Approximate Optimal Solution Research Articles

DNA Genetic Algorithm in Digital Intelligent Design of Environmental Art

In recent years, digital technology has been widely used in various fields, and the concept of environmental art design has naturally changed, moving closer to digital technology. Genetic algorithm is a way to find approximate optimal solutions by simulating natural evolutionary processes and can solve various problems in the environmental art design process. Based on genetic algorithm, this article proposes a digital environmental art design based on DNA genetic theory. Unlike traditional design methods that generally only generate one design scheme, genetic algorithms can generate large-scale schemes and calculate the optimal scheme among many schemes. Through three interrelated experiments ranging from simple to complex, the results demonstrate the feasibility of the model proposed in this article. The construction elements and important links of environmental art design integrated with digital technology provide a good reference for the research on digital environmental art design based on DNA genetic theory.

A direct method for the simultaneous updating of finite element mass, damping and stiffness matrices

This paper is mainly concerned with a model updating problem for damped structural systems, which can be described as the following inverse quadratic eigenvalue problem (IQEP) and an optimal approximate problem (OAP). Problem IQEP: Given matrices and with , for , , and both Λ and X being closed under complex conjugation, find real symmetric matrices M, D and K such that . Problem OAP: Given real symmetric matrices and , find such that , where is the solution set of Problem IQEP and is a weighted Frobenius norm. The representation of the general solution to Problem IQEP and the explicit formula for the optimal approximate solution of Problem OAP are given by applying the singular value decomposition. A given numerical example shows that the updated model can be in good agreement with the modal test data.

Optimal Task Allocation Algorithm Based on Queueing Theory for Future Internet Application in Mobile Edge Computing Platform.

For 5G and future Internet, in this paper, we propose a task allocation method for future Internet application to reduce the total latency in a mobile edge computing (MEC) platform with three types of servers: a dedicated MEC server, a shared MEC server, and a cloud server. For this platform, we first calculate the delay between sending a task and receiving a response for the dedicated MEC server, shared MEC server, and cloud server by considering the processing time and transmission delay. Here, the transmission delay for the shared MEC server is derived using queueing theory. Then, we formulate an optimization problem for task allocation to minimize the total latency for all tasks. By solving this optimization problem, tasks can be allocated to the MEC servers and cloud server appropriately. In addition, we propose a heuristic algorithm to obtain the approximate optimal solution in a shorter time. This heuristic algorithm consists of four algorithms: a main algorithm and three additional algorithms. In this algorithm, tasks are divided into two groups, and task allocation is executed for each group. We compare the performance of our proposed heuristic algorithm with the solution obtained by three other methods and investigate the effectiveness of our algorithm. Numerical examples are used to demonstrate the effectiveness of our proposed heuristic algorithm. From some results, we observe that our proposed heuristic algorithm can perform task allocation in a short time and can effectively reduce the total latency in a short time. We conclude that our proposed heuristic algorithm is effective for task allocation in a MEC platform with multiple types of MEC servers.

A new vocation queuing model to optimize truck appointments and yard handling-equipment use in dual transactions systems of container terminals

In a dual transaction at a marine terminal, an external truck drops off one container and picks up another on a single trip. To ensure a successful dual transaction operation and smooth external truck arrivals, a bi-objective mixed integer programming model is developed that optimizes the allocation of appointment quotas simultaneously with the deployment of (yard) cargo handling equipment. Our model addresses the challenges posed by the different types of truck movement in the terminal, i.e., delivery, pickup, and dual transaction. These require different handling equipment, various deadlines, and multiple priorities. To estimate the queuing length of external trucks in single or dual transactions (as well as that of internal trucks), a novel three-level vocation queuing model is set up. For the bi-objectives optimization, we propose a revised non-dominated genetic algorithm to obtain the approximate optimal solution. Experimental results prove the efficiency and effectiveness of the method. It shows that the newly built vocation queuing model can estimate the prioritized queuing process more effectively in three respects: a) the 3-level queuing; b) discrete truck arrivals in the queuing system; c) non-interruption of servers. Our quota optimization design improves the model’s applicability to real cases, especially in the case of dual transactions. It is demonstrated that the method proposed in the paper could help terminal operators allocate quotas and simultaneously match the capacity of yard handling, thus improving truck services and terminal profitability.

Design and Optimization of the Pedestal Structure for the Sealed Cabin Used in Capsized Vessels Rescuing

The bottom hole opening method is generally used to rescue the people trapped inside the capsized vessels. In this paper, a new sealed cabin with flexible cabin shell and rigid pedestal was proposed to rescue people in distress through the inner hole cut on the bottom hull. The parameters of the cabin pedestal and the sealed pedestal are optimized respectively to reduce the weight of the whole cabin. According to response surface methodology to analysis the relationship between the tress and the structural parameters. The maximum equivalent stress and maximum deformation are the constraint conditions and the total mass of the structure is the objective function, and the multi-island genetic algorithm is used to optimize the model, and the approximate optimal solution was finally obtained. The results show that the strength of cabin pedestal and sealing pedestal meet the application requirements.

A multi-objective evolutionary algorithm based on niche selection in solving irregular Pareto fronts

The key characteristic of multi-objective evolutionary algorithm is that it can find a good approximate multi-objective optimal solution set when solving multi-objective optimization problems(MOPs). However, most multi-objective evolutionary algorithms perform well on regular multi-objective optimization problems, but their performance on irregular fronts deteriorates. In order to remedy this issue, this paper studies the existing algorithms and proposes a multi-objective evolutionary based on niche selection to deal with irregular Pareto fronts. In this paper, the crowding degree is calculated by the niche method in the process of selecting parents when the non-dominated solutions converge to the first front, which improves the the quality of offspring solutions and which is beneficial to local search. In addition, niche selection is adopted into the process of environmental selection through considering the number and the location of the individuals in its niche radius, which improve the diversity of population. Finally, experimental results on 23 benchmark problems including MaF and IMOP show that the proposed algorithm exhibits better performance than the compared MOEAs.

BatchUp: Achieve fast TCAM update with batch processing optimization in SDN

The parallel access mechanism supported by TCAM has made it popular with commercial switches. However, due to the ordered arrangement of rules, TCAM’s update speed cannot keep up with policy update requests, especially for software-defined networks, which expect to achieve fine-grained control over the network. Meanwhile, the legacy single-rule update solutions cause redundant rule moves due to weak global view. In this paper, we present a new two-stage batch processing solution BatchUp to alleviate the high time cost of the rule update process. In stage 1, we propose the costless rule insertion algorithm CRIA. CRIA models the rules to be inserted with the available locations in TCAM as a bipartite graph. By solving for maximum matching, CRIA obtains an upper bound on the number of rules that can be inserted without TCAM movement. However, the high utilization of TCAM makes it unrealizable to find available locations for all rules to be inserted directly. Therefore, in stage 2, we model the remaining rules insertion as an optimization problem for solving the minimum movement cost and prove that it has NP-hard complexity. A heuristic updating algorithm HRIA based on simulated annealing and greedy algorithm is proposed to search for approximate optimal solution. The evaluation results present that BatchUp has advantages over existing state-of-the-art solutions in terms of the number of TCAM moves and overall time cost, and has applicability and robustness in different scenarios.

Toward Response Time Minimization Considering Energy Consumption in Caching-Assisted Vehicular Edge Computing

The advent of vehicular edge computing (VEC) has generated enormous attention in recent years. It pushes the computational resources in close proximity to the data sources and thus, caters for the explosive growth of vehicular applications. Owing to the high mobility of vehicles, these applications are of latency-sensitive requirements in most cases. Accordingly, such requirements still pose a great challenge to the computing capabilities of VEC, when these applications are outsourced and executed in VEC. Against this backdrop, we propose a new mathematical model, which, respectively, generalizes the computation and communication models, and applies application-oriented caching into VEC in this article. Based on this model, a new strategy is further proposed to optimize the average response time of applications over an infinite time-slotted horizon for VEC. A long-term energy consumption constraint is imposed to guarantee the stability of the VEC system, and the Lyapunov optimization technology is adopted to tackle this constraint issue. Two greedy heuristics are put forward to help find the approximate optimal solution in the drift-plus-penalty-based algorithm. Extensive experiments have been conducted to evaluate the response time and energy consumption in the caching-assisted VEC. The simulation results have shown that the proposed strategy can dramatically optimize the average response time while satisfying the long-term energy consumption constraint.

Joint Optimization in Intelligent Reflecting Surface-Aided UAV Communication for Multiaccess Edge Computing

Intelligent reflecting surface (IRS) is a key enabling technology for b5G and 6G networks, which can provide a reconfigurable electromagnetic environment while reducing energy consumption. In this article, the communication link between user equipment (UE) and the base station (BS) is severely blocked, so we deployed IRS on the Unmanned Aerial Vehicle (UAV) to assist UE for offloading the computing task to the multiaccess edge computing (MEC) server on the base station, which provides mobile users with low-latency edge computing services. By jointly optimizing active beamforming of UE transmitter, passive beamforming of the IRS, UAV hovering position, and computing task scheduling, the response time of user tasks is minimized. In order to solve this complex nonconvex problem, we propose an alternating optimization (AO) algorithm combined with the genetic algorithm to decouple the problem, alternate optimization, until the convergence condition is met, to find the approximate optimal solution of the problem. Numerical results show that with the assistance of IRS, MIMO channels can significantly improve the performance of edge computing and meet the needs of users for high speed and low latency.

Advanced Phasmatodea Population Evolution Algorithm for Capacitated Vehicle Routing Problem

Capacitated Vehicle Routing Problem (CVRP) is difficult to solve by the traditional precise methods in the transportation area. The metaheuristic algorithm is often used to solve CVRP and can obtain approximate optimal solutions. Phasmatodea population evolution algorithm (PPE) is a recently proposed metaheuristic algorithm. Given the shortcomings of PPE, such as its low convergence precision, its nature to fall into local optima easily, and it being time-consuming, we propose an advanced Phasmatodea population evolution algorithm (APPE). In APPE, we delete competition, delete conditional acceptance and correspondingevolutionary trend update, and add jump mechanism, history-based searching, and population closing moving. Deleting competition and conditional acceptance and correspondingevolutionary trend update can shorten PPE running time. Adding a jump mechanism makes PPE more likely to jump out of the local optimum. Adding history-based searching and population closing moving improves PPE’s convergence accuracy. Then, we test APPE by CEC2013. We compare the proposed APPE with differential evolution (DE), sparrow search algorithm (SSA), Harris Hawk optimization (HHO), and PPE. Experiment results show that APPE has higher convergence accuracy and shorter running time. Finally, APPE also is applied to solve CVRP. From the test results of the instances, APPE is more suitable to solve CVRP.

Efficient Orchestration of Virtualization Resource in RAN Based on Chemical Reaction Optimization and Q-Learning

Virtualized network function (VNF) orchestration dynamically deploys network slices, which provides an effective means of customized service provision. To achieve a realistic and comprehensive perspective of the decision process for customized service provision, we propose a virtualized resource orchestration strategy in radio access network (RAN) of Internet of things (Iots) based on chemical reaction optimization (CRO). Specifically, we apply particle swarm optimization (PSO), a Gaussian process, random walk model, and Q-learning to enhance the CRO algorithm to quickly obtain the approximate optimal solution for the proposed CRO-based resource orchestration strategy (CROROS). Simulation results show that, compared with existing access methods, CROROS can reduce the service rejection rate of a virtualized radio access network and improve the utilization rate of network system resources. Compared with other heuristic algorithms (e.g., PSO, genetic algorithm (GA), and CRO), CROROS can accelerate the global approximate optimal solution and improve the approximate fitness of the approximate optimal solution within a specified time.

Optimization for Feeder Bus Route Model Design with Station Transfer

To fully take the advantages of conventional bus and subway, and to maximize the overall feeder efficiency of the public transport system, the topic of feeder bus route optimization is studied in this paper. Considering the origin destination demand of passenger flow between subway stations and bus stations and transfer characteristics, the objective function is established with the minimum sum of bus operation cost and passenger travel cost. Taking into account the integrity of the feeder bus route, the rationality of the route, the route capacity and the station transfer factors, the constraints of the optimization model are constructed. Based on the idea of the genetic algorithm, the solution algorithm of the optimization model is developed. The genetic algorithm and enumeration algorithm are used to solve the optimization of the feeder bus route in this case, and the accuracy and efficiency of the solution are analyzed. The influence of the number of feeder bus routes on the system in the case network is compared and discussed. We compare and analyze the differences between the original bus network and the feeder bus network in terms of bus operation cost, passenger flow demand and total passenger travel cost. The research shows that the model and algorithm can find the approximate optimal solution of the feeder bus network scheme related to the subway through fewer iterations. The number of routes in the model has little impact on the whole feeder system, and the optimization scheme using five routes is effective and reasonable in this paper. Compared with the existing bus network, the optimization scheme has obvious advantages in improving the passenger-carrying rate, reducing the per capita travel cost and improving the overall operation efficiency of the system.

Solving the Max-3-Cut Problem with Coherent Networks

Many computational problems are intractable through classical computing and, as Moore's law is drawing to a halt, demand for finding alternative methods in tackling these problems is growing. Here, we realize a liquid light machine for the NP-hard max-3-cut problem based on a network of synchronized exciton-polariton condensates. We overcome the binary limitation of the decision variables in Ising machines using the continuous-phase degrees of freedom of a coherent network of polariton condensates. The condensate network dynamical transients provide optically-fast annealing of the XY Hamiltonian. We apply the Goemans and Williamson random hyperplane technique, discretizing the XY ground state spin configuration to serve as ternary decision variables for an approximate optimal solution to the max-3-cut problem. Applications of the presented coherent network are investigated in image-segmentation tasks and in circuit design.

Relative Continuity, Proximal Boundedness and Best Proximity Point Theorems

This articles discusses some properties of relatively continuous mappings, a natural generalization of continuous mappings. Also, we introduce the notion of proximal boundedness and dilate upon a relationship among proximal boundedness, proximal completeness and proximal compactness. Finally, we utilize such results to elicit an extension of a Schauder’s fixed point theorem, which states that every continuous self-mapping on a non-void compact convex subset of a normed linear space has a fixed point, to the case of non-self relatively continuous mappings. In fact, such an extension is proved in the form of a best proximity point theorem for relatively continuous mappings in the framework of a proximally compact space that has semi-sharp proximinality, thereby ascertaining the existence of an optimal approximate solution to some equations. Such an optimal approximate solution is known as a best proximity point and elicited as a result of approximation with the minimization of the error due to approximation. Further, an application of such a result is explored to elicit a common best proximity point theorem for a family of commuting affine mappings. Also, we furnish another application of our main result to find best proximity solution to an ordinary differential equation.

Data-driven mixed-Integer linear programming-based optimisation for efficient failure detection in large-scale distributed systems

Failure detectors (FDs) are fundamental building blocks for distributed systems. An FD detects whether a process has crashed or not based on the reception of heartbeats’ messages sent by this process over a communication channel. A key challenge of FDs is to tune their parameters to achieve optimal performance which satisfies the desired system requirements. This is challenging due to the complexities of large-scale networks. Existing FDs ignore such optimisation and adopt ad-hoc parameters. In this paper, we propose a new Mixed Integer Linear Programming (MILP) optimisation-based FD algorithm. We obtain the MILP formulation via piecewise linearisation relaxations. The MILP involves obtaining optimal FD parameters that meet the optimal trade-off between its performance metrics requirements, network conditions and system parameters. The MILP maximises our FD’s accuracy under bounded failure detection time while considering network and system conditions as constraints. The MILP’s solution represents optimised FD parameters that maximise FD’s expected performance. To adapt to real-time network changes, our proposed MILP-based FD fits the probability distribution of heartbeats’ inter-arrivals. To address our FD scalability challenge in large-scale systems where the MILP model needs to compute approximate optimal solutions quickly, we also propose a heuristic algorithm. To test our proposed approach, we adopt Amazon Cloud as a realistic testing environment and develop a simulator for robustness tests. Our results show consistent improvement of overall FD performance and scalability. To the best of our knowledge, this is the first attempt to combine the MILP-based optimisation modelling with FD to achieve performance guarantees.

Multi-Connection Based Scalable Video Streaming in UDNs: A Multi-Agent Multi-Armed Bandit Approach

Scalable video coding (SVC) has received much attention for video transmission over wireless due to its flexibility. However, most previous work only considered SVC video streaming from a single base station (BS). At present, the densification of BSs enables a user equipment (UE) to connect to multiple BSs in ultra-dense networks (UDNs). In this paper, we consider the problem of SVC video streaming in a UDN, which allows different layers of a video block to be downloaded from different BSs. An optimization problem is formulated aiming to maximize the quality of experience (QoE) of users by selecting the optimal connection strategy and optimal number of video layers. Considering the complexity, to efficiently solve the problem in a distributed manner, the problem of choosing connection strategy is formulated as a multi-agent multi-armed bandit (MA-MAB) problem with only few information exchange. Each user can adapt its connection strategy in a distributed self-learning system. To obtain the optimal arm for the MA-MAB problem, we propose a multi-user arm decision algorithm. To avoid large computation and handover costs, we adopt the same connection strategy for the entire video sequence. Then for each video block, with the given connection strategy, the number of video layers is adjusted adaptively according to dynamic network conditions. Finally, based on the above designs, we provide the SVC-based video downloading scheme to obtain an approximate optimal solution to the original optimization problem. Extensive simulations and comparisons show the feasibility and superiority of the proposed scheme.

Jointly optimized demand-oriented train timetable and passenger flow control strategy for a congested subway line under a short-turning operation pattern

With excessive passenger demand and uneven distribution of passenger flow, long-distance subway lines face oversaturated conditions during peak hours, leading to potential safety problems for subway systems. To improve travel efficiency and reduce safety problems, this study proposes a method of constructing a passenger flow control jointly optimized train timetable for an oversaturated subway line under a short-turning operation pattern. Considering the time-dependent and dynamic characteristics of passenger demand, an integer nonlinear programming model is formulated to minimize the total passenger waiting time. To solve the problem, the tabu search algorithm and the IBM ILOG CPLEX solver are combined to seek the approximate optimal solution. Finally, a series of numerical experiments are conducted on the Beijing Fangshan line to demonstrate the effectiveness of the proposed model and approach, which shows that the method of jointly optimizing the train timetable and passenger flow control can drastically decrease the total passenger waiting time and reduce congestion.

A novel convex relaxation-strategy-based algorithm for solving linear multiplicative problems

Linear multiplicative programming (LMP) problems have many applications, although their solving can be difficult. To solve LMPs, we propose a convex approximation approach with a standard partition in intervals. First, a novel convex relaxation strategy is designed, which is used to obtain a convex relaxation problem, and provides a lower bound for LMPs. Then, through solving a sequence of convex relaxation programming problems, we can obtain an approximate optimal solution of LMPs. The main calculation of the algorithm focuses on solving these convex programming problems, which can be completed by a convex optimization software. Furthermore, the convergence and the complexity of the algorithm are discussed theoretically. Finally, numerical experiments show the effectiveness of the designed algorithm in terms of running time and the number of iterations.

Optimal guidance and estimation of a 2D diffusion–advection process by a team of mobile sensors

This paper describes an optimization framework to design guidance for a possibly heterogeneous team of multiple mobile sensors to estimate a spatiotemporal process modeled by a 2D diffusion–advection process. Owing to the abstract linear system representation of the process, we apply the Kalman–Bucy filter for estimation, where the sensors provide linear outputs. We propose an optimization problem that minimizes the sum of the trace of the covariance operator of the Kalman–Bucy filter and a generic mobility cost of the mobile sensors, subject to the sensors’ motion modeled by linear dynamics. We establish the existence of a solution to this problem. Moreover, we prove convergence to the exact optimal solution of the approximate optimal solution. That is, when evaluating these two solutions using the original cost function, the difference becomes arbitrarily small as the approximation gets finer. To compute the approximate solution, we use Pontryagin’s minimum principle after approximating the infinite-dimensional terms originating from the diffusion–advection process. The approximate solution is applied in simulation to analyze how a single mobile sensor’s performance depends on two important parameters: sensor noise variance and mobility penalty. We also illustrate the application of the framework to multiple sensors, in particular the performance of a heterogeneous team of sensors.

Green closed-loop supply chain optimization strategy considering CER and incentive-compatibility theory under uncertainty.

Under the uncertain market demand and quality level, a total profit model of green closed-loop supply chain system (GCL-SCS) considering corporate environmental responsibility (CER) and government differential weight subsidy (GDWS) is constructed. Based on incentive-compatibility theory, the optimal subsidy allocation policy and green investment level were explored. Fuzzy chance-constrained programming (FCCP) is used to clarify the uncertainty factors of this model; while genetic algorithm (GA) and CPLEX are used to find and compare a calculating example's approximate optimal solution about this model. The main calculating results indicate that: (1) Enterprises can make optimal recycling, production and sales strategies according to different potential demand; (2) Without government subsidy, enterprises' higher green investment level will reduce their average gross profit, increase the quality level of recycled products and decrease the recycling rate, hence reduce their environmental protection willingness; (3) Based on incentive-compatibility theory, when government subsidy weight is set as 0.34~0.41 for consumers, enterprises' higher green investment level will enhance their average gross profit, reduce the quality level of recycled products and increase the recycling rate, which will improve their environmental protection willingness; (4) Under uncertain environment, the combination of reasonable government subsidy policy and enterprises green investment can make up for the defect of enterprises green investment alone, maximize utilities of government and enterprises, and optimize the green closed loop supply chain.