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.

Multi-Objective Optimization with Artificial Neural Network Based Robust Paddy Yield Prediction Model

Agriculture plays a vital role in the food production process that occupies nearly one-third of the total surface of the earth.Rice is propagated from the seeds of paddy and it is a stable food almost used byfifty percent of the total world population.The extensive growth of the human population alarms us to ensure food security and the country should take proper food steps to improve the yield of food grains.This paper concentrates on improving the yield of paddy by predicting the factors that influence the growth of paddy with the help of Evolutionary Computation Techniques.Most of the researchers used to relay on historical records of meteorological parameters to predict the yield of paddy.There is a lack in analyzing the day to day impact of meteorological parameters such as direction of wind,relative humidity,Instant Wind Speed in paddy cultivation.The real time meteorological data collected and analysis the impact of weather parameters from the day of paddy sowing to till the last day of paddy harvesting with regular time series.A Robust Optimized Artificial Neural Network(ROANN)Algorithm with Genetic Algorithm(GA)and Multi Objective Particle Swarm Optimization Algorithm(MOPSO)proposed to predict the factors that to be concentrated by farmers to improve the paddy yield in cultivation.A real time paddy data collected from farmers of Tamilnadu and the meteorological parameters were matched with the cropping pattern of the farmers to construct the database.The input parameters were optimized either by using GA or MOPSO optimization algorithms to reconstruct the database.Reconstructed database optimized by using Artificial Neural Network Back Propagation Algorithm.The reason for improving the growth of paddy was identified using the output of the Neural Network.Performance metrics such as Accuracy,Error Rate etc were used to measure the performance of the proposed algorithm.Comparative analysis made between ANN with GA and ANN with MOPSO to identify the recommendations for improving the paddy yield.

Bi-Objective Optimization: A Pareto Method with Analytical Solutions

Multiple objectives to be optimized simultaneously are prevalent in real-life problems. This paper develops a new Pareto Method for bi-objective optimization which yields analytical solutions. The Pareto optimal front is obtained in closed-form, enabling the derivation of various solutions in a convenient and efficient way. The advantage of analytical solution is the possibility of deriving accurate, exact and well-understood solutions, which is especially useful for policy analysis. An extension of the method to include multiple objectives is provided with the objectives being classified into two types. Such an extension expands the applicability of the developed techniques.

Multi-Objective Cold Chain Path Optimization Based on Customer Satisfaction

To improve customer satisfaction of cold chain logistics of fresh agricultural goods enterprises and reduce the comprehensive distribution cost composed of fixed cost, transportation cost, cargo damage cost, refrigeration cost, and time penalty cost, a multi-objective path optimization model of fresh agricultural products distribution considering client satisfaction is constructed. The model is solved using an enhanced Elitist Non-dominated Sorting Genetic Algorithm (NSGA-II), and differential evolution is incorporated to the evolution operator. The algorithm produced by the revised algorithm produces a better Pareto optimum solution set, efficiently balances the relationship between customer pleasure and cost, and serves as a reference for the long-term growth of organizations. .

Multi‐objective particle swarm optimisation of complex product change plan considering service performance

Design change is an inevitable part of the product development process.This study proposes an improved binary multi‐objective PSO algorithm guided by problem char-acteristics(P‐BMOPSO)to solve the optimisation problem of complex product change plan considering service performance.Firstly,a complex product multi‐layer network with service performance is established for the first time to reveal the impact of change effect propagation on the product service performance.Secondly,the concept of service performance impact(SPI)is defined by decoupling the impact of strongly associated nodes on the service performance in the process of change affect propagation.Then,a triple‐objective selection model of change nodes is established,which includes the three indicators:SPI degree,change cost,and change time.Furthermore,an integer multi‐objective particle swarm optimisation algorithm guided by problem characteristics is developed to solve the model above.Experimental results on the design change problem of a certain type of Skyworth TV verify the effectiveness of the established optimisation model and the proposed P‐BMOPSO algorithm.

Multi Objective Multireservoir Optimization in Fuzzy Environment for River Sub Basin Development and Management

In this paper, a multi objective, multireservoir operation model is proposed using Genetic algorithm (GA) under fuzzy environment. A monthly Multi Objective Genetic Algorithm Fuzzy Optimization (MOGAFU-OPT) model for the present study is developed in ‘C’ Language. The GA parameters i.e. population size, number of generations, crossover probability, and mutation probability are decided based on optimized val-ues of fitness function. The GA operators adopted are stochastic remainder selection, one point crossover and binary mutation. Initially the model is run for maximization of irrigation releases. Then the model is run for maximization of hydropower production. These objectives are fuzzified by assuming a linear membership function. These fuzzified objectives are simultaneously maximized by defining level of satisfaction (?) and then maximizing it. This approach is applied to a multireservoir system in Godavari river sub basin in Ma-harashtra State, India. Problem is formulated with 4 reservoirs and a barrage. The optimal operation policy for maximization of irrigation releases, maximization of hydropower production and maximization of level of satisfaction is presented for existing demand in command area. This optimal operation policy so deter-mined is compared with the actual average operation policy for Jayakwadi Stage-I reservoir.

Overview of multi-objective optimization methods

To assist readers to have a comprehensive understanding, the classical and intelligent methods roundly based on precursory research achievements are summarized in this paper. First, basic conception and description about multi-objective (MO) optimization are introduced. Then some definitions and related terminologies are given. Furthermore several MO optimization methods including classical and current intelligent methods are discussed one by one succinctly. Finally evaluations on advantages and disadvantages about these methods are made at the end of the paper.

OPTIMALITY CONDITIONS AND DUALITY RESULTS FOR NONSMOOTH VECTOR OPTIMIZATION PROBLEMS WITH THE MULTIPLE INTERVAL-VALUED OBJECTIVE FUNCTION

In this paper, both Fritz John and Karush-Kuhn-Tucker necessary optimality conditions are established for a （weakly） LU-efficient solution in the considered nonsmooth multiobjective programming problem with the multiple interval-objective function. Further, the sufficient optimality conditions for a （weakly） LU-efficient solution and several duality results in Mond-Weir sense are proved under assumptions that the functions constituting the considered nondifferentiable multiobjective programming problem with the multiple interval- objective function are convex.

Evolutionary many objective optimization based on bidirectional decomposition

The decomposition based approach decomposes a multi-objective problem into a series of single objective subproblems, which are optimized along contours towards the ideal point. But non-dominated solutions cannot spread uniformly, since the Pareto front shows different features, such as concave and convex. To improve the distribution uniformity of non-dominated solutions, a bidirectional decomposition based approach that constructs two search directions is proposed to provide a uniform distribution no matter what features problems have. Since two populations along two search directions show differently on diversity and convergence, an adaptive neighborhood selection approach is presented to choose suitable parents for the offspring generation. In order to avoid the problem of the shrinking search region caused by the close distance of the ideal and nadir points, a reference point update approach is presented. The performance of the proposed algorithm is validated with four state-of-the-art algorithms. Experimental results demonstrate the superiority of the proposed algorithm on all considered test problems.

Multi-Objective Optimization and Analysis Model of Sintering Process Based on BP Neural Network

A multi-objective optimization and analysis model of the sintering process based on BP neural network is presented. Genetic algorithms are combined to simplify the BP neural network, which can reduce the learning time and increase the forecasting accuracy of the network model. This model has been experimented in the sintering process, and the production cost, the energy consumption, the quality （revolving intensity）, and the output are considered at the same time. Moreover, the relation between some factors and the multi-objectives has been analyzed, and the results are consistent with the process. Different objectives are emphasized at different practical periods, and this can provide a theoretical basis for the manager.

Multidisciplinary Design Optimization of Vehicle Instrument Panel Based on Multi-objective Genetic Algorithm

Typical multidisciplinary design optimization（MDO） has gradually been proposed to balance performances of lightweight, noise, vibration and harshness（NVH） and safety for instrument panel（IP） structure in the automotive development. Nevertheless, plastic constitutive relation of Polypropylene（PP） under different strain rates, has not been taken into consideration in current reliability-based and collaborative IP MDO design. In this paper, based on tensile test under different strain rates, the constitutive relation of Polypropylene material is studied. Impact simulation tests for head and knee bolster are carried out to meet the regulation of FMVSS 201 and FMVSS 208, respectively. NVH analysis is performed to obtain mainly the natural frequencies and corresponding mode shapes, while the crashworthiness analysis is employed to examine the crash behavior of IP structure. With the consideration of lightweight, NVH, head and knee bolster impact performance, design of experiment（DOE）, response surface model（RSM）, and collaborative optimization（CO） are applied to realize the determined and reliability-based optimizations, respectively. Furthermore, based on multi-objective genetic algorithm（MOGA）, the optimal Pareto sets are completed to solve the multi-objective optimization（MOO） problem. The proposed research ensures the smoothness of Pareto set, enhances the ability of engineers to make a comprehensive decision about multi-objectives and choose the optimal design, and improves the quality and efficiency of MDO.

Well production optimization using streamline features-based objective function and Bayesian adaptive direct search algorithm

Well production optimization is a complex and time-consuming task in the oilfield development.The combination of reservoir numerical simulator with optimization algorithms is usually used to optimize well production.This method spends most of computing time in objective function evaluation by reservoir numerical simulator which limits its optimization efficiency.To improve optimization efficiency,a well production optimization method using streamline features-based objective function and Bayesian adaptive direct search optimization(BADS)algorithm is established.This new objective function,which represents the water flooding potential,is extracted from streamline features.It only needs to call the streamline simulator to run one time step,instead of calling the simulator to calculate the target value at the end of development,which greatly reduces the running time of the simulator.Then the well production optimization model is established and solved by the BADS algorithm.The feasibility of the new objective function and the efficiency of this optimization method are verified by three examples.Results demonstrate that the new objective function is positively correlated with the cumulative oil production.And the BADS algorithm is superior to other common algorithms in convergence speed,solution stability and optimization accuracy.Besides,this method can significantly accelerate the speed of well production optimization process compared with the objective function calculated by other conventional methods.It can provide a more effective basis for determining the optimal well production for actual oilfield development.

Evolutionary Multi-objective Portfolio Optimization in Practical Context

This paper addresses evolutionary multi-objective portfolio optimization in the practical context by incorporating realistic constraints into the problem model and preference criterion into the optimization search process. The former is essential to enhance the realism of the classical mean-variance model proposed by Harry Markowitz, since portfolio managers often face a number of realistic constraints arising from business and industry regulations, while the latter reflects the fact that portfolio managers are ultimately interested in specific regions or points along the efficient frontier during the actual execution of their investment orders. For the former, this paper proposes an order-based representation that can be easily extended to handle various realistic constraints like floor and ceiling constraints and cardinality constraint. An experimental study, based on benchmark problems obtained from the OR-library, demonstrates its capability to attain a better approximation of the efficient frontier in terms of proximity and diversity with respect to other conventional representations. The experimental results also illustrated its viability and practicality in handling the various realistic constraints. A simple strategy to incorporate preferences into the multi-objective optimization process is highlighted and the experimental study demonstrates its capability in driving the evolutionary search towards specific regions of the efficient frontier.

Rotary unmanned aerial vehicles path planning in rough terrain based on multi-objective particle swarm optimization

This paper presents a path planning approach for rotary unmanned aerial vehicles(R-UAVs)in a known static rough terrain environment.This approach aims to find collision-free and feasible paths with minimum altitude,length and angle variable rate.First,a three-dimensional(3D)modeling method is proposed to reduce the computation burden of the dynamic models of R-UAVs.Considering the length,height and tuning angle of a path,the path planning of R-UAVs is described as a tri-objective optimization problem.Then,an improved multi-objective particle swarm optimization algorithm is developed.To render the algorithm more effective in dealing with this problem,a vibration function is introduced into the collided solutions to improve the algorithm efficiency.Meanwhile,the selection of the global best position is taken into account by the reference point method.Finally,the experimental environment is built with the help of the Google map and the 3D terrain generator World Machine.Experimental results under two different rough terrains from Guilin and Lanzhou of China demonstrate the capabilities of the proposed algorithm in finding Pareto optimal paths.

Multi-objective Fuzzy Optimization Algorithm for Separation-Recycle System

Separation-recycle system is an important part in chemical process, and its optimization is a multiobjective problem. In this paper the process optimization procedure is proposed. The fuzzy optimization algorithm with the concept of relative importance degree (RID) is utilized to transfer multi-objective optimization (MO-O) model into a single-objective optimization (SO-O) framework. The treatment of process condensate in synthesisa mmonia plant is taken as example to illustrate the optimization procedure, and the satisfactory result demonstrates feasibility and effectiveness of the suggested method.

Modeling and Multi-objective Optimization of Refinery Hydrogen Network

在炼油厂的氢的需求作为市场力量和环境立法正在增加，因此氢网络管理在精炼厂正在变得日益重要。大多数研究集中了于单身者 -- 为氢网络的客观优化问题，而是为多客观的优化问题的很少报道。这份报纸为在精炼厂为氢网络当模特儿和多客观的优化论述一条新奇途径。一个改进多客观的优化模型基于上层建筑的概念被建议。优化包括操作费用的最小化和设备的投资费用的最小化。为氢网络的多客观的优化的建议方法论考虑流动率限制，压力限制，纯净限制，杂质限制，回报时期，等等。方法认为所有可行连接和题目是这到混合整数非线性的编程(MINLP ) 。一个确定的优化方法被使用解决这个多客观的优化问题。最后，真实案例研究被介绍说明途径的适用性。

Improved non-dominated sorting genetic algorithm (NSGA)-II in multi-objective optimization studies of wind turbine blades

The non-dominated sorting genetic algorithm （NSGA） is improved with the controlled elitism and dynamic crowding distance. A novel multi-objective optimization algorithm is obtained for wind turbine blades. As an example, a 5 MW wind turbine blade design is presented by taking the maximum power coefficient and the minimum blade mass as the optimization objectives. The optimal results show that this algorithm has good performance in handling the multi-objective optimization of wind turbines, and it gives a Pareto-optimal solution set rather than the optimum solutions to the conventional multi objective optimization problems. The wind turbine blade optimization method presented in this paper provides a new and general algorithm for the multi-objective optimization of wind turbines.

Multi-objective optimization of membrane structures based on Pareto Genetic Algorithm

A multi-objective optimization method based on Pareto Genetic Algorithm is presented for shape design of membrane structures from a structural view point.Several non-dimensional variables are defined as optimization variables,which are decision factors of shapes of membrane structures.Three objectives are proposed including maximization of stiffness,maximum uniformity of stress and minimum reaction under external loads.Pareto Multi-objective Genetic Algorithm is introduced to solve the Pareto solutions.Consequently,the dependence of the optimality upon the optimization variables is derived to provide guidelines on how to determine design parameters.Moreover,several examples illustrate the proposed methods and applications.The study shows that the multi-objective optimization method in this paper is feasible and efficient for membrane structures;the research on Pareto solutions can provide explicit and useful guidelines for shape design of membrane structures.

A Strategy for Multi-objective Optimization under Uncertainty in Chemical Process Design

在许多情形，化学加工设计能作为多客观的优化(哞) 被提出问题。例子包括双性人目的优化问题，在经济目的被最大化，环境影响同时被最小化的地方。而且，在这进程的随机的行为，性质，市场变化，在模型预言的错误将等等影响进程的性能。因此，在不确定性下面开发哞方法论是必要的。在这篇文章，作者在不确定性下面为化学加工设计建议通用、系统的优化方法论。它瞄准从很多个候选人识别最佳的设计。这方法论的用途被案例研究在氨植物基于一个冷凝物处理单位的设计表明。

Waste Minimization Through Process Integration and Multi-objective Optimization

By avoiding or reducing the production of waste, waste minimization is an effective approach to solve the pollution problem in chemical industry. Process integration supported by multi-objective optimization provides a framework for process design or process retrofit by simultaneously optimizing on the aspects of environment and economics. Multi-objective genetic algorithm is applied in this area as the solution approach for the multi-objective optimization problem.