Journal articles: 'Nondominated set'

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Regan, Kevin, and Craig Boutilier. "Robust Policy Computation in Reward-Uncertain MDPs Using Nondominated Policies." Proceedings of the AAAI Conference on Artificial Intelligence 24, no. 1 (July 4, 2010): 1127–33. http://dx.doi.org/10.1609/aaai.v24i1.7740.

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The precise specification of reward functions for Markov decision processes (MDPs) is often extremely difficult, motivating research into both reward elicitation and the robust solution of MDPs with imprecisely specified reward (IRMDPs). We develop new techniques for the robust optimization of IRMDPs, using the minimax regret decision criterion, that exploit the set of nondominated policies, i.e., policies that are optimal for some instantiation of the imprecise reward function. Drawing parallels to POMDP value functions, we devise a Witness-style algorithm for identifying nondominated policies. We also examine several new algorithms for computing minimax regret using the nondominated set, and examine both practically and theoretically the impact of approximating this set. Our results suggest that a small subset of the nondominated set can greatly speed up computation, yet yield very tight approximations to minimax regret.

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Nyiam, Paschal B., and Abdellah Salhi. "A Comparison of Benson’s Outer Approximation Algorithm with an Extended Version of Multiobjective Simplex Algorithm." Advances in Operations Research 2021 (July 5, 2021): 1–11. http://dx.doi.org/10.1155/2021/1857030.

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The multiple objective simplex algorithm and its variants work in the decision variable space to find the set of all efficient extreme points of multiple objective linear programming (MOLP). Other approaches to the problem find either the entire set of all efficient solutions or a subset of them and also return the corresponding objective values (nondominated points). This paper presents an extension of the multiobjective simplex algorithm (MSA) to generate the set of all nondominated points and no redundant ones. This extended version is compared to Benson’s outer approximation (BOA) algorithm that also computes the set of all nondominated points of the problem. Numerical results on nontrivial MOLP problems show that the total number of nondominated points returned by the extended MSA is the same as that returned by BOA for most of the problems considered.

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Noghin, Vladimir D. "Estimation of the set of nondominated solutions." Numerical Functional Analysis and Optimization 12, no. 5-6 (January 1991): 507–15. http://dx.doi.org/10.1080/01630569108816446.

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Henig, M. I. "Characterizing the nondominated set by separable functions." Journal of Optimization Theory and Applications 59, no. 3 (December 1988): 423–44. http://dx.doi.org/10.1007/bf00940308.

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Noghin, Vladimir D. "Upper estimate for a fuzzy set of nondominated solutions." Fuzzy Sets and Systems 67, no. 3 (November 1994): 303–15. http://dx.doi.org/10.1016/0165-0114(94)90258-5.

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Pereira, Javier, Broderick Crawford, Fernando Paredes, and Ricardo Soto. "A Bicriteria Approach Identifying Nondominated Portfolios." Journal of Applied Mathematics 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/957108.

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We explore a portfolio constructive model, formulated in terms of satisfaction of a given set of technical requirements, with the minimum number of projects and minimum redundancy. An algorithm issued from robust portfolio modeling is adapted to a vector model, modifying the dominance condition as convenient, in order to find the set of nondominated portfolios, as solutions of a bicriteria integer linear programming problem. In order to improve the former algorithm, a process finding an optimal solution of a monocriteria version of this problem is proposed, which is further used as a first feasible solution aiding to find nondominated solutions more rapidly. Next, a sorting process is applied on the input data or information matrix, which is intended to prune nonfeasible solutions early in the constructive algorithm. Numerical examples show that the optimization and sorting processes both improve computational efficiency of the original algorithm. Their limits are also shown on certain complex instances.

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Abd Elazeem, Abd Elazeem M., Abd Allah A. Mousa, Mohammed A. El-Shorbagy, Sayed K. Elagan, and Yousria Abo-Elnaga. "Detecting All Non-Dominated Points for Multi-Objective Multi-Index Transportation Problems." Sustainability 13, no. 3 (January 28, 2021): 1372. http://dx.doi.org/10.3390/su13031372.

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Multi-dimensional transportation problems denoted as multi-index are considered as the extension of classical transportation problems and are appropriate practical modeling for solving real–world problems with multiple supply, multiple demand, as well as different modes of transportation demands or delivering different kinds of commodities. This paper presents a method for detecting the complete nondominated set (efficient solutions) of multi-objective four-index transportation problems. The proposed approach implements weighted sum method to convert multi-objective four-index transportation problem into a single objective four-index transportation problem, that can then be decomposed into a set of two-index transportation sub-problems. For each two-index sub-problem, parametric analysis was investigated to determine the range of the weights values that keep the efficient solution unchanged, which enable the decision maker to detect the set of all nondominated solutions for the original multi-objective multi-index transportation problem, and also to find the stability set of the first kind for each efficient solution. Finally, an illustrative example is presented to illustrate the efficiency and robustness of the proposed approach. The results demonstrate the effectiveness and robustness for the proposed approach to detect the set of all nondominated solutions.

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Ginanjar, Rikip, and Nur Hadisukmana. "An Algorithm to construct nondominated k-coteries." Indonesian Journal of Electrical Engineering and Computer Science 18, no. 2 (May 1, 2020): 953. http://dx.doi.org/10.11591/ijeecs.v18.i2.pp953-960.

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<p><span>One of the solution in solving k mutual exclusion problem is the concept of k-coterie. A k-coterie under a set S is a set of subsets of S or quorums such that any k + 1 quorums, there are at least two quorums intersect each other. The k mutual exclusion problern is the problem of managing processes in such a way that at most k processes can enter their critical sections simultaneously. Nondominated k-coteries are more resilient to network and site failures than doninated k-coteries; that is the availability and reliability of a distributed system is better if nondominated k-coteries are used. Algorithms to construct k-coteries have been proposed, unfortunately they have some restrictions, especially in constructing nondominated k-coteries. The restrictions are due to the combination of N, the number of nodes in a distributed system, and k, the number of processes allowed to enter their critical sections simultaneously. To solve this problem, this paper proposes an algorithm to construct nondominated k-coteries for all combination of N and k.</span></p>

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Qu, Dan, Xianfeng Ding, and Hongmei Wang. "An Improved Multiobjective Algorithm: DNSGA2-PSA." Journal of Robotics 2018 (September 2, 2018): 1–11. http://dx.doi.org/10.1155/2018/9697104.

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In general, the proximities to a certain diversity along the front and the Pareto front have the equal importance for solving multiobjective optimization problems (MOPs). However, most of the existing evolutionary algorithms give priority to the proximity over the diversity. To improve the diversity and decrease execution time of the nondominated sorting genetic algorithm II (NSGA-II), an improved algorithm is presented in this paper, which adopts a new vector ranking scheme to decrease the whole runtime and utilize Part and Select Algorithm (PSA) to maintain the diversity. In this algorithm, a more efficient implementation of nondominated sorting, namely, dominance degree approach for nondominated sorting (DDA-NS), is presented. Moreover, an improved diversity preservation mechanism is proposed to select a well-diversified set out of an arbitrary given set. By embedding PSA and DDA-NS into NSGA-II, denoted as DNSGA2-PSA, the whole runtime of the algorithm is decreased significantly and the exploitation of diversity is enhanced. The computational experiments show that the combination of both (DDA-NS, PSA) to NSGA-II is better than the isolated use cases, and DNSGA2-PSA still performs well in the high-dimensional cases.

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Savsani, Vimal, Vivek Patel, Bhargav Gadhvi, and Mohamed Tawhid. "Pareto Optimization of a Half Car Passive Suspension Model Using a Novel Multiobjective Heat Transfer Search Algorithm." Modelling and Simulation in Engineering 2017 (2017): 1–17. http://dx.doi.org/10.1155/2017/2034907.

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Most of the modern multiobjective optimization algorithms are based on the search technique of genetic algorithms; however the search techniques of other recently developed metaheuristics are emerging topics among researchers. This paper proposes a novel multiobjective optimization algorithm named multiobjective heat transfer search (MOHTS) algorithm, which is based on the search technique of heat transfer search (HTS) algorithm. MOHTS employs the elitist nondominated sorting and crowding distance approach of an elitist based nondominated sorting genetic algorithm-II (NSGA-II) for obtaining different nondomination levels and to preserve the diversity among the optimal set of solutions, respectively. The capability in yielding a Pareto front as close as possible to the true Pareto front of MOHTS has been tested on the multiobjective optimization problem of the vehicle suspension design, which has a set of five second-order linear ordinary differential equations. Half car passive ride model with two different sets of five objectives is employed for optimizing the suspension parameters using MOHTS and NSGA-II. The optimization studies demonstrate that MOHTS achieves the better nondominated Pareto front with the widespread (diveresed) set of optimal solutions as compared to NSGA-II, and further the comparison of the extreme points of the obtained Pareto front reveals the dominance of MOHTS over NSGA-II, multiobjective uniform diversity genetic algorithm (MUGA), and combined PSO-GA based MOEA.

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Ceyhan, Gökhan, Murat Köksalan, and Banu Lokman. "Finding a representative nondominated set for multi-objective mixed integer programs." European Journal of Operational Research 272, no. 1 (January 2019): 61–77. http://dx.doi.org/10.1016/j.ejor.2018.06.012.

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Wu, Hsien-Chung. "Solving Fuzzy Optimization Problems Using Shapley Values and Evolutionary Algorithms." Mathematics 11, no. 24 (December 5, 2023): 4871. http://dx.doi.org/10.3390/math11244871.

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The fusion of evolutionary algorithms and the solution concepts of cooperative game theory is proposed in this paper to solve the fuzzy optimization problems. The original fuzzy optimization problem is transformed into a scalar optimization problem by assigning some suitable coefficients. The assignment of those coefficients is frequently determined by the decision-makers via their subjectivity, which may cause some biases. In order to avoid these subjective biases, a cooperative game is formulated by considering the α-level functions of the fuzzy objective function. Using the Shapley values of this formulated cooperative game, the suitable coefficients can be reasonably set up. Under these settings, the transformed scalar optimization problem is solved to obtain the nondominated solution, which will depend on the coefficients. In other words, we shall obtain a bunch of nondominated solutions depending on the coefficients. Finally, the evolutionary algorithms are invoked to find the best nondominated solution by evolving the coefficients.

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Liu, Yi, Jun Guo, Huaiwei Sun, Wei Zhang, Yueran Wang, and Jianzhong Zhou. "Multiobjective Optimal Algorithm for Automatic Calibration of Daily Streamflow Forecasting Model." Mathematical Problems in Engineering 2016 (2016): 1–13. http://dx.doi.org/10.1155/2016/8215308.

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Single-objection function cannot describe the characteristics of the complicated hydrologic system. Consequently, it stands to reason that multiobjective functions are needed for calibration of hydrologic model. The multiobjective algorithms based on the theory of nondominate are employed to solve this multiobjective optimal problem. In this paper, a novel multiobjective optimization method based on differential evolution with adaptive Cauchy mutation and Chaos searching (MODE-CMCS) is proposed to optimize the daily streamflow forecasting model. Besides, to enhance the diversity performance of Pareto solutions, a more precise crowd distance assigner is presented in this paper. Furthermore, the traditional generalized spread metric (SP) is sensitive with the size of Pareto set. A novel diversity performance metric, which is independent of Pareto set size, is put forward in this research. The efficacy of the new algorithm MODE-CMCS is compared with the nondominated sorting genetic algorithm II (NSGA-II) on a daily streamflow forecasting model based on support vector machine (SVM). The results verify that the performance of MODE-CMCS is superior to the NSGA-II for automatic calibration of hydrologic model.

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Altinoz, O. Tolga, and A. Egemen Yilmaz. "A Population Size Reduction Approach for Nondominated Sorting-Based Optimization Algorithms." International Journal of Computational Intelligence and Applications 16, no. 01 (March 2017): 1750005. http://dx.doi.org/10.1142/s1469026817500055.

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The solution set of any multi-objective optimization problem can be expressed as an approximation set of Pareto front. The number of solution candidates in this set could be large enough to cover the entire Pareto front as a general belief. However, among the sufficiently close points on the objective space, almost same accurate solutions can obtain. Hence, in this set, it is possible to eliminate some of the solutions without detriment to the overall performance. Therefore, in this research, the authors propose a population size reduction method which systematically reduced the population size based on the distance and angle relations between any consecutive solutions. The results are evaluated based on two-objective benchmark problems and compared with the results of NSGA-II algorithm with respect to three different performance evaluation metrics.

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Liu, Banteng, Junjie Lu, Yourong Chen, Ping Sun, Kehua Zhao, Meng Han, Rengong Zhang, and Zegao Yin. "AI-Driven Multiobjective Scheduling Algorithm of Flood Control Materials Based on Pareto Artificial Bee Colony." Wireless Communications and Mobile Computing 2021 (June 22, 2021): 1–15. http://dx.doi.org/10.1155/2021/5557543.

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Considering the competition between rescue points, we use artificial intelligence (AI) driven Internet of Thing (IoT) and regional material storage data to propose a multiobjective scheduling algorithm of flood control materials based on Pareto artificial bee colony (MSA_PABC). To address the scheduling of flood control materials, the multiple types of flood control materials, the multiple disaster sites, and entertain both emergency and fairness of rescue need to be considered comprehensively. The MSA_PABC has the constraints such as storage quantity constraint of warehouse materials, material demand constraint, and maximum transportation distance of flood control materials. We establish the scheduling optimization model of flood control materials for each disaster rescue point and the total scheduling optimization model for all flood control materials. Then, MSA_PABC uses the modified Pareto artificial bee colony algorithm to solve the multiobjective models. Three types of initialization strategies are proposed to calculate the fitness of each rescue point and the overall evaluation value of the food source. We propose the employ bee operations such as niche technology and local search of the variable neighborhood, the onlooker bee operations such as Pareto nondominated sorting and crossover operation, the scout bee operations such as maximum evolutionary threshold, and end elimination mechanism. Finally, our proposed solution obtains the nondominated solution set and its optimal solution. The experimental results show that no matter how the number of rescue points changes, MSA_PABC can find the nondominated solution set and optimal solution quickly. It improves the convergence rate of MSA_PABC and material satisfaction rate. Our solution also reduces the average maximum transportation distance, the standard deviation of maximum transportation distance, and the standard deviation of material satisfaction rate. The evaluation also demonstrates MSA_PABC outperforms the state-of-arts such as ABC (artificial bee colony), NSGA2 (nondominated sorting genetic algorithm 2), and MOPSO (multiobjective particle swarm optimization).

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Zhang, Jingling, Wanliang Wang, Yanwei Zhao, and Carlo Cattani. "Multiobjective Quantum Evolutionary Algorithm for the Vehicle Routing Problem with Customer Satisfaction." Mathematical Problems in Engineering 2012 (2012): 1–19. http://dx.doi.org/10.1155/2012/879614.

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The multiobjective vehicle routing problem considering customer satisfaction (MVRPCS) involves the distribution of orders from several depots to a set of customers over a time window. This paper presents a self-adaptive grid multi-objective quantum evolutionary algorithm (MOQEA) for the MVRPCS, which takes into account customer satisfaction as well as travel costs. The degree of customer satisfaction is represented by proposing an improved fuzzy due-time window, and the optimization problem is modeled as a mixed integer linear program. In the MOQEA, nondominated solution set is constructed by the Challenge Cup rules. Moreover, an adaptive grid is designed to achieve the diversity of solution sets; that is, the number of grids in each generation is not fixed but is automatically adjusted based on the distribution of the current generation of nondominated solution set. In the study, the MOQEA is evaluated by applying it to classical benchmark problems. Results of numerical simulation and comparison show that the established model is valid and the MOQEA is effective for MVRPCS.

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Srinivas, N., and Kalyanmoy Deb. "Muiltiobjective Optimization Using Nondominated Sorting in Genetic Algorithms." Evolutionary Computation 2, no. 3 (September 1994): 221–48. http://dx.doi.org/10.1162/evco.1994.2.3.221.

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In trying to solve multiobjective optimization problems, many traditional methods scalarize the objective vector into a single objective. In those cases, the obtained solution is highly sensitive to the weight vector used in the scalarization process and demands that the user have knowledge about the underlying problem. Moreover, in solving multiobjective problems, designers may be interested in a set of Pareto-optimal points, instead of a single point. Since genetic algorithms (GAs) work with a population of points, it seems natural to use GAs in multiobjective optimization problems to capture a number of solutions simultaneously. Although a vector evaluated GA (VEGA) has been implemented by Schaffer and has been tried to solve a number of multiobjective problems, the algorithm seems to have bias toward some regions. In this paper, we investigate Goldberg's notion of nondominated sorting in GAs along with a niche and speciation method to find multiple Pareto-optimal points simultaneously. The proof-of-principle results obtained on three problems used by Schaffer and others suggest that the proposed method can be extended to higher dimensional and more difficult multiobjective problems. A number of suggestions for extension and application of the algorithm are also discussed.

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Knowles, Joshua D., and David W. Corne. "Approximating the Nondominated Front Using the Pareto Archived Evolution Strategy." Evolutionary Computation 8, no. 2 (June 2000): 149–72. http://dx.doi.org/10.1162/106365600568167.

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We introduce a simple evolution scheme for multiobjective optimization problems, called the Pareto Archived Evolution Strategy (PAES). We argue that PAES may represent the simplest possible nontrivial algorithm capable of generating diverse solutions in the Pareto optimal set. The algorithm, in its simplest form, is a (1+1) evolution strategy employing local search but using a reference archive of previously found solutions in order to identify the approximate dominance ranking of the current and candidate solution vectors. (1+1)-PAES is intended to be a baseline approach against which more involved methods may be compared. It may also serve well in some real-world applications when local search seems superior to or competitive with population-based methods. We introduce (1+λ) and (μ+λ) variants of PAES as extensions to the basic algorithm. Six variants of PAES are compared to variants of the Niched Pareto Genetic Algorithm and the Nondominated Sorting Genetic Algorithm over a diverse suite of six test functions. Results are analyzed and presented using techniques that reduce the attainment surfaces generated from several optimization runs into a set of univariate distributions. This allows standard statistical analysis to be carried out for comparative purposes. Our results provide strong evidence that PAES performs consistently well on a range of multiobjective optimization tasks.

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Wang, Ruihua. "An Improved Nondominated Sorting Genetic Algorithm for Multiobjective Problem." Mathematical Problems in Engineering 2016 (2016): 1–7. http://dx.doi.org/10.1155/2016/1519542.

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In this paper, an improved NSGA2 algorithm is proposed, which is used to solve the multiobjective problem. For the original NSGA2 algorithm, the paper made one improvement: joining the local search strategy into the NSGA2 algorithm. After each iteration calculation of the NSGA2 algorithm, a kind of local search strategy is performed in the Pareto optimal set to search better solutions, such that the NSGA2 algorithm can gain a better local search ability which is helpful to the optimization process. Finally, the proposed modified NSGA2 algorithm (MNSGA2) is simulated in the two classic multiobjective problems which is called KUR problem and ZDT3 problem. The calculation results show the modified NSGA2 outperforms the original NSGA2, which indicates that the improvement strategy is helpful to improve the algorithm.

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Valipour, E., M. A. Yaghoobi, and M. Mashinchi. "An approximation to the nondominated set of a multiobjective linear fractional programming problem." Optimization 65, no. 8 (June 3, 2016): 1539–52. http://dx.doi.org/10.1080/02331934.2016.1180387.

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Stanojević, Milan, Mirko Vujošević, and Bogdana Stanojević. "On the cardinality of the nondominated set of multi-objective combinatorial optimization problems." Operations Research Letters 41, no. 2 (March 2013): 197–200. http://dx.doi.org/10.1016/j.orl.2013.01.006.

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Shao, Lizhen, and Matthias Ehrgott. "Approximating the nondominated set of an MOLP by approximately solving its dual problem." Mathematical Methods of Operations Research 68, no. 3 (January 25, 2008): 469–92. http://dx.doi.org/10.1007/s00186-007-0194-5.

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Dai, Cai, and Xiujuan Lei. "A Decomposition-Based Multiobjective Evolutionary Algorithm with Adaptive Weight Adjustment." Complexity 2018 (September 12, 2018): 1–20. http://dx.doi.org/10.1155/2018/1753071.

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Recently, decomposition-based multiobjective evolutionary algorithms have good performances in the field of multiobjective optimization problems (MOPs) and have been paid attention by many scholars. Generally, a MOP is decomposed into a number of subproblems through a set of weight vectors with good uniformly and aggregate functions. The main role of weight vectors is to ensure the diversity and convergence of obtained solutions. However, these algorithms with uniformity of weight vectors cannot obtain a set of solutions with good diversity on some MOPs with complex Pareto optimal fronts (PFs) (i.e., PFs with a sharp peak or low tail or discontinuous PFs). To deal with this problem, an improved decomposition-based multiobjective evolutionary algorithm with adaptive weight adjustment (IMOEA/DA) is proposed. Firstly, a new method based on uniform design and crowding distance is used to generate a set of weight vectors with good uniformly. Secondly, according to the distances of obtained nondominated solutions, an adaptive weight vector adjustment strategy is proposed to redistribute the weight vectors of subobjective spaces. Thirdly, a selection strategy is used to help each subobjective space to obtain a nondominated solution (if have). Comparing with six efficient state-of-the-art algorithms, for example, NSGAII, MOEA/D, MOEA/D-AWA, EMOSA, RVEA, and KnEA on some benchmark functions, the proposed algorithm is able to find a set of solutions with better diversity and convergence.

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Duan, Lini, Yuanyuan Liu, Haiyan Li, Kyung-Hye Park, and Kerang Cao. "Nondominated Sorting Differential Evolution Algorithm to Solve the Biobjective Multi-AGV Routing Problem in Hazardous Chemicals Warehouse." Mathematical Problems in Engineering 2022 (September 16, 2022): 1–20. http://dx.doi.org/10.1155/2022/3785039.

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For the multiple automated guided vehicle (multi-AGV) routing problems in the warehousing link of logistics, where the optimization objective is to minimize both the number of AGVs used and the maximum pickup time simultaneously, a nondominant sorting differential evolution (NSDE) algorithm is proposed. In the encoding and decoding stages, the pickup point area is divided. AGVs are allocated to each region according to the proposed rule based on avoiding duplicate paths. Meanwhile, the pickup points within the region can be adjusted to optimize the pickup paths and improve the pickup efficiency. The fast nondominated sorting method and elitist selection strategy in the nondominated sorting genetic algorithm II (NSGA-II) are introduced into the differential evolution algorithm, which sorts all the regions to obtain the best Pareto solution set. Lastly, the domination of the proposed NSDE algorithm in Pareto frontier evaluation indicators is verified by some numerical experiments.

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Rajesh, Kummari, and N. Visali. "Hybrid method for achieving Pareto front on economic emission dispatch." International Journal of Electrical and Computer Engineering (IJECE) 10, no. 4 (August 1, 2020): 3358. http://dx.doi.org/10.11591/ijece.v10i4.pp3358-3366.

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In this paper hybrid method, Modified Nondominated Sorted Genetic Algorithm (MNSGA-II) and Modified Population Variant Differential Evolution(MPVDE) have been placed in effect in achieving the best optimal solution of Multiobjective economic emission load dispatch optimization problem. In this technique latter, one is used to enforce the assigned percent of the population and the remaining with the former one. To overcome the premature convergence in an optimization problem diversity preserving operator is employed, from the tradeoff curve the best optimal solution is predicted using fuzzy set theory. This methodology validated on IEEE 30 bus test system with six generators, IEEE 118 bus test system with fourteen generators and with a forty generators test system. The solutions are dissimilitude with the existing metaheuristic methods like Strength Pareto Evolutionary Algorithm-II, Multiobjective differential evolution, Multi-objective Particle Swarm optimization, Fuzzy clustering particle swarm optimization, Nondominated sorting genetic algorithm-II.

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Korhonen, P., and J. Karaivanova. "An algorithm for projecting a reference direction onto the nondominated set of given points." IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans 29, no. 5 (1999): 429–35. http://dx.doi.org/10.1109/3468.784168.

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Vijayakumar, K. "Multiobjective Optimization Methods for Congestion Management in Deregulated Power Systems." Journal of Electrical and Computer Engineering 2012 (2012): 1–8. http://dx.doi.org/10.1155/2012/962402.

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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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Guo, Xiaofang, and Xiaoli Wang. "A Novel Objective Grouping Evolutionary Algorithm for Many-Objective Optimization Problems." International Journal of Pattern Recognition and Artificial Intelligence 34, no. 06 (September 24, 2019): 2059018. http://dx.doi.org/10.1142/s0218001420590181.

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The thorniest difficulties for multi-objective evolutionary algorithms (MOEAs) handling many-objective optimization problems (MaOPs) are the inefficiency of selection operators and high computational cost. To alleviate such difficulties and simplify the MaOPs, objective reduction algorithms have been proposed to remove the redundant objectives during the search process. However, those algorithms can only be applicable to specific problems with redundant objectives. Worse still, the Pareto solutions obtained by reduced objective set may not be the Pareto solutions of the original MaOPs. In this paper, we present a novel objective grouping evolutionary algorithm (OGEA) for general MaOPs. First, by dividing original objective set into several overlapping lower-dimensional subsets in terms of interdependence correlation information, we aim to separate the MaOPs into a number of sub-problems so that each of them can be able to preserve as much dominance structure in the original objective set as possible. Subsequently, we employ the nondominated sorting genetic algorithm II (NSGA-II) to generate Pareto solutions. Besides, instead of nondominated sorting on the whole population, a novel dual selection mechanism is proposed to choose individuals either having high ranks in subspaces or locating sparse region in the objective space for better proximity and diversity. Finally, we compare the proposed strategy with the other two classical space partition methods on benchmark DTLZ5 (I, M), DTLZ2 and a practical engineering problem. Numerical results show the proposed objective grouping algorithm can preserve more dominance structure in original objective set and achieve better quality of Pareto solutions.

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Huque, Ziaul, Ghizlane Zemmouri, Donald Harby, and Raghava Kommalapati. "Optimization of Wind Turbine Airfoil Using Nondominated Sorting Genetic Algorithm and Pareto Optimal Front." International Journal of Chemical Engineering 2012 (2012): 1–9. http://dx.doi.org/10.1155/2012/193021.

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A Computational Fluid Dynamics (CFD) and response surface-based multiobjective design optimization were performed for six different 2D airfoil profiles, and the Pareto optimal front of each airfoil is presented. FLUENT, which is a commercial CFD simulation code, was used to determine the relevant aerodynamic loads. The Lift Coefficient (CL) and Drag Coefficient (CD) data at a range of 0°to 12°angles of attack (α) and at three different Reynolds numbers (Re=68,459, 479, 210, and 958, 422) for all the six airfoils were obtained. Realizablek-εturbulence model with a second-order upwind solution method was used in the simulations. The standard least square method was used to generate response surface by the statistical code JMP. Elitist Non-dominated Sorting Genetic Algorithm (NSGA-II) was used to determine the Pareto optimal set based on the response surfaces. Each Pareto optimal solution represents a different compromise between design objectives. This gives the designer a choice to select a design compromise that best suits the requirements from a set of optimal solutions. The Pareto solution set is presented in the form of a Pareto optimal front.

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Sörensen, Kenneth, and Johan Springael. "Progressive Multi-Objective Optimization." International Journal of Information Technology & Decision Making 13, no. 05 (September 2014): 917–36. http://dx.doi.org/10.1142/s0219622014500308.

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This paper introduces progressive multi-objective optimization (PMOO), a novel technique to include the decision maker's preferences into the multi-objective optimization process. PMOO integrates a well-known method for multi-criteria decision making (PROMETHEE) into a simple multi-objective metaheuristic by maintaining and updating a small reference archive of nondominated solutions throughout the search. By applying this novel technique to a set of instances of the multi-objective knapsack problem, the superiority of PMOO over the commonly accepted sequential approach of generating a Pareto set approximation first and selecting a single solution afterwards is demonstrated.

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Yang, Zhen, Deyun Zhou, Weiren Kong, Haiyin Piao, Kai Zhang, and Yiyang Zhao. "Nondominated Maneuver Strategy Set With Tactical Requirements for a Fighter Against Missiles in a Dogfight." IEEE Access 8 (2020): 117298–312. http://dx.doi.org/10.1109/access.2020.3004864.

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Trawinski, Krzysztof, Manuel Chica, David P. Pancho, Sergio Damas, and Oscar Cordon. "moGrams: A Network-Based Methodology for Visualizing the Set of Nondominated Solutions in Multiobjective Optimization." IEEE Transactions on Cybernetics 48, no. 2 (February 2018): 474–85. http://dx.doi.org/10.1109/tcyb.2016.2642886.

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Huang, Weichao, Ganggang Zhang, and Jing Wang. "Multiobjective Optimization of Process Parameters of Silicon Single Crystal Growth." Wireless Communications and Mobile Computing 2022 (July 27, 2022): 1–10. http://dx.doi.org/10.1155/2022/5312590.

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In order to obtain higher quality silicon single crystal, a hybrid strategy for modeling of Czochralski silicon crystal growth and optimizing of process parameters is presented in the paper. The hybrid strategy includes the computational fluid dynamics (CFD) method, neural network of group method of data handing (GMDH), and improved nondominated sorting genetic algorithm II (NSGA-II). The shape variable of solid-liquid interface h and the defect evaluation criteria V / G are set to objective functions according to engineering experience and process requirement. The polynomial of the objective functions is produced by GMDH and CFD. Ultimately, an improved elitist strategy and crowding distance NSGA-II is proposed in the paper to obtain the Pareto optimum solution by the objective functions identified by the GMDH. Compared with other optimization algorithms, the improved NSGA-II can increase the lateral diversity and the uniform distribution of the nondominated solutions. Engineering validation proved that the proposed hybrid strategy can effectively solve the complex uncertain multiobjective optimization problem of system and provides a new method for obtaining high-quality crystal growth process parameters.

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Zhang, Qian, Jinjin Ding, Weixiang Shen, Jinhui Ma, and Guoli Li. "Multiobjective Particle Swarm Optimization for Microgrids Pareto Optimization Dispatch." Mathematical Problems in Engineering 2020 (March 25, 2020): 1–13. http://dx.doi.org/10.1155/2020/5695917.

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Multiobjective optimization (MOO) dispatch for microgrids (MGs) can achieve many benefits, such as minimized operation cost, greenhouse gas emission reduction, and enhanced reliability of service. In this paper, a MG with the PV-battery-diesel system is introduced to establish its characteristic and economic models. Based on the models and three objectives, the constrained MOO problem is formulated. Then, an advanced multiobjective particle swarm optimization (MOPSO) algorithm is proposed to obtain Pareto optimization dispatch for MGs. The combination of archive maintenance and Pareto selection enables the MOPSO algorithm to maintain enough nondominated solutions and seek Pareto frontiers. The final trade-off solutions are decided based on the fuzzy set. The benchmark function tests and simulation results demonstrate that the proposed MOPSO algorithm has better searching ability than nondominated sorting genetic algorithm-II (NSGA-II), which is widely used in generation dispatch for MGs. The proposed method can efficiently offer more Pareto solutions and find a trade-off one to simultaneously achieve three benefits: minimized operation cost, reduced environmental cost, and maximized reliability of service.

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Wiecek, Margaret M. "Advances in Cone-Based Preference Modeling for Decision Making with Multiple Criteria." Decision Making in Manufacturing and Services 1, no. 2 (October 11, 2007): 153–73. http://dx.doi.org/10.7494/dmms.2007.1.2.153.

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Decision making with multiple criteria requires preferences elicited from the decision maker to determine a solution set. Models of preferences, that follow upon the concept of nondominated solutions introduced by Yu (1974), are presented and compared within a unified framework of cones. Polyhedral and nonpolyhedral, convex and nonconvex, translated, and variable cones are used to model different types of preferences. Common mathematical properties of the preferences are discussed. The impact of using these preferences in decision making is emphasized.

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Garcia-Bernabeu, A., J. V. Salcedo, A. Hilario, D. Pla-Santamaria, and Juan M. Herrero. "Computing the Mean-Variance-Sustainability Nondominated Surface by ev-MOGA." Complexity 2019 (December 11, 2019): 1–12. http://dx.doi.org/10.1155/2019/6095712.

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Despite the widespread use of the classical bicriteria Markowitz mean-variance framework, a broad consensus is emerging on the need to include more criteria for complex portfolio selection problems. Sustainable investing, also called socially responsible investment, is becoming a mainstream investment practice. In recent years, some scholars have attempted to include sustainability as a third criterion to better reflect the individual preferences of those ethical or green investors who are willing to combine strong financial performance with social benefits. For this purpose, new computational methods for optimizing this complex multiobjective problem are needed. Multiobjective evolutionary algorithms (MOEAs) have been recently used for portfolio selection, thus extending the mean-variance methodology to obtain a mean-variance-sustainability nondominated surface. In this paper, we apply a recent multiobjective genetic algorithm based on the concept of ε-dominance called ev-MOGA. This algorithm tries to ensure convergence towards the Pareto set in a smart distributed manner with limited memory resources. It also adjusts the limits of the Pareto front dynamically and prevents solutions belonging to the ends of the front from being lost. Moreover, the individual preferences of socially responsible investors could be visualised using a novel tool, known as level diagrams, which helps investors better understand the range of values attainable and the tradeoff between return, risk, and sustainability.

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Bergman, David, Merve Bodur, Carlos Cardonha, and Andre A. Cire. "Network Models for Multiobjective Discrete Optimization." INFORMS Journal on Computing 34, no. 2 (March 2022): 990–1005. http://dx.doi.org/10.1287/ijoc.2021.1066.

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This paper provides a novel framework for solving multiobjective discrete optimization problems with an arbitrary number of objectives. Our framework represents these problems as network models, in that enumerating the Pareto frontier amounts to solving a multicriteria shortest-path problem in an auxiliary network. We design techniques for exploiting network models in order to accelerate the identification of the Pareto frontier, most notably a number of operations to simplify the network by removing nodes and arcs while preserving the set of nondominated solutions. We show that the proposed framework yields orders-of-magnitude performance improvements over existing state-of-the-art algorithms on five problem classes containing both linear and nonlinear objective functions. Summary of Contribution: Multiobjective optimization has a long history of research with applications in several domains. Our paper provides an alternative modeling and solution approach for multiobjective discrete optimization problems by leveraging graphical structures. Specifically, we encode the decision space of a problem as a layered network and propose graph reduction operators to preserve only solutions whose image are part of the Pareto frontier. The nondominated solutions can then be extracted through shortest-path algorithms on such a network. Numerical results comparing our method with state-of-the-art approaches on several problem classes, including the knapsack, set covering, and the traveling salesperson problem (TSP), suggest orders-of-magnitude runtime speed-ups for exactly enumerating the Pareto frontier, especially when the number of objective functions grows.

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Yeung, S. H., and K. F. Man. "A New Jumping Genes Paradigm for an E-Shaped Folded Patch Feed Antenna Design." International Journal of Microwave Science and Technology 2007 (September 20, 2007): 1–10. http://dx.doi.org/10.1155/2007/10672.

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A novel evolutionary computing algorithm, namely, jumping genes evolutionary algorithm (JGEA) is used for the optimization of antenna designs. This scheme incorporates with a multiobjective strategy that enables the gene mobility within the same chromosome, or even to a different chromosome. This type of horizontal gene movement causes the genes to find the suitable locations to achieve the necessary building blocks in such a way that the quality of nondominated solutions and/or the Pareto-optimal solutions can be enhanced. This new scheme is robust and provides outputs in speed and accuracy. It also generates a range of widespread extreme solutions. The design of an E-shaped patch antenna was adopted for the purpose of design demonstration. An antenna structure with 91% impedance bandwidth for a frequency range of 3.6–9.6 GHz was selected amongst the nondominated solutions set for the hardware fabrication. Its measured performances both for impedance bandwidth and frequency range were in good agreement with the simulated solution. The cross-polarized field was found to be small in comparison, and the copolarized field can sustain the broadside radiation pattern over the frequency band. This methodology of optimization can be of an alternative approach for antenna design.

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Osuna-Enciso, Valentín, Erik Cuevas, Diego Oliva, Virgilio Zúñiga, Marco Pérez-Cisneros, and Daniel Zaldívar. "A Multiobjective Approach to Homography Estimation." Computational Intelligence and Neuroscience 2016 (2016): 1–12. http://dx.doi.org/10.1155/2016/3629174.

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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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Arana-Jiménez, Manuel, and Carmen Sánchez-Gil. "On generating the set of nondominated solutions of a linear programming problem with parameterized fuzzy numbers." Journal of Global Optimization 77, no. 1 (October 24, 2019): 27–52. http://dx.doi.org/10.1007/s10898-019-00841-7.

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Xie, Yuan. "Fuzzy Parallel Machines Scheduling Problem Based on Genetic Algorithm." Advanced Materials Research 204-210 (February 2011): 856–61. http://dx.doi.org/10.4028/www.scientific.net/amr.204-210.856.

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A kind of unrelated parallel machines scheduling problem is discussed. The memberships of fuzzy due dates denote the grades of satisfaction with respect to completion times with jobs. Objectives of scheduling are to maximize the minimum grade of satisfaction while makespan is minimized in the meantime. Two kind of genetic algorithms are employed to search optimal solution set of the problem. Both Niched Pareto Genetic Algorithm (NPGA) and Nondominated Sorting Genetic Algorithm (NSGA-II) can find the Pareto optimal solutions. Numerical simulation illustrates that NSGA-II has better results than NPGA.

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D’Ambrosio, Joseph G., and William P. Birmingham. "Preference-directed design." Artificial Intelligence for Engineering Design, Analysis and Manufacturing 9, no. 3 (June 1995): 219–30. http://dx.doi.org/10.1017/s0890060400002456.

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AbstractCurrent design practices mandate that engineering designs be evaluated based on multiple attributes, e.g., cost, power, and area. For multiattribute design problems, generation and evaluation of the Pareto optimal set guarantees the optimal design will be found, but is not practical for a large class of problems. Iterative techniques can be applied to most problems, but sacrifice optimality. In this paper, we introduce a new technique that extends the set of design problems that can be solved optimally. By first constructing an imprecise value function, the number of nondominated alternatives that must be generated is reduced. We describe an implementation based on combinatorial optimization and constraint satisfaction which achieves additional performance gains by decomposing the value function to identify dominated design-variable assignments. Test results indicate that our approach extends the set of problems that can be solved optimally.

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Mo, Hongwei, Zhidan Xu, Lifang Xu, Zhou Wu, and Haiping Ma. "Constrained Multiobjective Biogeography Optimization Algorithm." Scientific World Journal 2014 (2014): 1–12. http://dx.doi.org/10.1155/2014/232714.

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Multiobjective optimization involves minimizing or maximizing multiple objective functions subject to a set of constraints. In this study, a novel constrained multiobjective biogeography optimization algorithm (CMBOA) is proposed. It is the first biogeography optimization algorithm for constrained multiobjective optimization. In CMBOA, a disturbance migration operator is designed to generate diverse feasible individuals in order to promote the diversity of individuals on Pareto front. Infeasible individuals nearby feasible region are evolved to feasibility by recombining with their nearest nondominated feasible individuals. The convergence of CMBOA is proved by using probability theory. The performance of CMBOA is evaluated on a set of 6 benchmark problems and experimental results show that the CMBOA performs better than or similar to the classical NSGA-II and IS-MOEA.

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Yu, Xiang, and Claudio Estevez. "Adaptive Multiswarm Comprehensive Learning Particle Swarm Optimization." Information 9, no. 7 (July 15, 2018): 173. http://dx.doi.org/10.3390/info9070173.

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Multiswarm comprehensive learning particle swarm optimization (MSCLPSO) is a multiobjective metaheuristic recently proposed by the authors. MSCLPSO uses multiple swarms of particles and externally stores elitists that are nondominated solutions found so far. MSCLPSO can approximate the true Pareto front in one single run; however, it requires a large number of generations to converge, because each swarm only optimizes the associated objective and does not learn from any search experience outside the swarm. In this paper, we propose an adaptive particle velocity update strategy for MSCLPSO to improve the search efficiency. Based on whether the elitists are indifferent or complex on each dimension, each particle adaptively determines whether to just learn from some particle in the same swarm, or additionally from the difference of some pair of elitists for the velocity update on that dimension, trying to achieve a tradeoff between optimizing the associated objective and exploring diverse regions of the Pareto set. Experimental results on various two-objective and three-objective benchmark optimization problems with different dimensional complexity characteristics demonstrate that the adaptive particle velocity update strategy improves the search performance of MSCLPSO significantly and is able to help MSCLPSO locate the true Pareto front more quickly and obtain better distributed nondominated solutions over the entire Pareto front.

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Niu, Wentie, Haiteng Sui, Yaxiao Niu, Kunhai Cai, and Weiguo Gao. "Ship Pipe Routing Design Using NSGA-II and Coevolutionary Algorithm." Mathematical Problems in Engineering 2016 (2016): 1–21. http://dx.doi.org/10.1155/2016/7912863.

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Pipe route design plays a prominent role in ship design. Due to the complex configuration in layout space with numerous pipelines, diverse design constraints, and obstacles, it is a complicated and time-consuming process to obtain the optimal route of ship pipes. In this article, an optimized design method for branch pipe routing is proposed to improve design efficiency and to reduce human errors. By simplifying equipment and ship hull models and dividing workspace into three-dimensional grid cells, the mathematic model of layout space is constructed. Based on the proposed concept of pipe grading method, the optimization model of pipe routing is established. Then an optimization procedure is presented to deal with pipe route planning problem by combining maze algorithm (MA), nondominated sorting genetic algorithm II (NSGA-II), and cooperative coevolutionary nondominated sorting genetic algorithm II (CCNSGA-II). To improve the performance in genetic algorithm procedure, a fixed-length encoding method is presented based on improved maze algorithm and adaptive region strategy. Fuzzy set theory is employed to extract the best compromise pipeline from Pareto optimal solutions. Simulation test of branch pipe and design optimization of a fuel piping system were carried out to illustrate the design optimization procedure in detail and to verify the feasibility and effectiveness of the proposed methodology.

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46

Zhang, Chengfen, and Xikui Ma. "NSGA-II Algorithm with a Local Search Strategy for Multiobjective Optimal Design of Dry-Type Air-Core Reactor." Mathematical Problems in Engineering 2015 (2015): 1–9. http://dx.doi.org/10.1155/2015/839035.

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Dry-type air-core reactor is now widely applied in electrical power distribution systems, for which the optimization design is a crucial issue. In the optimization design problem of dry-type air-core reactor, the objectives of minimizing the production cost and minimizing the operation cost are both important. In this paper, a multiobjective optimal model is established considering simultaneously the two objectives of minimizing the production cost and minimizing the operation cost. To solve the multi-objective optimization problem, a memetic evolutionary algorithm is proposed, which combines elitist nondominated sorting genetic algorithm version II (NSGA-II) with a local search strategy based on the covariance matrix adaptation evolution strategy (CMA-ES). NSGA-II can provide decision maker with flexible choices among the different trade-off solutions, while the local-search strategy, which is applied to nondominated individuals randomly selected from the current population in a given generation and quantity, can accelerate the convergence speed. Furthermore, another modification is that an external archive is set in the proposed algorithm for increasing the evolutionary efficiency. The proposed algorithm is tested on a dry-type air-core reactor made of rectangular cross-section litz-wire. Simulation results show that the proposed algorithm has high efficiency and it converges to a better Pareto front.

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Sánchez-Oro, Jesús, Ana D. López-Sánchez, Anna Martínez-Gavara, Alfredo G. Hernández-Díaz, and Abraham Duarte. "A Hybrid Strategic Oscillation with Path Relinking Algorithm for the Multiobjective k-Balanced Center Location Problem." Mathematics 9, no. 8 (April 14, 2021): 853. http://dx.doi.org/10.3390/math9080853.

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This paper presents a hybridization of Strategic Oscillation with Path Relinking to provide a set of high-quality nondominated solutions for the Multiobjective k-Balanced Center Location problem. The considered location problem seeks to locate k out of m facilities in order to serve n demand points, minimizing the maximum distance between any demand point and its closest facility while balancing the workload among the facilities. An extensive computational experimentation is carried out to compare the performance of our proposal, including the best method found in the state-of-the-art as well as traditional multiobjective evolutionary algorithms.

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Gu, Zheng Gang, and Kun Hong Liu. "Microarray Data Classification Based on Evolutionary Multiple Classifier System." Applied Mechanics and Materials 130-134 (October 2011): 2077–80. http://dx.doi.org/10.4028/www.scientific.net/amm.130-134.2077.

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Designing an evolutionary multiple classifier system (MCS) is a relatively new research area. In this paper, we propose a genetic algorithm (GA) based MCS for microarray data classification. We construct a feature poll with different feature selection methods first, and then a multi-objective GA is applied to implement ensemble feature selection process so as to generate a set of classifiers. When this GA stops, a set of base classifiers are generated. Here we use all the nondominated individuals in last generation to build an ensemble system and test the proposed ensemble method and the method that apply a classifier selection process to select proper classifiers from all the individuals in last generation. The experimental results show the proposed ensemble method is roubust and can lead to promising results.

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Aguilera-Rueda, Vicente-Josué, Nicandro Cruz-Ramírez, and Efrén Mezura-Montes. "Data-Driven Bayesian Network Learning: A Bi-Objective Approach to Address the Bias-Variance Decomposition." Mathematical and Computational Applications 25, no. 2 (June 20, 2020): 37. http://dx.doi.org/10.3390/mca25020037.

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We present a novel bi-objective approach to address the data-driven learning problem of Bayesian networks. Both the log-likelihood and the complexity of each candidate Bayesian network are considered as objectives to be optimized by our proposed algorithm named Nondominated Sorting Genetic Algorithm for learning Bayesian networks (NS2BN) which is based on the well-known NSGA-II algorithm. The core idea is to reduce the implicit selection bias-variance decomposition while identifying a set of competitive models using both objectives. Numerical results suggest that, in stark contrast to the single-objective approach, our bi-objective approach is useful to find competitive Bayesian networks especially in the complexity. Furthermore, our approach presents the end user with a set of solutions by showing different Bayesian network and their respective MDL and classification accuracy results.

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Tougma, Appolinaire, and Kounhinir Some. "Inexact Exponential Penalty Function with the Augmented Lagrangian for Multiobjective Optimization Algorithms." Journal of Applied Mathematics 2024 (January 10, 2024): 1–19. http://dx.doi.org/10.1155/2024/9615743.

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This paper uses an augmented Lagrangian method based on an inexact exponential penalty function to solve constrained multiobjective optimization problems. Two algorithms have been proposed in this study. The first algorithm uses a projected gradient, while the second uses the steepest descent method. By these algorithms, we have been able to generate a set of nondominated points that approximate the Pareto optimal solutions of the initial problem. Some proofs of theoretical convergence are also proposed for two different criteria for the set of generated stationary Pareto points. In addition, we compared our method with the NSGA-II and augmented the Lagrangian cone method on some test problems from the literature. A numerical analysis of the obtained solutions indicates that our method is competitive with regard to the test problems used for the comparison.

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Journal articles on the topic 'Nondominated set'

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