A Multiobjective Approach to Homography Estimation

In several machine vision problems, a relevant issue is the estimation of homographies between two different perspectives that hold an extensive set of abnormal data. A method to find such estimation is the random sampling consensus (RANSAC); in this, the goal is to maximize the number of matching points given a permissible error (Pe), according to a candidate model. However, those objectives are in conflict: a low Pe value increases the accuracy of the model but degrades its generalization ability that refers to the number of matching points that tolerate noisy data, whereas a high Pe value improves the noise tolerance of the model but adversely drives the process to false detections. This work considers the estimation process as a multiobjective optimization problem that seeks to maximize the number of matching points whereas Pe is simultaneously minimized. In order to solve the multiobjective formulation, two different evolutionary algorithms have been explored: the Nondominated Sorting Genetic Algorithm II (NSGA-II) and the Nondominated Sorting Differential Evolution (NSDE). Results considering acknowledged quality measures among original and transformed images over a well-known image benchmark show superior performance of the proposal than Random Sample Consensus algorithm.

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Thermoeconomic Optimization and Comparison of Plate-Fin Heat Exchangers Using Louver, Offset Strip, Triangular and Rectangular Fins Applied in 200 kW Microturbines

Journal of Heat Transfer ◽

10.1115/1.4036618 ◽

2017 ◽

Vol 139 (10) ◽

Cited By ~ 6

Author(s):

Peyman Maghsoudi ◽

Sadegh Sadeghi ◽

Pedram Hanafizadeh

Keyword(s):

Heat Exchangers ◽

Optimization Problem ◽

Net Present Value ◽

Optimal Solutions ◽

Counter Flow ◽

Nsga Ii ◽

Triangular Fin ◽

Offset Strip Fin ◽

Cycle Efficiency ◽

Nondominated Sorting

In this paper, four types of plate-fin heat exchangers applied in 200 kW microturbines are investigated. Multi-objective optimization algorithm, NSGA-II (nondominated sorting genetic algorithm (GA)), is employed to maximize the efficiency of the recuperator and minimize its total cost, simultaneously. Feasible ranges of pressure drop, Reynolds number, and recuperator efficiency are obtained according to a penalty function. The optimizations are conducted for rectangular fin, triangular fin, louver fin, and offset strip fin recuperators with cross and counter flow arrangements. The results of each optimization problem are presented as a set of designs, called “Pareto-optimal solutions.” Afterward, for the designs, cycle efficiency and net present value (NPV) are compared based on technical and economic criteria, respectively. Maximum cycle efficiency occurring in a recuperator with louver fin and counter flow arrangement is found to be 38.17%. Finally, the optimum designs are compared based on nondominated sorting concept leading to the optimal solutions.

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Hybrid QPSO-NNIA2 Algorithm for Multi-Objective Optimization Problem

International Journal of Pattern Recognition and Artificial Intelligence ◽

10.1142/s0218001419590250 ◽

2019 ◽

Vol 33 (08) ◽

pp. 1959025

Author(s):

Lan Zhang

Keyword(s):

Optimization Algorithm ◽

Optimization Problem ◽

Nearest Neighbor ◽

Superior Performance ◽

Optimal Solutions ◽

Multi Objective Optimization ◽

Nsga Ii ◽

Multi Objective ◽

Evolution Algebra ◽

Neighbor List

To improve the convergence and distribution of a multi-objective optimization algorithm, a hybrid multi-objective optimization algorithm, based on the quantum particle swarm optimization (QPSO) algorithm and adaptive ranks clone and neighbor list-based immune algorithm (NNIA2), is proposed. The contribution of this work is threefold. First, the vicinity distance was used instead of the crowding distance to update the archived optimal solutions in the QPSO algorithm. The archived optimal solutions are updated and maintained by using the dynamic vicinity distance based m-nearest neighbor list in the QPSO algorithm. Secondly, an adaptive dynamic threshold of unfitness function for constraint handling is introduced in the process. It is related to the evolution algebra and the feasible solution. Thirdly, a new metric called the distribution metric is proposed to depict the diversity and distribution of the Pareto optimal. In order to verify the validity and feasibility of the QPSO-NNIA2 algorithm, we compare it with the QPSO, NNIA2, NSGA-II, MOEA/D, and SPEA2 algorithms in solving unconstrained and constrained multi-objective problems. The simulation results show that the QPSO-NNIA2 algorithm achieves superior convergence and superior performance by three metrics compared to other algorithms.

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Multiobjective optimization of hard coating parameters designing for damping of the bladed disk

Proceedings of the Institution of Mechanical Engineers Part G Journal of Aerospace Engineering ◽

10.1177/0954410017703149 ◽

2017 ◽

Vol 232 (9) ◽

pp. 1609-1619 ◽

Cited By ~ 1

Author(s):

Yugang Chen ◽

Jingyu Zhai ◽

Qingkai Han

Keyword(s):

Pareto Front ◽

Engineering Application ◽

Front Surface ◽

Model Material ◽

Superior Performance ◽

Hard Coating ◽

Damping Capacity ◽

Nsga Ii ◽

Bladed Disk ◽

Design Variables

In this paper, the damping capacity and the structural influence of the hard coating on the given bladed disk are optimized by the non-dominated sorting genetic algorithm (NSGA-II) coupled with the Kriging surrogate model. Material and geometric parameters of the hard coating are taken as the design variables, and the loss factors, frequency variations and weight gain are considered as the objective functions. Results of the bi-objective optimization are obtained as curved line of Pareto front, and results of the triple-objective optimization are obtained as Pareto front surface with an obvious frontier. The results can give guidance to the designer, which can help to achieve more superior performance of hard coating in engineering application.

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Modeling and Optimizing the Multi-Objective Portfolio Optimization Problem with Trapezoidal Fuzzy Parameters

Mathematical and Computational Applications ◽

10.3390/mca26020036 ◽

2021 ◽

Vol 26 (2) ◽

pp. 36

Author(s):

Alejandro Estrada-Padilla ◽

Daniela Lopez-Garcia ◽

Claudia Gómez-Santillán ◽

Héctor Joaquín Fraire-Huacuja ◽

Laura Cruz-Reyes ◽

...

Keyword(s):

Steady State ◽

Portfolio Optimization ◽

Optimization Problem ◽

Solution Process ◽

Density Estimator ◽

Nsga Ii ◽

Spatial Spread ◽

Multi Objective ◽

Significant Difference ◽

Portfolio Optimization Problem

A common issue in the Multi-Objective Portfolio Optimization Problem (MOPOP) is the presence of uncertainty that affects individual decisions, e.g., variations on resources or benefits of projects. Fuzzy numbers are successful in dealing with imprecise numerical quantities, and they found numerous applications in optimization. However, so far, they have not been used to tackle uncertainty in MOPOP. Hence, this work proposes to tackle MOPOP’s uncertainty with a new optimization model based on fuzzy trapezoidal parameters. Additionally, it proposes three novel steady-state algorithms as the model’s solution process. One approach integrates the Fuzzy Adaptive Multi-objective Evolutionary (FAME) methodology; the other two apply the Non-Dominated Genetic Algorithm (NSGA-II) methodology. One steady-state algorithm uses the Spatial Spread Deviation as a density estimator to improve the Pareto fronts’ distribution. This research work’s final contribution is developing a new defuzzification mapping that allows measuring algorithms’ performance using widely known metrics. The results show a significant difference in performance favoring the proposed steady-state algorithm based on the FAME methodology.

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Elite Exploitation: A Combination of Mathematical Concept and EMO Approach for Multi-Objective Decision Making

Symmetry ◽

10.3390/sym13010136 ◽

2021 ◽

Vol 13 (1) ◽

pp. 136

Author(s):

Wenxiao Li ◽

Yushui Geng ◽

Jing Zhao ◽

Kang Zhang ◽

Jianxin Liu

Keyword(s):

Decision Making ◽

Optimization Problems ◽

Hybrid Genetic Algorithm ◽

Decision Makers ◽

Superior Performance ◽

Test Problems ◽

Mathematical Function ◽

Hyperbolic Tangent ◽

Nsga Ii ◽

Multi Objective

This paper explores the combination of a classic mathematical function named “hyperbolic tangent” with a metaheuristic algorithm, and proposes a novel hybrid genetic algorithm called NSGA-II-BnF for multi-objective decision making. Recently, many metaheuristic evolutionary algorithms have been proposed for tackling multi-objective optimization problems (MOPs). These algorithms demonstrate excellent capabilities and offer available solutions to decision makers. However, their convergence performance may be challenged by some MOPs with elaborate Pareto fronts such as CFs, WFGs, and UFs, primarily due to the neglect of diversity. We solve this problem by proposing an algorithm with elite exploitation strategy, which contains two parts: first, we design a biased elite allocation strategy, which allocates computation resources appropriately to elites of the population by crowding distance-based roulette. Second, we propose a self-guided fast individual exploitation approach, which guides elites to generate neighbors by a symmetry exploitation operator, which is based on mathematical hyperbolic tangent function. Furthermore, we designed a mechanism to emphasize the algorithm’s applicability, which allows decision makers to adjust the exploitation intensity with their preferences. We compare our proposed NSGA-II-BnF with four other improved versions of NSGA-II (NSGA-IIconflict, rNSGA-II, RPDNSGA-II, and NSGA-II-SDR) and four competitive and widely-used algorithms (MOEA/D-DE, dMOPSO, SPEA-II, and SMPSO) on 36 test problems (DTLZ1–DTLZ7, WGF1–WFG9, UF1–UF10, and CF1–CF10), and measured using two widely used indicators—inverted generational distance (IGD) and hypervolume (HV). Experiment results demonstrate that NSGA-II-BnF exhibits superior performance to most of the algorithms on all test problems.

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An Improved MOEA/D Based on Reference Distance for Software Project Portfolio Optimization

Complexity ◽

10.1155/2018/3051854 ◽

2018 ◽

Vol 2018 ◽

pp. 1-16 ◽

Cited By ~ 7

Author(s):

Jing Xiao ◽

Jing-Jing Li ◽

Xi-Xi Hong ◽

Min-Mei Huang ◽

Xiao-Min Hu ◽

...

Keyword(s):

Genetic Algorithm ◽

Evolutionary Algorithms ◽

Portfolio Optimization ◽

Optimization Problem ◽

Experimental Comparison ◽

Software Project ◽

Project Portfolio ◽

Multiobjective Evolutionary Algorithms ◽

Reference Distance ◽

Nondominated Sorting

As it is becoming extremely competitive in software industry, large software companies have to select their project portfolio to gain maximum return with limited resources under many constraints. Project portfolio optimization using multiobjective evolutionary algorithms is promising because they can provide solutions on the Pareto-optimal front that are difficult to be obtained by manual approaches. In this paper, we propose an improved MOEA/D (multiobjective evolutionary algorithm based on decomposition) based on reference distance (MOEA/D_RD) to solve the software project portfolio optimization problems with optimizing 2, 3, and 4 objectives. MOEA/D_RD replaces solutions based on reference distance during evolution process. Experimental comparison and analysis are performed among MOEA/D_RD and several state-of-the-art multiobjective evolutionary algorithms, that is, MOEA/D, nondominated sorting genetic algorithm II (NSGA2), and nondominated sorting genetic algorithm III (NSGA3). The results show that MOEA/D_RD and NSGA2 can solve the software project portfolio optimization problem more effectively. For 4-objective optimization problem, MOEA/D_RD is the most efficient algorithm compared with MOEA/D, NSGA2, and NSGA3 in terms of coverage, distribution, and stability of solutions.

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Shape optimization of egg-shaped sewer pipes based on the nondominated sorting genetic algorithm (NSGA-II)

Environmental Research ◽

10.1016/j.envres.2021.111999 ◽

2022 ◽

Vol 204 ◽

pp. 111999

Author(s):

Hanting Wu ◽

Yangrui Huang ◽

Lei Chen ◽

Yingjie Zhu ◽

Huaizheng Li

Keyword(s):

Genetic Algorithm ◽

Shape Optimization ◽

Nsga Ii ◽

Sewer Pipes ◽

Nondominated Sorting

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Multiobjective Optimization Methods for Congestion Management in Deregulated Power Systems

Journal of Electrical and Computer Engineering ◽

10.1155/2012/962402 ◽

2012 ◽

Vol 2012 ◽

pp. 1-8 ◽

Cited By ~ 6

Author(s):

K. Vijayakumar

Keyword(s):

Genetic Algorithm ◽

Power Systems ◽

Electricity Market ◽

Optimization Methods ◽

Evolutionary Programming ◽

Congestion Management ◽

Transmission Congestion ◽

Nsga Ii ◽

Line Overload ◽

Nondominated Sorting

Congestion management is one of the important functions performed by system operator in deregulated electricity market to ensure secure operation of transmission system. This paper proposes two effective methods for transmission congestion alleviation in deregulated power system. Congestion or overload in transmission networks is alleviated by rescheduling of generators and/or load shedding. The two objectives conflicting in nature (1) transmission line over load and (2) congestion cost are optimized in this paper. The multiobjective fuzzy evolutionary programming (FEP) and nondominated sorting genetic algorithm II methods are used to solve this problem. FEP uses the combined advantages of fuzzy and evolutionary programming (EP) techniques and gives better unique solution satisfying both objectives, whereas nondominated sorting genetic algorithm (NSGA) II gives a set of Pareto-optimal solutions. The methods propose an efficient and reliable algorithm for line overload alleviation due to critical line outages in a deregulated power markets. The quality and usefulness of the algorithm is tested on IEEE 30 bus system.

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A biobjective capacitated vehicle routing problem using metaheuristic ILS and decomposition

International Journal of Industrial Engineering Computations ◽

10.5267/j.ijiec.2021.2.002 ◽

2021 ◽

Vol 12 (3) ◽

pp. 293-304 ◽

Cited By ~ 1

Author(s):

Luis Fernando Galindres-Guancha ◽

Eliana Toro-Ocampo ◽

Ramón Gallego-Rendón

Keyword(s):

Approximate Method ◽

Vehicle Routing ◽

Real Life ◽

Minimum Cost ◽

Iterated Local Search ◽

Test Cases ◽

Nsga Ii ◽

Routing Problem ◽

Decomposition Approach ◽

Multiobjective Approach

Vehicle routing problems (VRPs) have usually been studied with a single objective function defined by the distances associated with the routing of vehicles. The central problem is to design a set of routes to meet the demands of customers at minimum cost. However, in real life, it is necessary to take into account other objective functions, such as social functions, which consider, for example, the drivers' workload balance. This has led to growth in both the formulation of multiobjective models and exact and approximate solution techniques. In this article, to verify the quality of the results, first, a mathematical model is proposed that takes into account both economic and work balance objectives simultaneously and is solved using an exact method based on the decomposition approach. This method is used to compare the accuracy of the proposed approximate method in test cases of medium mathematical complexity. Second, an approximate method based on the Iterated Local Search (ILS) metaheuristic and Decomposition (ILS/D) is proposed to solve the biobjective Capacitated VRP (bi-CVRP) using test cases of medium and high mathematical complexity. Finally, the nondominated sorting genetic algorithm (NSGA-II) approximate method is implemented to compare both medium- and high-complexity test cases with a benchmark. The obtained results show that ILS/D is a promising technique for solving VRPs with a multiobjective approach.

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Technical note: the caRamel R package for Automatic Calibration by Evolutionary Multi Objective Algorithm

10.5194/hess-2019-259 ◽

2019 ◽

Author(s):

Céline Monteil ◽

Fabrice Zaoui ◽

Nicolas Le Moine ◽

Frédéric Hendrickx

Keyword(s):

Stable Solution ◽

R Package ◽

Technical Note ◽

Main Function ◽

Nsga Ii ◽

Multiple Criteria Optimization ◽

Multi Objective ◽

Study Case ◽

Nondominated Sorting

Abstract. Environmental modelling is complex, and models often require the calibration of several parameters that are not directly evaluable from a physical quantity or a field measurement. The R package caRamel has been designed to easily implement a multi-objective optimizer in the R environment to calibrate these parameters. A multiobjective calibration allows to find a compromise between different goals by defining a set of optimal parameters. The algorithm is a hybrid of the Multiobjective Evolutionary Annealing Simplex method (MEAS) and the Nondominated Sorting Genetic Algorithm II (ε-NSGA-II algorithm). The optimizer was initially developed for the calibration of hydrological models but can be used for any environmental model. The main function of the package, caRamel(), requires to define a multi-objective calibration function as well as bounds on the variation of the underlying parameters to optimize. CaRamel is well adapted to complex modelling. As an example, caRamel converges quickly and has a stable solution after 5,000 model evaluations with robust results for a real study case of a hydrological problem with 8 parameters and 3 objectives of calibration. The comparison with another well-known optimizer (i.e. MCO, for Multiple Criteria Optimization) confirms the quality of the algorithm.

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