A review of unmanned vehicle distribution optimization models and algorithms

With the development of globalization and artificial intelligence,as well as the outbreak of COVID-19,unmanned vehicles have played an important role in cargo distribution.In order to better analyze the research directions of unmanned vehicle distribution,this paper summarizes the models and algorithms of unmanned vehicle distribution optimization.The research results show that most of the studies have established the goal of optimizing the total costs or travel time.Many researchers have begun to study multi-objective optimization problems,but there are certain limitations,so some studies convert these problems into single-objective optimization for solving,such as converting time and energy consumption into cost,waiting time into distance,and time delay into penalty cost.With the development of unmanned vehicle distribution technology,in future research,a multi-objective model with the lowest cost,the shortest distance and the best security should be established and solved.Most studies have proposed heuristic algorithms for solving the unmanned vehicle distribution problem,and improved optimization solutions have been obtained.In order to ensure the diversity of solution methods,and give consideration to solution time and solution quality,hybrid methods with other algorithms will be a future research direction,for example,the combination of heuristic algorithm and exact algorithm.With the gradual deepening of research,integrated distribution of multiple types of unmanned equipment will become the focus of future research.

Performance analysis and material distribution optimization for sound barriers using a semianalytical meshless method

With the increase in car ownership,traffic noise pollution has increased considerably and is one of the most severe types of noise pollution that affects living standards.Noise reduction by sound barriers is a common protective measure used in this country and abroad.The acoustic performance of a sound barrier is highly dependent on its shape and material.In this paper,a semianalytical meshless Burton-Miller‐type singular boundary method is proposed to analyze the acoustic performance of various shapes of sound barriers,and the distribution of sound‐absorbing materials on the surface of sound barriers is optimized by combining a solid isotropic material with a penalization method.The acoustic effect of the sound‐absorbing material is simplified as the acoustical impedance boundary condition.The objective of optimization is to minimize the sound pressure in a given reference plane.The volume of the sound‐absorbing material is used as a constraint.The density of the nodes covered with the sound‐absorbing material is used as the design variable.The method of moving asymptotes was used to update the design variables.This model completely avoids the mesh discretization process in the finite element method and requires only boundary nodes.In addition,the approach also does not require the singular integral calculation in the boundary element method.The method is illustrated and validated using numerical examples to demonstrate its accuracy and efficiency.

Distributionally robust optimization based chance-constrained energy management for hybrid energy powered cellular networks

Energy harvesting has been recognized as a promising technique with which to effectively reduce carbon emis-sions and electricity expenses of base stations.However,renewable energy is inherently stochastic and inter-mittent,imposing formidable challenges on reliably satisfying users'time-varying wireless traffic demands.In addition,the probability distribution of the renewable energy or users’wireless traffic demand is not always fully known in practice.In this paper,we minimize the total energy cost of a hybrid-energy-powered cellular network by jointly optimizing the energy sharing among base stations,the battery charging and discharging rates,and the energy purchased from the grid under the constraint of a limited battery size at each base station.In solving the formulated non-convex chance-constrained stochastic optimization problem,a new ambiguity set is built to characterize the uncertainties in the renewable energy and wireless traffic demands according to interval sets of the mean and covariance.Using this ambiguity set,the original optimization problem is transformed into a more tractable second-order cone programming problem by exploiting the distributionally robust optimization approach.Furthermore,a low-complexity distributionally robust chance-constrained energy management algo-rithm,which requires only interval sets of the mean and covariance of stochastic parameters,is proposed.The results of extensive simulation are presented to demonstrate that the proposed algorithm outperforms existing methods in terms of the computational complexity,energy cost,and reliability.

Distributed Stochastic Optimization with Compression for Non-Strongly Convex Objectives

We are investigating the distributed optimization problem,where a network of nodes works together to minimize a global objective that is a finite sum of their stored local functions.Since nodes exchange optimization parameters through the wireless network,large-scale training models can create communication bottlenecks,resulting in slower training times.To address this issue,CHOCO-SGD was proposed,which allows compressing information with arbitrary precision without reducing the convergence rate for strongly convex objective functions.Nevertheless,most convex functions are not strongly convex(such as logistic regression or Lasso),which raises the question of whether this algorithm can be applied to non-strongly convex functions.In this paper,we provide the first theoretical analysis of the convergence rate of CHOCO-SGD on non-strongly convex objectives.We derive a sufficient condition,which limits the fidelity of compression,to guarantee convergence.Moreover,our analysis demonstrates that within the fidelity threshold,this algorithm can significantly reduce transmission burden while maintaining the same convergence rate order as its no-compression equivalent.Numerical experiments further validate the theoretical findings by demonstrating that CHOCO-SGD improves communication efficiency and keeps the same convergence rate order simultaneously.And experiments also show that the algorithm fails to converge with low compression fidelity and in time-varying topologies.Overall,our study offers valuable insights into the potential applicability of CHOCO-SGD for non-strongly convex objectives.Additionally,we provide practical guidelines for researchers seeking to utilize this algorithm in real-world scenarios.

A Distributionally Robust Optimization Method for Passenger Flow Control Strategy and Train Scheduling on an Urban Rail Transit Line

Regular coronavirus disease 2019(COVID-19)epidemic prevention and control have raised new require-ments that necessitate operation-strategy innovation in urban rail transit.To alleviate increasingly seri-ous congestion and further reduce the risk of cross-infection,a novel two-stage distributionally robust optimization(DRO)model is explicitly constructed,in which the probability distribution of stochastic scenarios is only partially known in advance.In the proposed model,the mean-conditional value-at-risk(CVaR)criterion is employed to obtain a tradeoff between the expected number of waiting passen-gers and the risk of congestion on an urban rail transit line.The relationship between the proposed DRO model and the traditional two-stage stochastic programming(SP)model is also depicted.Furthermore,to overcome the obstacle of model solvability resulting from imprecise probability distributions,a discrepancy-based ambiguity set is used to transform the robust counterpart into its computationally tractable form.A hybrid algorithm that combines a local search algorithm with a mixed-integer linear programming(MILP)solver is developed to improve the computational efficiency of large-scale instances.Finally,a series of numerical examples with real-world operation data are executed to validate the pro-posed approaches.

Distributed Momentum-Based Frank-Wolfe Algorithm for Stochastic Optimization

This paper considers distributed stochastic optimization,in which a number of agents cooperate to optimize a global objective function through local computations and information exchanges with neighbors over a network.Stochastic optimization problems are usually tackled by variants of projected stochastic gradient descent.However,projecting a point onto a feasible set is often expensive.The Frank-Wolfe(FW)method has well-documented merits in handling convex constraints,but existing stochastic FW algorithms are basically developed for centralized settings.In this context,the present work puts forth a distributed stochastic Frank-Wolfe solver,by judiciously combining Nesterov's momentum and gradient tracking techniques for stochastic convex and nonconvex optimization over networks.It is shown that the convergence rate of the proposed algorithm is O(k^(-1/2))for convex optimization,and O(1/log_(2)(k))for nonconvex optimization.The efficacy of the algorithm is demonstrated by numerical simulations against a number of competing alternatives.

Fully asynchronous distributed optimization with linear convergence over directed networks

We study distributed optimization problems over a directed network,where nodes aim to minimize the sum of local objective functions via directed communications with neighbors.Many algorithms are designed to solve it for synchronized or randomly activated implementation,which may create deadlocks in practice.In sharp contrast,we propose a fully asynchronous push-pull gradient(APPG) algorithm,where each node updates without waiting for any other node by using possibly delayed information from neighbors.Then,we construct two novel augmented networks to analyze asynchrony and delays,and quantify its convergence rate from the worst-case point of view.Particularly,all nodes of APPG converge to the same optimal solution at a linear rate of O(λ^(k)) if local functions have Lipschitz-continuous gradients and their sum satisfies the Polyak-?ojasiewicz condition(convexity is not required),where λ ∈(0,1) is explicitly given and the virtual counter k increases by one when any node updates.Finally,the advantage of APPG over the synchronous counterpart and its linear speedup efficiency are numerically validated via a logistic regression problem.

Distributionally Robust Newsvendor Model for Fresh Products under Cap-and-Offset Regulation

The cap-and-offset regulation is a practical scheme to lessen carbon emissions.The retailer selling fresh products can adopt sustainable technologies to lessen greenhouse gas emissions.We aim to analyze the optimal joint strategies on order quantity and sustainable technology investment when the retailer faces stochastic market demand and can only acquire the mean and variance of distribution information.We construct a distributionally robust optimization model and use the Karush-Kuhn-Tucker(KKT)conditions to solve the analytic formula of optimal solutions.By comparing the models with and without investing in sustainable technologies,we examine the effect of sustainable technologies on the operational management decisions of the retailer.Finally,some computational examples are applied to analyze the impact of critical factors on operational strategies,and some managerial insights are given based on the analysis results.

Risk Constrained Self-scheduling of AA-CAES Facilities in Electricity and Heat Markets:A Distributionally Robust Optimization Approach

Advanced adiabatic compressed air energy storage(AA-CAES)has the advantages of large capacity,long service time,combined heat and power generation(CHP),and does not consume fossil fuels,making it a promising storage technology in a low-carbon society.An appropriate self-scheduling model can guarantee AA-CAES’s profit and attract investments.However,very few studies refer to the cogeneration ability of AA-CAES,which enables the possibility to trade in the electricity and heat markets at the same time.In this paper,we propose a multimarket self-scheduling model to make full use of heat produced in compressors.The volatile market price is modeled by a set of inexact distributions based on historical data through-divergence.Then,the self-scheduling model is cast as a robust risk constrained program by introducing Stackelberg game theory,and equivalently reformulated as a mixed-integer linear program(MILP).The numerical simulation results validate the proposed method and demonstrate that participating in multienergy markets increases overall profits.The impact of uncertainty parameters is also discussed in the sensibility analysis.

Medical Feature Selection Approach Based on Generalized Normal Distribution Algorithm

This paper proposes a new pre-processing technique to separate the most effective features from those that might deteriorate the performance of the machine learning classifiers in terms of computational costs and classification accuracy because of their irrelevance,redundancy,or less information;this pre-processing process is often known as feature selection.This technique is based on adopting a new optimization algorithm known as generalized normal distribution optimization(GNDO)supported by the conversion of the normal distribution to a binary one using the arctangent transfer function to convert the continuous values into binary values.Further,a novel restarting strategy(RS)is proposed to preserve the diversity among the solutions within the population by identifying the solutions that exceed a specific distance from the best-so-far and replace them with the others created using an effective updating scheme.This strategy is integrated with GNDO to propose another binary variant having a high ability to preserve the diversity of the solutions for avoiding becoming stuck in local minima and accelerating convergence,namely improved GNDO(IGNDO).The proposed GNDO and IGNDO algorithms are extensively compared with seven state-of-the-art algorithms to verify their performance on thirteen medical instances taken from the UCI repository.IGNDO is shown to be superior in terms of fitness value and classification accuracy and competitive with the others in terms of the selected features.Since the principal goal in solving the FS problem is to find the appropriate subset of features that maximize classification accuracy,IGNDO is considered the best.

Fully Distributed Learning for Deep Random Vector Functional-Link Networks

In the contemporary era, the proliferation of information technology has led to an unprecedented surge in data generation, with this data being dispersed across a multitude of mobile devices. Facing these situations and the training of deep learning model that needs great computing power support, the distributed algorithm that can carry out multi-party joint modeling has attracted everyone’s attention. The distributed training mode relieves the huge pressure of centralized model on computer computing power and communication. However, most distributed algorithms currently work in a master-slave mode, often including a central server for coordination, which to some extent will cause communication pressure, data leakage, privacy violations and other issues. To solve these problems, a decentralized fully distributed algorithm based on deep random weight neural network is proposed. The algorithm decomposes the original objective function into several sub-problems under consistency constraints, combines the decentralized average consensus (DAC) and alternating direction method of multipliers (ADMM), and achieves the goal of joint modeling and training through local calculation and communication of each node. Finally, we compare the proposed decentralized algorithm with several centralized deep neural networks with random weights, and experimental results demonstrate the effectiveness of the proposed algorithm.

Cooperative and Competitive Multi-Agent Systems:From Optimization to Games

Multi-agent systems can solve scientific issues related to complex systems that are difficult or impossible for a single agent to solve through mutual collaboration and cooperation optimization.In a multi-agent system,agents with a certain degree of autonomy generate complex interactions due to the correlation and coordination,which is manifested as cooperative/competitive behavior.This survey focuses on multi-agent cooperative optimization and cooperative/non-cooperative games.Starting from cooperative optimization,the studies on distributed optimization and federated optimization are summarized.The survey mainly focuses on distributed online optimization and its application in privacy protection,and overviews federated optimization from the perspective of privacy protection me-chanisms.Then,cooperative games and non-cooperative games are introduced to expand the cooperative optimization problems from two aspects of minimizing global costs and minimizing individual costs,respectively.Multi-agent cooperative and non-cooperative behaviors are modeled by games from both static and dynamic aspects,according to whether each player can make decisions based on the information of other players.Finally,future directions for cooperative optimization,cooperative/non-cooperative games,and their applications are discussed.

A Primal-Dual SGD Algorithm for Distributed Nonconvex Optimization

The distributed nonconvex optimization problem of minimizing a global cost function formed by a sum of n local cost functions by using local information exchange is considered.This problem is an important component of many machine learning techniques with data parallelism,such as deep learning and federated learning.We propose a distributed primal-dual stochastic gradient descent(SGD)algorithm,suitable for arbitrarily connected communication networks and any smooth(possibly nonconvex)cost functions.We show that the proposed algorithm achieves the linear speedup convergence rate O(1/(√nT))for general nonconvex cost functions and the linear speedup convergence rate O(1/(nT)) when the global cost function satisfies the Polyak-Lojasiewicz(P-L)condition,where T is the total number of iterations.We also show that the output of the proposed algorithm with constant parameters linearly converges to a neighborhood of a global optimum.We demonstrate through numerical experiments the efficiency of our algorithm in comparison with the baseline centralized SGD and recently proposed distributed SGD algorithms.

Distributed Subgradient Algorithm for Multi-Agent Optimization With Dynamic Stepsize

In this paper,we consider distributed convex optimization problems on multi-agent networks.We develop and analyze the distributed gradient method which allows each agent to compute its dynamic stepsize by utilizing the time-varying estimate of the local function value at the global optimal solution.Our approach can be applied to both synchronous and asynchronous communication protocols.Specifically,we propose the distributed subgradient with uncoordinated dynamic stepsizes(DS-UD)algorithm for synchronous protocol and the AsynDGD algorithm for asynchronous protocol.Theoretical analysis shows that the proposed algorithms guarantee that all agents reach a consensus on the solution to the multi-agent optimization problem.Moreover,the proposed approach with dynamic stepsizes eliminates the requirement of diminishing stepsize in existing works.Numerical examples of distributed estimation in sensor networks are provided to illustrate the effectiveness of the proposed approach.

Distributed optimization of electricity-Gas-Heat integrated energy system with multi-agent deep reinforcement learning

The coordinated optimization problem of the electricity-gas-heat integrated energy system(IES)has the characteristics of strong coupling,non-convexity,and nonlinearity.The centralized optimization method has a high cost of communication and complex modeling.Meanwhile,the traditional numerical iterative solution cannot deal with uncertainty and solution efficiency,which is difficult to apply online.For the coordinated optimization problem of the electricity-gas-heat IES in this study,we constructed a model for the distributed IES with a dynamic distribution factor and transformed the centralized optimization problem into a distributed optimization problem in the multi-agent reinforcement learning environment using multi-agent deep deterministic policy gradient.Introducing the dynamic distribution factor allows the system to consider the impact of changes in real-time supply and demand on system optimization,dynamically coordinating different energy sources for complementary utilization and effectively improving the system economy.Compared with centralized optimization,the distributed model with multiple decision centers can achieve similar results while easing the pressure on system communication.The proposed method considers the dual uncertainty of renewable energy and load in the training.Compared with the traditional iterative solution method,it can better cope with uncertainty and realize real-time decision making of the system,which is conducive to the online application.Finally,we verify the effectiveness of the proposed method using an example of an IES coupled with three energy hub agents.

Optimization of Composite Wind Turbine Blade Based on Modal Sensitivity

This study develops a method for the full-size structural design of blade,involving the optimal layer thickness configuration of the blade to maximize its bending stiffness using a genetic algorithm.Numerical differentiation is employed to solve the sensitivity of blade modal frequency to the layer thickness of each part of blade.The natural frequencies of first-order flapwise and edgewise modes are selected as the optimal objectives.Based on the modal sensitivity analysis of all design variables,the effect of discretized layer thickness on bending stiffness of the blade is explored,and 14 significant design variables are filtered to drive the structural optimization.The best solution predicts an increase in natural frequencies of first-order flapwise and edgewise blade modes by up to 12%and 10.4%,respectively.The results show that the structural optimization method based on modal sensitivity is more effective to improve the structural performance.

Distributionally Robust Optimal Dispatch of Virtual Power Plant Based on Moment of Renewable Energy Resource

Virtual power plants can effectively integrate different types of distributed energy resources,which have become a new operation mode with substantial advantages such as high flexibility,adaptability,and economy.This paper proposes a distributionally robust optimal dispatch approach for virtual power plants to determine an optimal day-ahead dispatch under uncertainties of renewable energy sources.The proposed distributionally robust approach characterizes probability distributions of renewable power output by moments.In this regard,the faults of stochastic optimization and traditional robust optimization can be overcome.Firstly,a second-order cone-based ambiguity set that incorporates the first and second moments of renewable power output is constructed,and a day-ahead two-stage distributionally robust optimization model is proposed for virtual power plants participating in day-ahead electricity markets.Then,an effective solution method based on the affine policy and second-order cone duality theory is employed to reformulate the proposed model into a deterministic mixed-integer second-order cone programming problem,which improves the computational efficiency of the model.Finally,the numerical results demonstrate that the proposed method achieves a better balance between robustness and economy.They also validate that the dispatch strategy of virtual power plants can be adjusted to reduce costs according to the moment information of renewable power output.

A novel hybrid estimation of distribution algorithm for solving hybrid flowshop scheduling problem with unrelated parallel machine

The hybrid flow shop scheduling problem with unrelated parallel machine is a typical NP-hard combinatorial optimization problem, and it exists widely in chemical, manufacturing and pharmaceutical industry. In this work, a novel mathematic model for the hybrid flow shop scheduling problem with unrelated parallel machine(HFSPUPM) was proposed. Additionally, an effective hybrid estimation of distribution algorithm was proposed to solve the HFSPUPM, taking advantage of the features in the mathematic model. In the optimization algorithm, a new individual representation method was adopted. The(EDA) structure was used for global search while the teaching learning based optimization(TLBO) strategy was used for local search. Based on the structure of the HFSPUPM, this work presents a series of discrete operations. Simulation results show the effectiveness of the proposed hybrid algorithm compared with other algorithms.

Distributed Chunk-Based Optimization for MultiCarrier Ultra-Dense Networks

In this paper,a distributed chunkbased optimization algorithm is proposed for the resource allocation in broadband ultra-dense small cell networks.Based on the proposed algorithm,the power and subcarrier allocation problems are jointly optimized.In order to make the resource allocation suitable for large scale networks,the optimization problem is decomposed first based on an effective decomposition algorithm named optimal condition decomposition(OCD) algorithm.Furthermore,aiming at reducing implementation complexity,the subcarriers are divided into chunks and are allocated chunk by chunk.The simulation results show that the proposed algorithm achieves more superior performance than uniform power allocation scheme and Lagrange relaxation method,and then the proposed algorithm can strike a balance between the complexity and performance of the multi-carrier Ultra-Dense Networks.

Distributed optimization for discrete-time multiagent systems with nonconvex control input constraints and switching topologies

This paper addresses the distributed optimization problem of discrete-time multiagent systems with nonconvex control input constraints and switching topologies.We introduce a novel distributed optimization algorithm with a switching mechanism to guarantee that all agents eventually converge to an optimal solution point,while their control inputs are constrained in their own nonconvex region.It is worth noting that the mechanism is performed to tackle the coexistence of the nonconvex constraint operator and the optimization gradient term.Based on the dynamic transformation technique,the original nonlinear dynamic system is transformed into an equivalent one with a nonlinear error term.By utilizing the nonnegative matrix theory,it is shown that the optimization problem can be solved when the union of switching communication graphs is jointly strongly connected.Finally,a numerical simulation example is used to demonstrate the acquired theoretical results.