Pub Date : 2022-04-11DOI: 10.1142/s0217595922500142
Chun-an Liu, Qian Lei, H. Jia
Diversification of investment is a well-established practice for reducing the total risk of investing. Portfolio optimization is an effective way for investors to disperse investment risk and increase portfolio return. Under the assumption of no short selling, a bi-objective minimizing portfolio optimization model, in which the first objective is a semi-absolute deviation mean function used to measure the portfolio risk, and the second objective is a maximum entropy smooth function used to measure the portfolio return, is given in this paper. Also, a maximum entropy multi-objective evolutionary algorithm is designed to solve the bi-objective portfolio optimization model. In order to obtain a sufficient number of uniformly distributed portfolio Pareto optimal solutions located on the true Pareto frontier and fully exploit the useful asset combination modes which can lead the search process toward the frontier direction quickly in the objective space, a subspace multi-parent uniform crossover operator and a subspace decomposition mutation operator are given. Furthermore, a normalization method to deal with the tight constraint and the convergence analysis of the proposed algorithm are also discussed. Finally, the performance of the proposed algorithm is verified by five benchmark investment optimization problems. The performance evaluations and results analyses illustrate that the proposed algorithm is capable of identifying good Pareto solutions and maintaining adequate diversity of the evolution population. Also, the proposed algorithm can obtain faster and better convergence to the true portfolio Pareto frontier compared with the three state-of-the-art multi-objective evolutionary algorithms. The result can also provide optimal portfolio plan and investment strategy for investors to allocate and manage asset effectively.
{"title":"Maximum Entropy Bi-Objective Model and its Evolutionary Algorithm for Portfolio Optimization","authors":"Chun-an Liu, Qian Lei, H. Jia","doi":"10.1142/s0217595922500142","DOIUrl":"https://doi.org/10.1142/s0217595922500142","url":null,"abstract":"Diversification of investment is a well-established practice for reducing the total risk of investing. Portfolio optimization is an effective way for investors to disperse investment risk and increase portfolio return. Under the assumption of no short selling, a bi-objective minimizing portfolio optimization model, in which the first objective is a semi-absolute deviation mean function used to measure the portfolio risk, and the second objective is a maximum entropy smooth function used to measure the portfolio return, is given in this paper. Also, a maximum entropy multi-objective evolutionary algorithm is designed to solve the bi-objective portfolio optimization model. In order to obtain a sufficient number of uniformly distributed portfolio Pareto optimal solutions located on the true Pareto frontier and fully exploit the useful asset combination modes which can lead the search process toward the frontier direction quickly in the objective space, a subspace multi-parent uniform crossover operator and a subspace decomposition mutation operator are given. Furthermore, a normalization method to deal with the tight constraint and the convergence analysis of the proposed algorithm are also discussed. Finally, the performance of the proposed algorithm is verified by five benchmark investment optimization problems. The performance evaluations and results analyses illustrate that the proposed algorithm is capable of identifying good Pareto solutions and maintaining adequate diversity of the evolution population. Also, the proposed algorithm can obtain faster and better convergence to the true portfolio Pareto frontier compared with the three state-of-the-art multi-objective evolutionary algorithms. The result can also provide optimal portfolio plan and investment strategy for investors to allocate and manage asset effectively.","PeriodicalId":8478,"journal":{"name":"Asia Pac. J. Oper. Res.","volume":"34 1","pages":"2250014:1-2250014:26"},"PeriodicalIF":0.0,"publicationDate":"2022-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73343600","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-04-05DOI: 10.1142/s0217595922500129
Caixia Jing, Wanzhen Huang, Lei Zhang, Heng Zhang
In this paper, we consider the scheduling of high multiplicity jobs on parallel multi-purpose machines with setup times and machine available times, with the objective of minimizing makespan. High multiplicity means that jobs are partitioned into several groups and in each group all jobs are identical. Whenever there is a switch from processing a job of one group to a job of another group, a setup time is needed. Multi-purpose machine implies that each job can only be processed by a specific subset of all the machines, called processing set. A mixed integer programming is formulated for this NP-hard problem. A heuristic is proposed to solve the problem. Lower bounds are developed to evaluate the heuristic algorithm. Extensive numerical computations are performed and the results show that the heuristic generates solutions with makespan within 2% above the lower bounds in average, and outperforms CPLEX 12.6 for large scale and complex problems.
{"title":"Scheduling High Multiplicity Jobs on Parallel Multi-Purpose Machines with Setup Times and Machine Available Times","authors":"Caixia Jing, Wanzhen Huang, Lei Zhang, Heng Zhang","doi":"10.1142/s0217595922500129","DOIUrl":"https://doi.org/10.1142/s0217595922500129","url":null,"abstract":"In this paper, we consider the scheduling of high multiplicity jobs on parallel multi-purpose machines with setup times and machine available times, with the objective of minimizing makespan. High multiplicity means that jobs are partitioned into several groups and in each group all jobs are identical. Whenever there is a switch from processing a job of one group to a job of another group, a setup time is needed. Multi-purpose machine implies that each job can only be processed by a specific subset of all the machines, called processing set. A mixed integer programming is formulated for this NP-hard problem. A heuristic is proposed to solve the problem. Lower bounds are developed to evaluate the heuristic algorithm. Extensive numerical computations are performed and the results show that the heuristic generates solutions with makespan within 2% above the lower bounds in average, and outperforms CPLEX 12.6 for large scale and complex problems.","PeriodicalId":8478,"journal":{"name":"Asia Pac. J. Oper. Res.","volume":"151 1","pages":"2250012:1-2250012:25"},"PeriodicalIF":0.0,"publicationDate":"2022-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77766952","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-03-24DOI: 10.1142/s0217595922500105
Bo Zhang, Yuelin Gao
Founded on the idea of subdividing the [Formula: see text]-dimensional output space, a branch-and-bound algorithm for solving the sum-of-linear-ratios(SLR) problem is proposed. First, a two-stage equivalent transformation method is adopted to obtain an equivalent problem(EP) for the problem SLR. Second, by dealing with all nonlinear constraints and bilinear terms in EP and its sub-problems, a corresponding convex relaxation subproblem is obtained. Third, all redundant constraints in each convex relaxation subproblem are eliminated, which leads to a linear programming problem with smaller scale and fewer constraints. Finally, the theoretical convergence and computational complexity of the algorithm are demonstrated, and a series of numerical experiments illustrate the effectiveness and feasibility of the proposed algorithm.
{"title":"An Output-Space Based Branch-and-Bound Algorithm for Sum-of-Linear-Ratios Problem","authors":"Bo Zhang, Yuelin Gao","doi":"10.1142/s0217595922500105","DOIUrl":"https://doi.org/10.1142/s0217595922500105","url":null,"abstract":"Founded on the idea of subdividing the [Formula: see text]-dimensional output space, a branch-and-bound algorithm for solving the sum-of-linear-ratios(SLR) problem is proposed. First, a two-stage equivalent transformation method is adopted to obtain an equivalent problem(EP) for the problem SLR. Second, by dealing with all nonlinear constraints and bilinear terms in EP and its sub-problems, a corresponding convex relaxation subproblem is obtained. Third, all redundant constraints in each convex relaxation subproblem are eliminated, which leads to a linear programming problem with smaller scale and fewer constraints. Finally, the theoretical convergence and computational complexity of the algorithm are demonstrated, and a series of numerical experiments illustrate the effectiveness and feasibility of the proposed algorithm.","PeriodicalId":8478,"journal":{"name":"Asia Pac. J. Oper. Res.","volume":"37 1","pages":"2250010:1-2250010:23"},"PeriodicalIF":0.0,"publicationDate":"2022-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80946821","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-03-10DOI: 10.1142/s0217595922500087
Arshpreet Kaur, M. K. Sharma, I. Ahmad
We introduce new classes of higher-order functional, termed higher-order [Formula: see text]convex and higher-order [Formula: see text]convex functionals. These classes are illustrated by nontrivial examples. A pair of higher-order multiobjective symmetric fractional variational programs with cone constraints and fixed boundary conditions is formulated. Appropriate duality results are discussed utilizing the aforementioned assumptions. The results in this paper are generalizations of the results already existing in literature.
{"title":"Multiobjective Symmetric Duality in Higher-Order Fractional Variational Programming","authors":"Arshpreet Kaur, M. K. Sharma, I. Ahmad","doi":"10.1142/s0217595922500087","DOIUrl":"https://doi.org/10.1142/s0217595922500087","url":null,"abstract":"We introduce new classes of higher-order functional, termed higher-order [Formula: see text]convex and higher-order [Formula: see text]convex functionals. These classes are illustrated by nontrivial examples. A pair of higher-order multiobjective symmetric fractional variational programs with cone constraints and fixed boundary conditions is formulated. Appropriate duality results are discussed utilizing the aforementioned assumptions. The results in this paper are generalizations of the results already existing in literature.","PeriodicalId":8478,"journal":{"name":"Asia Pac. J. Oper. Res.","volume":"17 1","pages":"2250008:1-2250008:24"},"PeriodicalIF":0.0,"publicationDate":"2022-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79899889","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-03-08DOI: 10.1142/s0217595922400127
Wenhua Li, Libo Wang, Hang Yuan
We consider online parallel-batch scheduling of [Formula: see text] incompatible unit-length job families with variable lookahead interval to minimize the maximum completion time, where [Formula: see text] is the number of job families which is known in advance. Incompatible job family means that a batch only contains the jobs from the same job family. At any time [Formula: see text], an online algorithm can foresee the information of the jobs arriving in the time interval [Formula: see text], where [Formula: see text] is variable. When the batch capacity [Formula: see text] and [Formula: see text], we provide a best possible online algorithm with competitive ratio [Formula: see text] for [Formula: see text] and [Formula: see text], where [Formula: see text] is a positive root of [Formula: see text]. When the batch capacity [Formula: see text] and [Formula: see text], we give an online algorithm with competitive ratio [Formula: see text] for [Formula: see text] and [Formula: see text], and prove that it is the best possible for [Formula: see text] and [Formula: see text].
{"title":"Online Batch Scheduling of Incompatible Job Families with Variable Lookahead Interval","authors":"Wenhua Li, Libo Wang, Hang Yuan","doi":"10.1142/s0217595922400127","DOIUrl":"https://doi.org/10.1142/s0217595922400127","url":null,"abstract":"We consider online parallel-batch scheduling of [Formula: see text] incompatible unit-length job families with variable lookahead interval to minimize the maximum completion time, where [Formula: see text] is the number of job families which is known in advance. Incompatible job family means that a batch only contains the jobs from the same job family. At any time [Formula: see text], an online algorithm can foresee the information of the jobs arriving in the time interval [Formula: see text], where [Formula: see text] is variable. When the batch capacity [Formula: see text] and [Formula: see text], we provide a best possible online algorithm with competitive ratio [Formula: see text] for [Formula: see text] and [Formula: see text], where [Formula: see text] is a positive root of [Formula: see text]. When the batch capacity [Formula: see text] and [Formula: see text], we give an online algorithm with competitive ratio [Formula: see text] for [Formula: see text] and [Formula: see text], and prove that it is the best possible for [Formula: see text] and [Formula: see text].","PeriodicalId":8478,"journal":{"name":"Asia Pac. J. Oper. Res.","volume":"29 1","pages":"2240012:1-2240012:15"},"PeriodicalIF":0.0,"publicationDate":"2022-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75078595","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-03-08DOI: 10.1142/s0217595922500075
L. Bai, Jiale Liu, Ning Huang, Kanyin Zheng, Tingting Hao
The need for enterprises to manage project portfolio risks over the life cycle has become increasingly prominent. It is essential to evaluate and manage them to achieve project portfolios and organizations’ success. Unlike project risk, project portfolio risk is more complex and uncertain due to risk interactions. Risk management is unsatisfactory in project portfolios due to the lack of awareness of risk interactions and the life cycle. The purpose of this paper is to identify the critical risks of project portfolios over the life cycle considering risk interactions. We primarily verified 20 identified risks through a questionnaire survey and an expert interview method and evaluated the interactions among them using the Delphi method. Furthermore, risk interactions were analyzed using the social network analysis (SNA) methodology to determine the important risks. Finally, a comprehensive evaluation of important risks was carried out to identify critical risks according to the evaluation principles. The results identified six critical portfolio risks, two key risk contagion paths and revealed risk characteristics of different life cycle phases. This research considerably contributes to the body of knowledge pertaining to project portfolio management that will enable organizations that implement project portfolios and similar multi projects to emphasize critical risks.
{"title":"Critical Interactive Risks in Project Portfolios from the Life Cycle Perspective","authors":"L. Bai, Jiale Liu, Ning Huang, Kanyin Zheng, Tingting Hao","doi":"10.1142/s0217595922500075","DOIUrl":"https://doi.org/10.1142/s0217595922500075","url":null,"abstract":"The need for enterprises to manage project portfolio risks over the life cycle has become increasingly prominent. It is essential to evaluate and manage them to achieve project portfolios and organizations’ success. Unlike project risk, project portfolio risk is more complex and uncertain due to risk interactions. Risk management is unsatisfactory in project portfolios due to the lack of awareness of risk interactions and the life cycle. The purpose of this paper is to identify the critical risks of project portfolios over the life cycle considering risk interactions. We primarily verified 20 identified risks through a questionnaire survey and an expert interview method and evaluated the interactions among them using the Delphi method. Furthermore, risk interactions were analyzed using the social network analysis (SNA) methodology to determine the important risks. Finally, a comprehensive evaluation of important risks was carried out to identify critical risks according to the evaluation principles. The results identified six critical portfolio risks, two key risk contagion paths and revealed risk characteristics of different life cycle phases. This research considerably contributes to the body of knowledge pertaining to project portfolio management that will enable organizations that implement project portfolios and similar multi projects to emphasize critical risks.","PeriodicalId":8478,"journal":{"name":"Asia Pac. J. Oper. Res.","volume":"115 1","pages":"2250007:1-2250007:38"},"PeriodicalIF":0.0,"publicationDate":"2022-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79071876","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-03-02DOI: 10.1142/s0217595922500452
Raoul Müller, A. Schöbel, Dominic Schuhmacher
In this paper we study a generalized version of the Weber problem of finding a point that minimizes the sum of its distances to a finite number of given points. In our setting these distances may be $cut$ $off$ at a given value $C>0$, and we allow for the option of an $empty$ solution at a fixed cost $C'$. We analyze under which circumstances these problems can be reduced to the simpler Weber problem, and also when we definitely have to solve the more complex problem with cutoff. We furthermore present adaptions of the algorithm of [Drezner et al., 1991, $Transportation$ $Science$ 25(3), 183--187] to our setting, which in certain situations are able to substantially reduce computation times as demonstrated in a simulation study. The sensitivity with respect to the cutoff value is also studied, which allows us to provide an algorithm that efficiently solves the problem simultaneously for all $C>0$.
在本文中，我们研究了韦伯问题的一个一般化版本，即求一个点与有限个给定点的距离之和最小。在我们的设置中，这些距离可以在给定值C>0时被截断，并且我们允许以固定成本C选择一个空的解决方案。我们分析了在哪些情况下这些问题可以简化为更简单的韦伯问题，以及在什么情况下我们必须用截止来解决更复杂的问题。我们进一步提出了[Drezner et al.， 1991， $Transportation$ Science$ 25(3)， 183—187]的算法，以适应我们的设置，这在某些情况下能够大大减少计算时间，如模拟研究所示。研究了对截止值的敏感性，从而提供了一种算法，可以有效地同时解决所有C>0的问题。
{"title":"Location Problems with Cutoff","authors":"Raoul Müller, A. Schöbel, Dominic Schuhmacher","doi":"10.1142/s0217595922500452","DOIUrl":"https://doi.org/10.1142/s0217595922500452","url":null,"abstract":"In this paper we study a generalized version of the Weber problem of finding a point that minimizes the sum of its distances to a finite number of given points. In our setting these distances may be $cut$ $off$ at a given value $C>0$, and we allow for the option of an $empty$ solution at a fixed cost $C'$. We analyze under which circumstances these problems can be reduced to the simpler Weber problem, and also when we definitely have to solve the more complex problem with cutoff. We furthermore present adaptions of the algorithm of [Drezner et al., 1991, $Transportation$ $Science$ 25(3), 183--187] to our setting, which in certain situations are able to substantially reduce computation times as demonstrated in a simulation study. The sensitivity with respect to the cutoff value is also studied, which allows us to provide an algorithm that efficiently solves the problem simultaneously for all $C>0$.","PeriodicalId":8478,"journal":{"name":"Asia Pac. J. Oper. Res.","volume":"14 1","pages":"2250045:1-2250045:33"},"PeriodicalIF":0.0,"publicationDate":"2022-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79687787","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-02-28DOI: 10.1142/s0217595922500099
Zhiang Zhou, Min Kuang
In this paper, our purpose is to use the improvement set to investigate the scalarization and optimality conditions of [Formula: see text]-globally proper efficient solution for the set-valued equilibrium problems with constraints. First, the notion of [Formula: see text]-globally proper efficient solution for set-valued equilibrium problems with constraints is introduced in locally convex Hausdorff topological spaces. Second, the linear scalarization theorems of [Formula: see text]-globally proper efficient solution are derived. Finally, under the assumption of nearly [Formula: see text]-subconvexlikeness, the Kuhn–Tucker and Lagrange optimality conditions for set-valued equilibrium problems with constraints are obtained in the sense of [Formula: see text]-globally proper efficiency. Meanwhile, we give some examples to illustrate our results. The results obtained in this paper improve and generalize some known results in the literature.
{"title":"Scalarization and Optimality Conditions of E-Globally Proper Efficient Solution for Set-Valued Equilibrium Problems","authors":"Zhiang Zhou, Min Kuang","doi":"10.1142/s0217595922500099","DOIUrl":"https://doi.org/10.1142/s0217595922500099","url":null,"abstract":"In this paper, our purpose is to use the improvement set to investigate the scalarization and optimality conditions of [Formula: see text]-globally proper efficient solution for the set-valued equilibrium problems with constraints. First, the notion of [Formula: see text]-globally proper efficient solution for set-valued equilibrium problems with constraints is introduced in locally convex Hausdorff topological spaces. Second, the linear scalarization theorems of [Formula: see text]-globally proper efficient solution are derived. Finally, under the assumption of nearly [Formula: see text]-subconvexlikeness, the Kuhn–Tucker and Lagrange optimality conditions for set-valued equilibrium problems with constraints are obtained in the sense of [Formula: see text]-globally proper efficiency. Meanwhile, we give some examples to illustrate our results. The results obtained in this paper improve and generalize some known results in the literature.","PeriodicalId":8478,"journal":{"name":"Asia Pac. J. Oper. Res.","volume":"7 10","pages":"2250009:1-2250009:16"},"PeriodicalIF":0.0,"publicationDate":"2022-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91442776","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-02-14DOI: 10.1142/s0217595922400115
Cuixia Miao, Fanyu Kong, Juan Zou, Ran Ma, Yujia Huo
In this paper, we consider the parallel-machine scheduling with step-deteriorating jobs. The actual processing time of each job deteriorates as a step function if its starting time is beyond a given deteriorating date. We focus on the case of the common job deteriorating date. For the minimization problem of total completion time, we first show that the problem is NP-hard in the strong sense. Then we propose one property of any optimal schedule. Furthermore, we prove that two special cases of common normal processing time or common penalty are polynomially solvable. For the minimization problem of total weighted completion time, we analyze the NP-hardness and present a polynomial time optimal algorithm for the case of common normal processing time and common penalty.
{"title":"Parallel-Machine Scheduling with Step-Deteriorating Jobs to Minimize the Total (Weighted) Completion Time","authors":"Cuixia Miao, Fanyu Kong, Juan Zou, Ran Ma, Yujia Huo","doi":"10.1142/s0217595922400115","DOIUrl":"https://doi.org/10.1142/s0217595922400115","url":null,"abstract":"In this paper, we consider the parallel-machine scheduling with step-deteriorating jobs. The actual processing time of each job deteriorates as a step function if its starting time is beyond a given deteriorating date. We focus on the case of the common job deteriorating date. For the minimization problem of total completion time, we first show that the problem is NP-hard in the strong sense. Then we propose one property of any optimal schedule. Furthermore, we prove that two special cases of common normal processing time or common penalty are polynomially solvable. For the minimization problem of total weighted completion time, we analyze the NP-hardness and present a polynomial time optimal algorithm for the case of common normal processing time and common penalty.","PeriodicalId":8478,"journal":{"name":"Asia Pac. J. Oper. Res.","volume":"59 1","pages":"2240011:1-2240011:13"},"PeriodicalIF":0.0,"publicationDate":"2022-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87124583","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-02-07DOI: 10.1142/s0217595922400097
Yunhe Xu, Chenchen Wu, Ling Gai, Lu Han
Clustering is one of the most important problems in the fields of data mining, machine learning, and biological population division, etc. Moreover, robust variant for [Formula: see text]-means problem, which includes [Formula: see text]-means with penalties and [Formula: see text]-means with outliers, is also an active research branch. Most of these problems are NP-hard even the most classical problem, [Formula: see text]-means problem. For the NP-hard problems, the heuristic algorithm is a powerful method. When the quality of the output can be guaranteed, the algorithm is called an approximation algorithm. In this paper, combining two types of robust settings, we consider [Formula: see text]-means problem with penalties and outliers ([Formula: see text]-MPO). In the [Formula: see text]-MPO, we are given an [Formula: see text]-point set [Formula: see text], a penalty cost [Formula: see text] for each [Formula: see text], an integer [Formula: see text], and an integer [Formula: see text]. The target is to find a center subset [Formula: see text] with [Formula: see text], a penalty subset [Formula: see text] and an outlier subset [Formula: see text] with [Formula: see text], such that the sum of the total costs, including the connection cost and the penalty cost, is minimized. We offer an approximation algorithm using a heuristic local search scheme. Based on a single-swap manipulation, we obtain [Formula: see text]-approximation algorithm.
{"title":"Effective Heuristic Techniques for Combined Robust Clustering Problem","authors":"Yunhe Xu, Chenchen Wu, Ling Gai, Lu Han","doi":"10.1142/s0217595922400097","DOIUrl":"https://doi.org/10.1142/s0217595922400097","url":null,"abstract":"Clustering is one of the most important problems in the fields of data mining, machine learning, and biological population division, etc. Moreover, robust variant for [Formula: see text]-means problem, which includes [Formula: see text]-means with penalties and [Formula: see text]-means with outliers, is also an active research branch. Most of these problems are NP-hard even the most classical problem, [Formula: see text]-means problem. For the NP-hard problems, the heuristic algorithm is a powerful method. When the quality of the output can be guaranteed, the algorithm is called an approximation algorithm. In this paper, combining two types of robust settings, we consider [Formula: see text]-means problem with penalties and outliers ([Formula: see text]-MPO). In the [Formula: see text]-MPO, we are given an [Formula: see text]-point set [Formula: see text], a penalty cost [Formula: see text] for each [Formula: see text], an integer [Formula: see text], and an integer [Formula: see text]. The target is to find a center subset [Formula: see text] with [Formula: see text], a penalty subset [Formula: see text] and an outlier subset [Formula: see text] with [Formula: see text], such that the sum of the total costs, including the connection cost and the penalty cost, is minimized. We offer an approximation algorithm using a heuristic local search scheme. Based on a single-swap manipulation, we obtain [Formula: see text]-approximation algorithm.","PeriodicalId":8478,"journal":{"name":"Asia Pac. J. Oper. Res.","volume":"369 1","pages":"2240009:1-2240009:17"},"PeriodicalIF":0.0,"publicationDate":"2022-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80423388","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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