial optimization problem was configured (considering a large benchmark suite). The experimental results are compared against those of a state-of-the-art parameter tuning method called IRACE. The results, validated by the Bayesian signed-rank statistical test, indicate that BCAP, even it is based on an usually costly model (i.e. a bilevel optimization problem), with only half of the calls to the target algorithm, is able to find better configurations than those obtained by the compared approach.

Brain Storm Optimization-Based Edge Caching in Fog Radio Access Networks

In this paper, the hierarchical cooperative caching problem in fog radio access networks (F-RANs) is investigated. To minimize the content request delay, we formulate the hierarchical cooperative caching optimization problem based on local content popularity to find the optimal caching policy, where both horizontal cooperation among fog access points (F-APs) and vertical cooperation between the cloud server and F-APs are jointly considered. Considering the non-deterministic polynomial hard (NP-hard) property of this problem, we propose a brain storm optimization (BSO) approach which utilizes the penalty-based fitness function in individuals evaluation to meet the storage capacity constraint and the genetic algorithm (GA) in new individuals generation to meet the integer constraint, respectively. Moreover, to improve the initialization performance of the BSO approach, we propose to utilize Opposition-based Learning(OBL) to improve the initial solution space. To further reduce the computational complexity, we propose to implement the convergent operation in the objective space via individuals classification. We then analyze the global convergence and computational complexity of the proposed policy theoretically. Simulation results show that our proposed BSO-based hierarchical cooperative caching policy achieves remarkable performance in minimizing the content request delay.

Unbounded Serial-Batching Scheduling on Hierarchical Optimization

The paper considers a serial-batching scheduling problem on hierarchical optimization with two regular maximum costs, where hierarchical optimization means the primary objective function is minimized, and keeping the minimum value of the primary objective function, the secondary objective function is also minimized. In serial-batching machine environment, the machine processes the jobs in batch, and the jobs in the identical batch are processed by entering into the machine together and leaving the machine together. The time taken to process a batch amounts to the total processing time of the jobs in the batch. Moreover, a fixed switching time s is inserted when a machine begins to process a new batch. We only study the unbounded model, i.e., the batch capacity is unbounded. We give an algorithm that can solve the hierarchical optimization problem in $$O(n^4)$$ time, where n denotes the number of jobs.

Hierarchical minimization of two maximum costs on a bounded serial-batching machine

This paper studies a hierarchical optimization problem of scheduling n jobs on a serial-batching machine, in which two objective functions are maximum costs. By a hierarchical optimization problem, we mean the problem of optimizing the secondary criterion under the constraint that the primary criterion is optimized. A serial-batching machine is a machine that can handle up to b jobs in a batch and jobs in a batch start and complete respectively at the same time and the processing time of a batch is equal to the sum of the processing times of jobs in the batch. When a new batch starts, a constant setup time s occurs. We confine ourselves to the bounded model, where b < n. We present an O(n4)-time algorithm for this hierarchical optimization problem. For the special case where two objective functions are maximum lateness, we give an O(n3 log n)-time algorithm.

PIE

Editing of portrait images is a very popular and important research topic with a large variety of applications. For ease of use, control should be provided via a semantically meaningful parameterization that is akin to computer animation controls. The vast majority of existing techniques do not provide such intuitive and fine-grained control, or only enable coarse editing of a single isolated control parameter. Very recently, high-quality semantically controlled editing has been demonstrated, however only on synthetically created StyleGAN images. We present the first approach for embedding real portrait images in the latent space of StyleGAN, which allows for intuitive editing of the head pose, facial expression, and scene illumination in the image. Semantic editing in parameter space is achieved based on StyleRig, a pretrained neural network that maps the control space of a 3D morphable face model to the latent space of the GAN. We design a novel hierarchical non-linear optimization problem to obtain the embedding. An identity preservation energy term allows spatially coherent edits while maintaining facial integrity. Our approach runs at interactive frame rates and thus allows the user to explore the space of possible edits. We evaluate our approach on a wide set of portrait photos, compare it to the current state of the art, and validate the effectiveness of its components in an ablation study.

An explicit Tikhonov algorithm for nested variational inequalities

We consider nested variational inequalities consisting in a (upper-level) variational inequality whose feasible set is given by the solution set of another (lower-level) variational inequality. Purely hierarchical convex bilevel optimization problems and certain multi-follower games are particular instances of nested variational inequalities. We present an explicit and ready-to-implement Tikhonov-type solution method for such problems. We give conditions that guarantee the convergence of the proposed method. Moreover, inspired by recent works in the literature, we provide a convergence rate analysis. In particular, for the simple bilevel instance, we are able to obtain enhanced convergence results.

Optimizing construction schedules and material deliveries in city logistics: a case study from the building industry

We consider the problem of designing a logistics system to assure efficient urban construction processes for an innovative urban building area in the city of Vienna. We address the challenges of coordinating workers and the timely delivery and storage of material with the objective of optimizing resource-efficiency as well as reducing traffic related to construction tasks. The problem is formulated as a hierarchical optimization problem, incorporating tactical construction logistics planning as well as operational construction logistics planning. On the tactical level a time schedule of tasks for different construction phases and the corresponding material transports and storage decisions are optimized on a weekly basis, while on the operational level the daily optimization of material transports, modeled as an inventory routing problem, is addressed. A mixed-integer programming formulation of the problem on each planning level is provided and solved using CPLEX. The suggested approach is tested on realistic data from the city of Vienna. The results associated with different scenarios are analyzed to illustrate the value of the proposed approach for the design of construction logistics processes.

Modified Evolutionary Algorithm and Chaotic Search for Bilevel Programming Problems

Bi-level programming problem (BLPP) is an optimization problem consists of two interconnected hierarchical optimization problems. Solving BLPP is one of the hardest tasks facing the optimization community. This paper proposes a modified genetic algorithm and a chaotic search to solve BLPP. Firstly, the proposed algorithm solves the upper-level problem using a modified genetic algorithm. The genetic algorithm has modified with a new selection technique. The new selection technique helps the upper-level decision-maker to take an appropriate decision in anticipation of a lower level’s reaction. It distinguishes the proposed algorithm with a very small number of solving the lower-level problem, enhances the algorithm performance and fasts convergence to the solution. Secondly, a local search based on chaos theory has applied around the modified genetic algorithm solution. Chaotic local search enables the algorithm to escape from local solutions and increase convergence to the global solution. The proposed algorithm has evaluated on forty different test problems to show the proposed algorithm effectiveness. The results have analyzed to illustrate the new selection technique effect and the chaotic search effect on the algorithm performance. A comparison between the proposed algorithm results and other state-of-the-art algorithms results has introduced to show the proposed algorithm superiority.

An Aspect of Bilevel Fixed Charge Fractional Transportation Problem

Bilevel Programming Problem (BLPP) is a hierarchical optimization problem. Here, the constraint set of the upper level problem, called the leader, is ascertained by the lower level problem, called the follower. In this paper, a BLPP is considered where the leader’s problem is a fractional transportation problem and the follower’s problem is a fixed charge transportation problem. Hence, a bilevel fixed charge fractional transportation problem (BLFCFTP) is formulated. The problem is also explained through graphical representation. The problem comes from a food chain industry which is utilizing its used vegetable cooking oil for the production of biodiesel. The mathematical model of the problem is presented and is also explained through graphical representation. The problem pertains to a food chain industry wherein the used vegetable cooking oil is utilized for the production of biodiesel. Another example quotes Indore city where waste is converted into bio-CNG which is used to run public transport. The managerial importance of the work is that it will promote a sustainable and environment friendly practice. This will result in reduction of waste and check environmental pollution. An algorithm to solve BLFCFTP is developed. The examples explaining the algorithm are exhibited by a viable situation. These examples are subsequently deciphered in MATLAB.

Heat and electricity market coordination: A scalable complementarity approach

The large penetration of stochastic and non-dispatchable renewable energy sources increases the need for operational flexibility in power systems. Flexibility can be unlocked by aligning the existing interactions and synergies between heat and power systems. However, in the current sequential order of heat and electricity market clearings, the heat market is myopic to its interactions with the electricity market. This paper designs a heat market, aimed at achieving the optimal coordination of heat and power systems while respecting the current market regulations. The proposed electricity-aware heat market yields a soft coordination between heat and power systems by endogenously modeling their interactions in the day-ahead heat market clearing. The proposed market framework requires to solve a hierarchical optimization problem under uncertainty, which can be computationally challenging in large-scale energy systems with many scenarios. To resolve this potential scalability issue, this paper develops an augmented regularized Benders decomposition algorithm. The performance of the proposed market framework is compared against the fully integrated and sequential market frameworks using an ex-post out-of-sample simulation. This comparison reveals that there is a significant room for improvement in the cost-effective operation of the overall energy system. In particular, the proposed electricity-aware heat market framework provides a trade-off between the sequential and fully integrated market frameworks by significantly reducing the inefficiencies in both heat and electricity systems while respecting the current sequence of clearing heat and electricity markets.

Coordinated Charging Scheduling of Electric Vehicles: A Mixed-Variable Differential Evolution Approach

The increasing popularity of battery-limited electric vehicles puts forward an important issue of how to charge the vehicles effectively. This problem, commonly referred to as Electric Vehicle Charging Scheduling (EVCS), has been proven to be NP-hard. Most of the existing works formulate the EVCS problem simply as a constrained shortest path finding problem and treat it by discrete optimization. However, other variables such as the charging amount of energy and the charging option at a station need to be considered in practical use. This paper hence formulates the EVCS problem as a hierarchical mixed-variable optimization problem, considering the dependency among the station selection, the charging option at each station and the charging amount settings. To adapt to the new problem model, we specifically design a Mixed-Variable Differentiate Evolution (MVDE) as the scheduling algorithm for our proposed EVCS system. The MVDE contains several specific operators, including a charging station route construction, a hierarchical mixed-variable mutation operator and a constraint-aware evaluation operator. Experimental results validate the effectiveness of our proposed MVDE-based system on both synthetic and real-world transportation networks.

Optimal Placement and Sizing of Distributed Generation Using Wale Optimization Algorithm Considering Voltage Stability and Voltage Profile Improvement, Power Loss and Investment Cost Reducing

This paper suggests a method for optimal locating and sizing problem of distributed generations (DGs) as a nonlinear and multi-objective optimization problem. The offered method creates a trade-off among static voltage stability index, power losses, voltage deviations and investment cost as important indexes in DG location and size selection. The research is carried out using a steady-state voltage stability index for evaluation of system security. The suggested optimization problem has been carried out as a hierarchical optimization problem. In the first step, Wale Optimization Algorithm method has been applied to attain the coordinated plan of quantity and assignment of DG. Also, a MATLAB program has been developed to assess the voltage stability index, respectively, each coordinated pattern during WOA search. Suggested MATLAB program is based on a nonlinear optimization problem which it efforts to evaluate voltage stability. The proposed method has been implemented on IEEE 30 bus test system, and the results show the proper performance and acceptable operation.

Solving inverse optimal control problems via value functions to global optimality

In this paper, we show how a special class of inverse optimal control problems of elliptic partial differential equations can be solved globally. Using the optimal value function of the underlying parametric optimal control problem, we transfer the overall hierarchical optimization problem into a nonconvex single-level one. Unfortunately, standard regularity conditions like Robinson’s CQ are violated at all the feasible points of this surrogate problem. It is, however, shown that locally optimal solutions of the problem solve a Clarke-stationarity-type system. Moreover, we relax the feasible set of the surrogate problem iteratively by approximating the lower level optimal value function from above by piecewise affine functions. This allows us to compute globally optimal solutions of the original inverse optimal control problem. The global convergence of the resulting algorithm is shown theoretically and illustrated by means of a numerical example.

Strong Convergence of a New Iterative Algorithm for Split Monotone Variational Inclusion Problems

The main aim of this work is to introduce an implicit general iterative method for approximating a solution of a split variational inclusion problem with a hierarchical optimization problem constraint for a countable family of mappings, which are nonexpansive, in the setting of infinite dimensional Hilbert spaces. Convergence theorem of the sequences generated in our proposed implicit algorithm is obtained under some weak assumptions.

On Per-Phase Topology Control and Switching in Emerging Distribution Systems

This paper presents a new concept and approach for topology control and switching in distribution systems by extending the traditional circuit switching to laterals and single-phase loads. Voltage unbalance and other key performance indicators including voltage magnitudes, line loading, and energy losses are used to characterize and demonstrate the technical value of optimizing system topology on a per-phase basis in response to feeder conditions. The near-optimal per-phase topology control is defined as a series of hierarchical optimization problems. The proposed approach is applied to IEEE 13-bus and 123-bus test systems for demonstration, which included the impact of integrating electric vehicles (EVs) in the test circuit. It is concluded that the proposed approach can be effectively leveraged to improve voltage profiles with electric vehicles, the extent of which depends on the performance of the base case without EVs.

A combination method using evolutionary algorithms in initial orbit determination for too short arc

With the combination of two evolutionary algorithms EDA and DE, a new method of initial orbit determination for satellites based on ground-based too-short-arc is established. Compared with other algorithms, the proposed method focuses on the most densely populated region in the solution space rather than the individual with best fitness value. Both the global information and local information are well fused in the search of optimum. In the method (a,e,M) are treated as variables of the optimization, and the optimization procedure is carried out as a two-stage hierarchical optimization problem which has three variables for each stage. Kernel density estimation is applied to build the probability distribution model without any assumptions of the specified distribution, accompanied by handling semi-major axis and eccentricity as a pair of dependent variables in the construction of the probability for the correlation between them in the practice. Numerical experiments with real ground-based observations show that the proposed method is applicable to too-short-arc with even 3 s, and the result of bias in several kilometers can be achieved with 5″ error added to angular measurements.

Multi-Objective Cooperative Salvo Attack Against Group Target

This paper proposes a solution for the problem of cooperative salvo attack of multiple cruise missiles against targets in a group. Synchronization of the arrival time of missiles to hit their common target, minimizing the time consumption of attack and maximizing the expected damage to group targets are taken into consideration simultaneously. These operational objectives result in a hierarchical mixed-variable optimization problem which includes two types of subproblems, namely the multi-objective missile-target assignment (MOMTA) problem at the upper level and the time-optimal coordinated path planning (TOCPP) problems at the lower level. In order to solve the challenging problem, a recently proposed coordinated path planning method is employed to solve the TOCPP problems to achieve the soonest salvo attack against each target. With the aim of finding a more competent solver for MOMTA, three state-of-the-art multi-objective optimization methods (MOMs), namely NSGA-II, MOEA/D and DMOEA-eC, are adopted. Finally, a typical example is used to demonstrate the advantage of the proposed method. A simple rule-based method is also employed for comparison. Comparative results show that DMOEA-eC is the best choice among the three MOMs for solving the MOMTA problem. The combination of DMOEA-eC for MOMTA and the coordinated path planning method for TOCPP can generate obviously better salvo attack schemes than the rule-based method.