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.

Tourism Route Recommendation Based on A Multi-Objective Evolutionary Algorithm Using Two-Stage Decomposition and Pareto Layering

Tourism route planning is widely applied in the smart tourism field.The Pareto-optimal front obtained by the traditional multi-objective evolutionary algorithm exhibits long tails,sharp peaks and disconnected regions problems,which leads to uneven distribution and weak diversity of optimization solutions of tourism routes.Inspired by these limitations,we propose a multi-objective evolutionary algorithm for tourism route recommendation(MOTRR)with two-stage and Pareto layering based on decomposition.The method decomposes the multiobjective problem into several subproblems,and improves the distribution of solutions through a two-stage method.The crowding degree mechanism between extreme and intermediate populations is used in the two-stage method.The neighborhood is determined according to the weight of the subproblem for crossover mutation.Finally,Pareto layering is used to improve the updating efficiency and population diversity of the solution.The two-stage method is combined with the Pareto layering structure,which not only maintains the distribution and diversity of the algorithm,but also avoids the same solutions.Compared with several classical benchmark algorithms,the experimental results demonstrate competitive advantages on five test functions,hypervolume(HV)and inverted generational distance(IGD)metrics.Using the experimental results of real scenic spot datasets from two famous tourism social networking sites with vast amounts of users and large-scale online comments in Beijing,our proposed algorithm shows better distribution.It proves that the tourism routes recommended by our proposed algorithm have better distribution and diversity,so that the recommended routes can better meet the personalized needs of tourists.

Efficiency-based Pareto Optimization of Building Energy Consumption and Thermal Comfort:A Case Study of a Residential Building in Bushehr,Iran

In Iran,the intensity of energy consumption in the building sector is almost 3 times the world average,and due to the consumption of fossil fuels as the main source of energy in this sector,as well as the lack of optimal design of buildings,it has led to excessive release of toxic gases into the environment.This research develops an efficient approach for the simulation-oriented Pareto optimization(SOPO)of building energy efficiency to assist engineers in optimal building design in early design phases.To this end,EnergyPlus,as one of the most powerful and well-known whole-building simulation programs,is combined with the Multi-objective Ant Colony Optimization(MOACO)algorithm through the JAVA programming language.As a result,the capabilities of JAVA programming are added to EnergyPlus without the use of other plugins and third parties.To evaluate the effectiveness of the developed method,it was performed on a residential building located in the hot and semi-arid region of Iran.To obtain the optimum configuration of the building under investigation,the building rotation,window-to-wall ratio,tilt angle of shading device,depth of shading device,color of the external walls,area of solar collector,tilt angle of solar collector,rotation of solar collector,cooling and heating setpoints of heating,ventilation,and air conditioning(HVAC)system are chosen as decision variables.Further,the building energy consumption(BEC),solar collector efficiency(SCE),and predicted percentage of dissatisfied(PPD)index as a measure of the occupants'thermal comfort level are chosen as the objective functions.The single-objective optimization(SO)and Pareto optimization(PO)are performed.The obtained results are compared to the initial values of the basic model.The optimization results depict that the PO provides optimal solutions more reliable than those obtained by the SOs,owing to the lower value of the deviation index.Moreover,the optimal solutions extracted through the PO are depicted in the form of Pareto fronts.Eventually,the Linear Programming Technique for Multidimensional Analysis of Preference(LINMAP)technique as one of the well-known multi-criteria decision-making(MCDM)methods is utilized to adopt the optimum building configuration from the set of Pareto optimal solutions.Further,the results of PO show that although BEC increases from 136 GJ to 140 GJ,PPD significantly decreases from 26%to 8%and SCE significantly increases from 16%to 25%.The introduced SOPO method suggests an effective and practical approach to obtain optimal solutions during the building design phase and provides an opportunity for building engineers to have a better picture of the range of options for decision-making.In addition,the method presented in this study can be applied to different types of buildings in different climates.

Multiobjective Optimization of Simulated Moving Bed by Tissue P System

The binaphthol enantiomers separation process using simulation moving bed technology is simulated with the true moving bed approach （TMB）. In order to systematically optimize the process with multiple productive objectives, this article develops a variant of tissue P system （TPS）. Inspired by general tissue P systems, the special TPS has a tissue-like structure with several membranes. The key rules of each membrane are the communication rule and mutation rule. These characteristics contribute to the diversity of the population, the conquest of the multimodal of objective function, and the convergence of algorithm. The results of comparison with a popular algorithm——the non-dominated sorting genetic algorithm 2（NSGA-2） illustrate that the new algorithm has satisfactory performance. Using the algorithm, this study maximizes synchronously several conflicting objectives, purities of different products, and productivity.

Optimization Method for Departure Flight Scheduling Problem Based on Genetic Algorithm

Except for the bad weather or other uncontrollable reasons,a reasonable queue of departure and arrival flights is one of the important methods to reduce the delay on busy airports.Here focusing on the Pareto optimization of departure flights,the take-off sequencing is taken as a single machine scheduling problem with two objective functions,i.e.,the minimum of total weighted delayed number of departure flights and the latest delay time of delayed flight.And the integer programming model is established and solved by multi-objective genetic algorithm.The simulation results show that the method can obtain the better goal,and provide a variety of options for controllers considering the scene situation,thus improving the flexibility and effectivity of flight plan.

A multiobjective evolutionary optimization method based critical rainfall thresholds for debris flows initiation

At present,most researches on the critical rainfall threshold of debris flow initiation use a linear model obtained through regression.With relatively weak fault tolerance,this method not only ignores nonlinear effects but also is susceptible to singular noise samples,which makes it difficult to characterize the true quantization relationship of the rainfall threshold.Besides,the early warning threshold determined by statistical parameters is susceptible to negative samples(samples where no debris flow has occurred),which leads to uncertainty in the reliability of the early warning results by the regression curve.To overcome the above limitations,this study develops a data-driven multiobjective evolutionary optimization method that combines an artificial neural network(ANN)and a multiobjective evolutionary optimization implemented by particle swarm optimization(PSO).Firstly,the Pareto optimality method is used to represent the nonlinear and conflicting critical thresholds for the rainfall intensity I and the rainfall duration D.An ANN is used to construct a dual-target(dual-task)predictive surrogate model,and then a PSO-based multiobjective evolutionary optimization algorithm is applied to train the ANN and stochastically search the trained ANN for obtaining the Pareto front of the I-D surrogate prediction model,which is intended to overcome the limitations of the existing linear regression-based threshold methods.Finally,a double early warning curve model that can effectively control the false alarm rate and negative alarm rate of hazard warnings are proposed based on the decision space and target space maps.This study provides theoretical guidance for the early warning and forecasting of debris flows and has strong applicability.

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.

Handling Multiple Objectives with Biogeography-based Optimization

Biogeography-based optimization （BBO） is a new evolutionary optimization method inspired by biogeography. In this paper, BBO is extended to a multi-objective optimization, and a biogeography-based multi-objective optimization （BBMO） is introduced, which uses the cluster attribute of islands to naturally decompose the problem. The proposed algorithm makes use of nondominated sorting approach to improve the convergence ability efficiently. It also combines the crowding distance to guarantee the diversity of Pareto optimal solutions. We compare the BBMO with two representative state-of-the-art evolutionary multi-objective optimization methods, non-dominated sorting genetic algorithm-II （NSGA-II） and archive-based micro genetic algorithm （AMGA） in terms of three metrics. Simulation results indicate that in most cases, the proposed BBMO is able to find much better spread of solutions and converge faster to true Pareto optimal fronts than NSGA-II and AMGA do.

Multi-objective optimization strategies using adjoint method and game theory in aerodynamics

There are currently three different game strategies originated in economics： （1） Cooperative games （Pareto front）, （2） Competitive games （Nash game） and （3） Hierarchical games （Stackelberg game）. Each game achieves different equilibria with different performance, and their players play different roles in the games. Here, we introduced game concept into aerodynamic design, and combined it with adjoint method to solve multi- criteria aerodynamic optimization problems. The performance distinction of the equilibria of these three game strategies was investigated by numerical experiments. We computed Pareto front, Nash and Stackelberg equilibria of the same optimization problem with two conflicting and hierarchical targets under different parameterizations by using the deterministic optimization method. The numerical results show clearly that all the equilibria solutions are inferior to the Pareto front. Non-dominated Pareto front solutions are obtained, however the CPU cost to capture a set of solutions makes the Pareto front an expensive tool to the designer.

海上风电半潜式基础初步选型 Pareto⁃Optimal 评价

针对半潜漂浮式风电基础初步选型,采用Pareto⁃Optimal评价方法对不同吃水、平台立柱直径、立柱间距和垂荡板直径四个参数的不同组合进行分析比较。基于浮体动力学频域计算方法,采用我国阳江某海域极限波浪条件计算得到叶轮中心水平加速度,同时考虑完整稳性的计算结果。对比分析表明平台吃水和立柱直径宜选择适中的取值,较大的排水量和立柱总体积并不会显著减小叶轮中心水平加速度。垂荡板对于改善平台整体性能是较为敏感的,垂荡板与立柱的直径比存在一定的最佳范围。平台立柱间距是影响平台运动性能最大的因素,增大立柱间距可以有效地降低叶轮中心水平加速度,但立柱间距的增大对立柱间的撑杆结构强度以及平台整体的建造和下水提出了较大的挑战。

Experimental investigation and multi-objective optimization of wire electrical discharge machining(WEDM) of 5083 aluminum alloy

The experimental analysis presented aims at the selection of the most optimal machining parameter combination for wire electrical discharge machining （WEDM） of 5083 aluminum alloy. Based on the Taguchi experimental design （L9 orthogonal array） method, a series of experiments were performed by considering pulse-on time, pulse-off time, peak current and wire tension as input parameters. The surface roughness and cutting speed were considered responses. Based on the signal-to-noise （S/N） ratio, the influence of the input parameters on the responses was determined. The optimal machining parameters setting for the maximum cutting speed and minimum surface roughness were found using Taguchi methodology. Then, additive model was employed for prediction of all （34） possible machining combinations. Finally, a handy technology table has been reported using Pareto optimality approach.

Novel electromagnetism-like mechanism method for multiobjective optimization problems

As a new-style stochastic algorithm, the electromagnetism-like mechanism（EM） method gains more and more attention from many researchers in recent years. A novel model based on EM（NMEM） for multiobjective optimization problems is proposed, which regards the charge of all particles as the constraints in the current population and the measure of the uniformity of non-dominated solutions as the objective function. The charge of the particle is evaluated based on the dominated concept, and its magnitude determines the direction of a force between two particles. Numerical studies are carried out on six complex test functions and the experimental results demonstrate that the proposed NMEM algorithm is a very robust method for solving the multiobjective optimization problems.

A self-adaptive linear evolutionary algorithm for solving constrained optimization problems

In many real-world applications of evolutionary algorithms,the fitness of an individual requires a quantitative measure.This paper proposes a self-adaptive linear evolutionary algorithm （ALEA） in which we introduce a novel strategy for evaluating individual＇s relative strengths and weaknesses.Based on this strategy,searching space of constrained optimization problems with high dimensions for design variables is compressed into two-dimensional performance space in which it is possible to quickly identify ＇good＇ individuals of the performance for a multiobjective optimization application,regardless of original space complexity.This is considered as our main contribution.In addition,the proposed new evolutionary algorithm combines two basic operators with modification in reproduction phase,namely,crossover and mutation.Simulation results over a comprehensive set of benchmark functions show that the proposed strategy is feasible and effective,and provides good performance in terms of uniformity and diversity of solutions.

Multi-objective steady-state optimization of two-chamber microbial fuel cells

A microbial fuel cell(MFC)is a novel promising technology for simultaneous renewable electricity generation and wastewater treatment.Three non-comparable objectives,i.e.power density,attainable current density and waste removal ratio,are often conflicting.A thorough understanding of the relationship among these three conflicting objectives can be greatly helpful to assist in optimal operation of MFC system.In this study,a multiobjective genetic algorithm is used to simultaneously maximizing power density,attainable current density and waste removal ratio based on a mathematical model for an acetate two-chamber MFC.Moreover,the level diagrams method is utilized to aid in graphical visualization of Pareto front and decision making.Three biobjective optimization problems and one three-objective optimization problem are thoroughly investigated.The obtained Pareto fronts illustrate the complex relationships among these three objectives,which is helpful for final decision support.Therefore,the integrated methodology of a multi-objective genetic algorithm and a graphical visualization technique provides a promising tool for the optimal operation of MFCs by simultaneously considering multiple conflicting objectives.

Synergetic Optimization of Missile Shapes for Aerodynamic and Radar Cross-Section Performance Based on Multi-objective Evolutionary Algorithm

A multiple-objective evolutionary algorithm (MOEA) with a new Decision Making (DM) scheme for MOD of conceptual missile shapes was presented, which is contrived to determine suitable tradeoffs from Pareto optimal set using interactive preference articulation. There are two objective functions, to maximize ratio of lift to drag and to minimize radar cross-section (RCS) value. 3D computational electromagnetic solver was used to evaluate RCS, electromagnetic performance. 3D Navier-Stokes flow solver was adopted to evaluate aerodynamic performance. A flight mechanics solver was used to analyze the stability of the missile. Based on the MOEA, a synergetic optimization of missile shapes for aerodynamic and radar cross-section performance is completed. The results show that the proposed approach can be used in more complex optimization case of flight vehicles.

A binary gridding path-planning method for plant-protecting UAVs on irregular fields

The use of plant-protecting unmanned aerial vehicles(UAVs)for pesticide spraying is an essential operation in modern agriculture.The balance between reducing pesticide consumption and energy consumption is a significant focus of current research in the path-planning of plant-protecting UAVs.In this study,we proposed a binarization multi-objective model for the irregular field area,specifically an improved non-dominated sorting genetic algorithm–II based on the knee point and plane measurement(KPPM-NSGA-ii).The binarization multi-objective model is applied to convex polygons,concave polygons and fields with complex terrain.The experiments demonstrated that the proposed KPPM-NSGA-ii can obtain better results than the unplanned path method whether the optimization of pesticide consumption or energy consumption is preferred.Hence,the proposed algorithm can save energy and pesticide usage and improve the efficiency in practical applications.

Isolation performances and optimization of triple quasi-zero stiffness isolators

In this paper,triple quasi-zero stiffness(QZS)passive vibration isolators whose restoring force curve has a three-stage softening effect are proposed.Multi-coupled SD oscillators with three independent geometrical parameters are used as negative stiffness mechanisms to achieve QZS characteristics at the origin and symmetrical positions on both sides of the origin.Isolation performances of different triple QZS isolators are analyzed to show influences of the selection of QZS regions away from the origin on the range of isolation regions.Pareto optimizations of system parameters are carried out to get a larger range of small restoring force regions and small stiffness regions.Isolation performances of two triple QZS isolators are discussed to show the influence of different Pareto optimization solutions through the comparisons with single and double QZS isolators.Results showed that triple QZS isolators have both the advantages of single and double QZS isolators which results in better isolation performances under both small and large excitation amplitudes.An improvement in isolation performances for triple QZS isolators is found with the decrease in average stiffness due to the appearance of two symmetrical QZS regions away from the origin.Larger displacements of QZS regions away from the origin result in better isolation performances when excitation amplitude is large,and triple QZS characteristics are similar to double QZS isolators at this time.Smaller restoring forces of QZS regions away from the origin lead to better isolation performances when excitation amplitude is small,and triple QZS characteristics are similar to single QZS isolators at this moment.Compared with the decrease in average stiffness,the improvement of isolation performances shows a hysteresis phenomenon due to the difference between static and dynamic characteristics.

Linear-Quadratic Pareto Cooperative Game for Mean-Field Backward Stochastic System

This paper focuses on a Pareto cooperative differential game with a linear mean-field backward stochastic system and a quadratic form cost functional. Based on a weighted sum optimality method, the Pareto game is equivalently converted to an optimal control problem. In the first place,the feedback form of Pareto optimal strategy is derived by virtue of decoupling technology, which is represented by four Riccati equations, a mean-field forward stochastic differential equation(MF-FSDE),and a mean-field backward stochastic differential equation(MF-BSDE). In addition, the corresponding Pareto optimal solution is further obtained. Finally, the author solves a problem in mathematical finance to illustrate the application of the theoretical results.

A NEW ALGORITHM FOR ALL EFFICIENT SPANNING TREES

In Corley′s algorithm for all efficient spanning trees, final solutions include many spanning trees, which are not all efficient. In this paper, a new algorithm is presented, which corrects and modifies Corley′s algorithm. A necessary condition is developed for the subtree of an efficient spanning tree. According to the condition the new algorithm is established and its efficiency is proved.

Multi-Objective Task Assignment for Maximizing Social Welfare in Spatio-Temporal Crowdsourcing

With the development of the Internet of Things(IoT),spatio-temporal crowdsourcing(mobile crowdsourcing)has become an emerging paradigm for addressing location-based sensing tasks.However,the delay caused by network transmission has led to low data processing efficiency.Fortunately,edge computing can solve this problem,effectively reduce the delay of data transmission,and improve data processing capacity,so that the crowdsourcing platform can make better decisions faster.Therefore,this paper combines spatio-temporal crowdsourcing and edge computing to study the Multi-Objective Optimization Task Assignment(MOO-TA)problem in the edge computing environment.The proposed online incentive mechanism considers the task difficulty attribute to motivate crowd workers to perform sensing tasks in the unpopular area.In this paper,the Weighted and Multi-Objective Particle Swarm Combination(WAMOPSC)algorithm is proposed to maximize both platform’s and crowd workers’utility,so as to maximize social welfare.The algorithm combines the traditional Linear Weighted Summation(LWS)algorithm and Multi-Objective Particle Swarm Optimization(MOPSO)algorithm to find pareto optimal solutions of multi-objective optimization task assignment problem as much as possible for crowdsourcing platform to choose.Through comparison experiments on real data sets,the effectiveness and feasibility of the proposed method are evaluated.