A Length-Adaptive Non-Dominated Sorting Genetic Algorithm for Bi-Objective High-Dimensional Feature Selection

As a crucial data preprocessing method in data mining,feature selection(FS)can be regarded as a bi-objective optimization problem that aims to maximize classification accuracy and minimize the number of selected features.Evolutionary computing(EC)is promising for FS owing to its powerful search capability.However,in traditional EC-based methods,feature subsets are represented via a length-fixed individual encoding.It is ineffective for high-dimensional data,because it results in a huge search space and prohibitive training time.This work proposes a length-adaptive non-dominated sorting genetic algorithm(LA-NSGA)with a length-variable individual encoding and a length-adaptive evolution mechanism for bi-objective highdimensional FS.In LA-NSGA,an initialization method based on correlation and redundancy is devised to initialize individuals of diverse lengths,and a Pareto dominance-based length change operator is introduced to guide individuals to explore in promising search space adaptively.Moreover,a dominance-based local search method is employed for further improvement.The experimental results based on 12 high-dimensional gene datasets show that the Pareto front of feature subsets produced by LA-NSGA is superior to those of existing algorithms.

A Min-Max Strategy to Aid Decision Making in a Bi-Objective Discrete Optimization Problem Using an Improved Ant Colony Algorithm

A multi-objective optimization problem has two or more objectives to be minimized or maximized simultaneously. It is usually difficult to arrive at a solution that optimizes every objective. Therefore, the best way of dealing with the problem is to obtain a set of good solutions for the decision maker to select the one that best serves his/her interest. In this paper, a ratio min-max strategy is incorporated (after Pareto optimal solutions are obtained) under a weighted sum scalarization of the objectives to aid the process of identifying a best compromise solution. The bi-objective discrete optimization problem which has distance and social cost (in rail construction, say) as the criteria was solved by an improved Ant Colony System algorithm developed by the authors. The model and methodology were applied to hypothetical networks of fourteen nodes and twenty edges, and another with twenty nodes and ninety-seven edges as test cases. Pareto optimal solutions and their maximum margins of error were obtained for the problems to assist in decision making. The proposed model and method is user-friendly and provides the decision maker with information on the quality of each of the Pareto optimal solutions obtained, thus facilitating decision making.

A Bi-Objective Green Vehicle Routing Problem: A New Hybrid Optimization Algorithm Applied to a Newspaper Distribution

The purpose of this work is to present a methodology to provide a solution to a Bi-objective Green Vehicle Routing Problem (BGVRP). The methodology, illustrated using a case study (newspaper distribution problem) and literature Instances, was divided into three stages: Stage 1, data treatment;Stage 2, “metaheuristic approaches” (hybrid or non-hybrid), used comparatively, more specifically: NSGA-II (Non-dominated Sorting Genetic Algorithm II), MOPSO (Multi-Objective Particle Swarm Optimization), which were compared with the new approaches proposed by the authors, CWNSGA-II (Clarke and Wright’s Savings with the Non-dominated Sorting Genetic Algorithm II) and CWTSNSGA-II (Clarke and Wright’s Savings, Tabu Search and Non-dominated Sorting Genetic Algorithm II);Stage 3, analysis of the results, with a comparison of the algorithms. An optimization of 19.9% was achieved for Objective Function 1 (OF1;minimization of CO2 emissions) and consequently the same percentage for the minimization of total distance, and 87.5% for Objective Function 2 (OF2;minimization of the difference in demand). Metaheuristic approaches hybrid achieved superior results for case study and instances. In this way, the procedure presented here can bring benefits to society as it considers environmental issues and also balancing work between the routes, ensuring savings and satisfaction for the users.

Bi-objective optimization models for mitigating traffic congestion in urban road networks

Traffic congestion in road transportation networks is a persistent problem in major metropolitan cities around the world.In this context,this paper deals with exploiting underutilized road capacities in a network to lower the congestion on overutilized links while simultaneously satisfying the system optimal flow assignment for sustainable transportation.Four congestion mitigation strategies are identified based on deviation and relative deviation of link volume from the corresponding capacity.Consequently,four biobjective mathematical programming optimal flow distribution(OFD)models are proposed.The case study results demonstrate that all the proposed models improve system performance and reduce congestion on high volume links by shifting flows to low volumeto-capacity links compared to UE and SO models.Among the models,the system optimality with minimal sum and maximum absolute relative-deviation models(SO-SAR and SO-MAR)showed superior results for different performance measures.The SO-SAR model yielded 50%and 30%fewer links at higher link utilization factors than UE and SO models,respectively.Also,it showed more than 25%improvement in path travel times compared to UE travel time for about 100 paths and resulted in the least network congestion index of1.04 compared to the other OFD and UE models.Conversely,the SO-MAR model yielded the least total distance and total system travel time,resulting in lower fuel consumption and emissions,thus contributing to sustainability.The proposed models contribute towards efficient transportation infrastructure management and will be of interest to transportation planners and traffic managers.

THE EFFECT OF WORKER LEARNING ON SCHEDULING JOBS IN A HYBRID FLOW SHOP： A BI-OBJECTIVE APPROACH

This paper studies learning effect as a resource utilization technique that can model improvement in worker＇s ability as a result of repeating similar tasks. By considering learning of workers while performing setup times, a schedule can be determined to place jobs that share similar tools and fixtures next to each other. The purpose of this paper is to schedule a set of jobs in a hybrid flow shop （HFS） environment with learning effect while minimizing two objectives that are in conflict： namely maximum completion time （makespan） and total tardiness. Minimizing makespan is desirable from an internal efficiency viewpoint, but may result in individual jobs being scheduled past their due date, causing customer dissatisfaction and penalty costs. A bi-objective mixed integer programming model is developed, and the complexity of the developed bi-objective model is compared against the bi-criteria one through numerical examples. The effect of worker learning on the structure of assigned jobs to machines and their sequences is analyzed. Two solution methods based on the hybrid water flow like algorithm and non-dominated sorting and ranking concepts are proposed to solve the problem. The quality of the approximated sets of Pareto solutions is evaluated using several performance criteria. The results show that the proposed algorithms with learning effect perform well in reducing setup times and eliminate the need for setups itself through proper scheduling.

Consensus Clustering for Bi-objective Power Network Partition

Partitioning a complex power network into a number of sub-zones can help realize a divide-and-conquer’management structure for the whole system,such as voltage and reactive power control,coherency identification,power system restoration,etc.Extensive partitioning methods have been proposed by defining various distances,applying different clustering methods,or formulating varying optimization models for one specific objective.However,a power network partition may serve two or more objectives,where a trade-off among these objectives is required.This paper proposes a novel weighted consensus clustering-based approach for bi-objective power network partition.By varying the weights of different partitions for different objectives,Pareto improvement can be explored based on the node-based and subset-based consensus clustering methods.Case studies on the IEEE 300-bus test system are conducted to verify the effectiveness and superiority of our proposed method.

Bi-objective mathematical model for choosing sugarcane varieties with harvest residual biomass in energy cogeneration

Sugarcane crop occupies an area of about 23.78 million hectares in 103 countries,and an estimated production of 1.66 billion tons,adding to this volume more than 6%to 17%concerning residual biomass resulting from harvest.The destination of this residual biomass is a major challenge to managers of mills.There are at least two alternatives which are reduction in residue production and increased output in electricity cogeneration.These two conflicting objectives are mathematically modeled as a bi-objective problem.This study developed a bi-objective mathematical model for choosing sugarcane varieties that result in maximum revenue from electricity sales and minimum gathering cost of sugarcane harvesting residual biomass.The approach used to solve the proposed model was based on theε-constraints method.Experiments were performed using real data from sugarcane varieties and costs and showed effectiveness of model and method proposed.These experiments showed the possibility of increasing net revenue from electricity sale,i.e.,already discounted the cost increase with residual biomass gathering,in up to 98.44%.

Bi-objective Layout Optimization for Multiple Wind Farms Considering Sequential Fluctuation of Wind Power Using Uniform Design

The fluctuation of wind power brings great challenges to the secure,stable,and cost-efficient operation of the power system.Because of the time-correlation of wind speed and the wake effect of wind turbines,the layout of wind farm has a significant impact on the wind power sequential fluctuation.In order to reduce the fluctuation of wind power and improve the operation security with lower operating cost,a bi-objective layout optimization model for multiple wind farms considering the sequential fluctuation of wind power is proposed in this paper.The goal is to determine the optimal installed capacity of wind farms and the location of wind turbines.The proposed model maximizes the energy production and minimizes the fluctuation of wind power simultaneously.To improve the accuracy of wind speed estimation and hence the power calculation,the timeshifting of wind speed between the wind tower and turbines’locations is also considered.A uniform design based two-stage genetic algorithm is developed for the solution of the proposed model.Case studies demonstrate the effectiveness of this proposed model.

Research on a stock-matching trading strategy based on bi-objective optimization

In recent years,with strict domestic financial supervision and other policy-oriented factors,some products are becoming increasingly restricted,including nonstandard products,bank-guaranteed wealth management products,and other products that can provide investors with a more stable income.Pairs trading,a type of stable strategy that has proved efficient in many financial markets worldwide,has become the focus of investors.Based on the traditional Gatev-Goetzmann-Rouwenhorst(GGR,Gatev et al.2006)strategy,this paper proposes a stock-matching strategy based on bi-objective quadratic programming with quadratic constraints(BQQ)model.Under the condition of ensuring a long-term equilibrium between pairedstock prices,the volatility of stock spreads is increased as much as possible,improving the profitability of the strategy.To verify the effectiveness of the strategy,we use the natural logs of the daily stock market indices in Shanghai.The GGR model and the BQQ model proposed in this paper are back-tested and compared.The results show that the BQQ model can achieve a higher rate of returns.

Efficient Network Selection Using Multi-Depot Routing Problem for Smart Cities

Smart cities make use of a variety of smart technology to improve societies in better ways.Such intelligent technologies,on the other hand,pose sig-nificant concerns in terms of power usage and emission of carbons.The suggested study is focused on technological networks for big data-driven systems.With the support of software-defined technologies,a transportation-aided multicast routing system is suggested.By using public transportation as another communication platform in a smart city,network communication is enhanced.The primary objec-tive is to use as little energy as possible while delivering as much data as possible.The Attribute Decision Making with Capacitated Vehicle(CV)Routing Problem(RP)and Half Open Multi-Depot Heterogeneous Vehicle Routing Problem is used in the proposed research.For the optimum network selection,a Multi-Attribute Decision Making(MADM)method is utilized.For the sake of reducing energy usage,the Capacitated Vehicle Routing Problem(CVRP)is employed.To reduce the transportation cost and risk,Half Open Multi-Depot Heterogeneous Vehicle Routing Problem is used.Moreover,a mixed-integer programming approach is used to deal with the problem.To produce Pareto optimal solutions,an intelligent algorithm based on the epsilon constraint approach and genetic algorithm is cre-ated.A scenario of Auckland Transport is being used to validate the concept of offloading the information onto the buses for energy-efficient and delay-tolerant data transfer.Therefore the experiments have demonstrated that the buses may be used effectively to carry out the data by customer requests while using 30%of less energy than the other systems.

Observation scheduling problem for AEOS with a comprehensive task clustering

Considering the flexible attitude maneuver and the narrow field of view of agile Earth observation satellite(AEOS)together,a comprehensive task clustering(CTC)is proposed to improve the observation scheduling problem for AEOS(OSPFAS).Since the observation scheduling problem for AEOS with comprehensive task clustering(OSWCTC)is a dynamic combination optimization problem,two optimization objectives,the loss rate(LR)of the image quality and the energy consumption(EC),are proposed to format OSWCTC as a bi-objective optimization model.Harnessing the power of an adaptive large neighborhood search(ALNS)algorithm with a nondominated sorting genetic algorithm II(NSGA-II),a bi-objective optimization algorithm,ALNS+NSGA-II,is developed to solve OSWCTC.Based on the existing instances,the efficiency of ALNS+NSGA-II is analyzed from several aspects,meanwhile,results of extensive computational experiments are presented which disclose that OSPFAS considering CTC produces superior outcomes.

Site selection of emergency material warehouse under fuzzy environment

The objective of this work was to determine the location of emergency material warehouses. For the site selection problem of emergency material warehouses, the triangular fuzzy numbers are respectively demand of the demand node, the distance between the warehouse and demand node and the cost of the warehouse, a bi-objective programming model was established with minimum total cost of the system and minimum distance between the selected emergency material warehouses and the demand node. Using the theories of fuzzy numbers, the fuzzy programming model was transformed into a determinate bi-objective mixed integer programming model and a heuristic algorithm for this model was designed. Then, the algorithm was proven to be feasible and effective through a numerical example. Analysis results show that the location of emergency material warehouse depends heavily on the values of degree a and weight wl. Accurate information of a certain emergency activity should be collected before making the decision.

A Novel Two-Level Optimization Strategy for Multi-Debris Active Removal Mission in LEO

Recent studies of the space debris environment in Low Earth Orbit(LEO)have shown that the critical density of space debris has been reached in certain regions.The Active Debris Removal(ADR)mission,to mitigate the space debris density and stabilize the space debris environment,has been considered as a most effective method.In this paper,a novel two-level optimization strategy for multi-debris removal mission in LEO is proposed,which includes the low-level and high-level optimization process.To improve the overall performance of the multi-debris active removal mission and obtain multiple Pareto-optimal solutions,the ADR mission is seen as a Time-Dependant Traveling Salesman Problem(TDTSP)with two objective functions to minimize the total mission duration and the total propellant consumption.The problem includes the sequence optimization to determine the sequence of removal of space debris and the transferring optimization to define the orbital maneuvers.Two optimization models for the two-level optimization strategy are built in solving the multi-debris removal mission,and the optimal Pareto solution is successfully obtained by using the non-dominated sorting genetic algorithm II(NSGA-II).Two test cases are presented,which show that the low level optimization strategy can successfully obtain the optimal sequences and the initial solution of the ADR mission and the high level optimization strategy can efficiently and robustly find the feasible optimal solution for long duration perturbed rendezvous problem.

A joint inventory–finance model for coordinating a capital‑constrained supply chain with financing limitations

Faced with economic recession,firms struggle to find ways to stay competitive and maintain market share.Effective coordination of the supply chain can solve this problem,but this may fail if existing capital constraints and financial flows are ignored.This study addresses the challenge by exploiting coordination through joint decision-making on the physical and financial flows of a capital-constrained supply chain.We also consider the capital-constrained member’s financing limitations that lead to lost sales.Two scenarios based on non-coordinated and coordinated structures are modeled in the form of bi-objective optimization problems that simultaneously optimize system costs and service levels.The models are solved using the -constraint method.The results indicate that the non-coordinated model cannot satisfy more than about 50%of the demand due to capital shortage and financing limitations,while the coordinated model can satisfy all of the demand via internal financing.Furthermore,the proposed coordination scheme leads to cost reduction for the members and the total system.To motivate all members to accept the proposed coordination scheme,a cost-sharing mechanism is applied to the coordination procedure.Finally,a sensitivity analysis concerning financial parameters is provided for validating the coordination model.

Budget constrained flow interception location model for congested systems

To study location problems with congestion demand, a bi-objective model based on flow intercep-tion problem is proposed.The model is formulated from the view of M/M/m queuing systems.Service quantity and quality are simultaneously considered as objectives, with constraint on total cost.Service quality includes deviation distance from preplanned trips and customers＇ waiting time.Service quantity is the number of intercep-tion customers.A multi-objective evolutionary algorithm combined with greedy heuristic is proposed.Finally a computational experiment is given, and the algorithm is proved to be efficient.

A robust joint frequency spectrum and power allocation strategy in a coexisting radar and communication system

The resource allocation technique is of great significance in achieving frequency spectrum coexistence in Joint Radar-Communication(JRC)systems,by which the problem of radio frequency spectrum congestion can be well alleviated.A Robust Joint Frequency Spectrum and Power Allocation(RJFSPA)strategy is proposed for the Coexisting Radar and Communication(CRC)system.Specifically,we consider the uncertainty of target Radar Cross Section(RCS)and communication channel gain to formulate a bi-objective optimization model.The joint probabilities that the Crame´r-Rao Lower Bound(CRLB)of each target satisfying the localization accuracy threshold and the Communication Data Ratio(CDR)of each user satisfying the communication threshold are simultaneously maximized,under the constraint of the total power budget.A Three-Stage Alternating Optimization Method(TSAOM)is proposed to obtain the Best-Known Pareto Subset(BKPS)of this problem,where the frequency spectrum,radar power,and communicator power are allocated using the greedy search and standard convex optimization methods,respectively.Simulation results confirm the effectiveness of the proposed RJFSPA strategy,compared with the resource allocation methods in a uniform manner and that ignores the uncertainties.The efficiency of the TSAOM is also verified by the comparison with the exhaustive search-based method.

AN AUGMENTED LAGRANGIAN TRUST REGION METHOD WITH A BI-OBJECT STRATEGY

An augmented Lagrangian trust region method with a bi=object strategy is proposed for solving nonlinear equality constrained optimization, which falls in between penalty-type methods and penalty-free ones. At each iteration, a trial step is computed by minimizing a quadratic approximation model to the augmented Lagrangian function within a trust region. The model is a standard trust region subproblem for unconstrained optimization and hence can efficiently be solved by many existing methods. To choose the penalty parameter, an auxiliary trust region subproblem is introduced related to the constraint violation. It turns out that the penalty parameter need not be monotonically increasing and will not tend to infinity. A bi-object strategy, which is related to the objective function and the measure of constraint violation, is utilized to decide whether the trial step will be accepted or not. Global convergence of the method is established under mild assumptions. Numerical experiments are made, which illustrate the efficiency of the algorithm on various difficult situations.

A Line Search SQP-type Method with Bi-object Strategy for Nonlinear Semidefinite Programming

We propose a line search exact penalty method with bi-object strategy for nonlinear semidefinite programming.At each iteration,we solve a linear semidefinite programming to test whether the linearized constraints are consistent or not.The search direction is generated by a piecewise quadratic-linear model of the exact penalty function.The penalty parameter is only related to the information of the current iterate point.The line search strategy is a penalty-free one.Global and local convergence are analyzed under suitable conditions.We finally report some numerical experiments to illustrate the behavior of the algorithm on various degeneracy situations.