Journal of Global Optimization最新文献_第7页

A performance analysis of Basin hopping compared to established metaheuristics for global optimization Basin hopping 的性能分析：与已建立的元优化全局优化相比

IF 1.8 3区数学

Journal of Global Optimization Pub Date : 2024-02-28 DOI: 10.1007/s10898-024-01373-5

Marco Baioletti, Valentino Santucci, Marco Tomassini

{"title":"A performance analysis of Basin hopping compared to established metaheuristics for global optimization","authors":"Marco Baioletti, Valentino Santucci, Marco Tomassini","doi":"10.1007/s10898-024-01373-5","DOIUrl":"https://doi.org/10.1007/s10898-024-01373-5","url":null,"abstract":"During the last decades many metaheuristics for global numerical optimization have been proposed. Among them, Basin Hopping is very simple and straightforward to implement, although rarely used outside its original Physical Chemistry community. In this work, our aim is to compare Basin Hopping, and two population variants of it, with readily available implementations of the well known metaheuristics Differential Evolution, Particle Swarm Optimization, and Covariance Matrix Adaptation Evolution Strategy. We perform numerical experiments using the IOH profiler environment with the BBOB test function set and two difficult real-world problems. The experiments were carried out in two different but complementary ways: by measuring the performance under a fixed budget of function evaluations and by considering a fixed target value. The general conclusion is that Basin Hopping and its newly introduced population variant are almost as good as Covariance Matrix Adaptation on the synthetic benchmark functions and better than it on the two hard cluster energy minimization problems. Thus, the proposed analyses show that Basin Hopping can be considered a good candidate for global numerical optimization problems along with the more established metaheuristics, especially if one wants to obtain quick and reliable results on an unknown problem.","PeriodicalId":15961,"journal":{"name":"Journal of Global Optimization","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140005393","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Fast deterministic algorithms for non-submodular maximization with strong performance guarantees 具有强大性能保证的非次模化最大化快速确定性算法

IF 1.8 3区数学

Journal of Global Optimization Pub Date : 2024-02-22 DOI: 10.1007/s10898-024-01371-7

Cheng Lu, Wenguo Yang

引用次数: 0

A new dual-based cutting plane algorithm for nonlinear adjustable robust optimization 用于非线性可调鲁棒优化的新型基于对偶的切割面算法

IF 1.8 3区数学

Journal of Global Optimization Pub Date : 2024-02-22 DOI: 10.1007/s10898-023-01360-2

{"title":"A new dual-based cutting plane algorithm for nonlinear adjustable robust optimization","authors":"","doi":"10.1007/s10898-023-01360-2","DOIUrl":"https://doi.org/10.1007/s10898-023-01360-2","url":null,"abstract":"<h3>Abstract</h3> This paper explores a class of nonlinear Adjustable Robust Optimization (ARO) problems, containing here-and-now and wait-and-see variables, with uncertainty in the objective function and constraints. By applying Fenchel’s duality on the wait-and-see variables, we obtain an equivalent dual reformulation, which is a nonlinear static robust optimization problem. Using the dual formulation, we provide conditions under which the ARO problem is convex on the here-and-now decision. Furthermore, since the dual formulation contains a non-concave maximization on the uncertain parameter, we use perspective relaxation and an alternating method to handle the non-concavity. By employing the perspective relaxation, we obtain an upper bound, which we show is the same as the static relaxation of the considered problem. Moreover, invoking the alternating method, we design a new dual-based cutting plane algorithm that is able to find a reasonable lower bound for the optimal objective value of the considered nonlinear ARO model. In addition to sketching and establishing the theoretical features of the algorithms, including convergence analysis, by numerical experiments we reveal the abilities of our cutting plane algorithm in producing locally robust solutions with an acceptable optimality gap.","PeriodicalId":15961,"journal":{"name":"Journal of Global Optimization","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139924360","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A criterion-space branch-reduction-bound algorithm for solving generalized multiplicative problems 解决广义乘法问题的准则空间分支还原约束算法

IF 1.8 3区数学

Journal of Global Optimization Pub Date : 2024-02-15 DOI: 10.1007/s10898-023-01358-w

Hongwei Jiao, Binbin Li, Wenqiang Yang

引用次数: 0

A K-means Supported Reinforcement Learning Framework to Multi-dimensional Knapsack 针对多维包的 K-means 支持强化学习框架

IF 1.8 3区数学

Journal of Global Optimization Pub Date : 2024-02-15 DOI: 10.1007/s10898-024-01364-6

Sabah Bushaj, İ. Esra Büyüktahtakın

{"title":"A K-means Supported Reinforcement Learning Framework to Multi-dimensional Knapsack","authors":"Sabah Bushaj, İ. Esra Büyüktahtakın","doi":"10.1007/s10898-024-01364-6","DOIUrl":"https://doi.org/10.1007/s10898-024-01364-6","url":null,"abstract":"In this paper, we address the difficulty of solving large-scale multi-dimensional knapsack instances (MKP), presenting a novel deep reinforcement learning (DRL) framework. In this DRL framework, we train different agents compatible with a discrete action space for sequential decision-making while still satisfying any resource constraint of the MKP. This novel framework incorporates the decision variable values in the 2D DRL where the agent is responsible for assigning a value of 1 or 0 to each of the variables. To the best of our knowledge, this is the first DRL model of its kind in which a 2D environment is formulated, and an element of the DRL solution matrix represents an item of the MKP. Our framework is configured to solve MKP instances of different dimensions and distributions. We propose a K-means approach to obtain an initial feasible solution that is used to train the DRL agent. We train four different agents in our framework and present the results comparing each of them with the CPLEX commercial solver. The results show that our agents can learn and generalize over instances with different sizes and distributions. Our DRL framework shows that it can solve medium-sized instances at least 45 times faster in CPU solution time and at least 10 times faster for large instances, with a maximum solution gap of 0.28% compared to the performance of CPLEX. Furthermore, at least 95% of the items are predicted in line with the CPLEX solution. Computations with DRL also provide a better optimality gap with respect to state-of-the-art approaches.","PeriodicalId":15961,"journal":{"name":"Journal of Global Optimization","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139759470","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Regret analysis of an online majorized semi-proximal ADMM for online composite optimization 用于在线复合优化的在线主要半近似 ADMM 的遗憾分析

IF 1.8 3区数学

Journal of Global Optimization Pub Date : 2024-02-15 DOI: 10.1007/s10898-024-01365-5

Zehao Xiao, Liwei Zhang

引用次数: 0

Consensus-based optimization for multi-objective problems: a multi-swarm approach 基于共识的多目标问题优化：多群方法

IF 1.8 3区数学

Journal of Global Optimization Pub Date : 2024-02-15 DOI: 10.1007/s10898-024-01369-1

Kathrin Klamroth, Michael Stiglmayr, Claudia Totzeck

引用次数: 0

A method for searching for a globally optimal k-partition of higher-dimensional datasets 搜索高维数据集全局最优 k 分区的方法

IF 1.8 3区数学

Journal of Global Optimization Pub Date : 2024-02-13 DOI: 10.1007/s10898-024-01372-6

{"title":"A method for searching for a globally optimal k-partition of higher-dimensional datasets","authors":"","doi":"10.1007/s10898-024-01372-6","DOIUrl":"https://doi.org/10.1007/s10898-024-01372-6","url":null,"abstract":"<h3>Abstract</h3> The problem of finding a globally optimal k-partition of a set (mathcal {A}) is a very intricate optimization problem for which in general, except in the case of one-dimensional data, i.e., for data with one feature ( (mathcal {A}subset mathbb {R}) ), there is no method to solve. Only in the one-dimensional case, there are efficient methods based on the fact that the search for a globally optimal k-partition is equivalent to solving a global optimization problem for a symmetric Lipschitz-continuous function using the global optimization algorithm DIRECT. In the present paper, we propose a method for finding a globally optimal k-partition in the general case ( (mathcal {A}subset mathbb {R}^n) , (nge 1) ), generalizing an idea for solving the Lipschitz global optimization for symmetric functions. To do this, we propose a method that combines a global optimization algorithm with linear constraints and the k-means algorithm. The first of these two algorithms is used only to find a good initial approximation for the k-means algorithm. The method was tested on a number of artificial datasets and on several examples from the UCI Machine Learning Repository, and an application in spectral clustering for linearly non-separable datasets is also demonstrated. Our proposed method proved to be very efficient. ","PeriodicalId":15961,"journal":{"name":"Journal of Global Optimization","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139759418","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Global solution of quadratic problems using interval methods and convex relaxations 利用区间法和凸松弛法求解二次函数问题的全局方案

IF 1.8 3区数学

Journal of Global Optimization Pub Date : 2024-02-12 DOI: 10.1007/s10898-024-01370-8

Sourour Elloumi, Amélie Lambert, Bertrand Neveu, Gilles Trombettoni

{"title":"Global solution of quadratic problems using interval methods and convex relaxations","authors":"Sourour Elloumi, Amélie Lambert, Bertrand Neveu, Gilles Trombettoni","doi":"10.1007/s10898-024-01370-8","DOIUrl":"https://doi.org/10.1007/s10898-024-01370-8","url":null,"abstract":"Interval branch-and-bound solvers provide reliable algorithms for handling non-convex optimization problems by ensuring the feasibility and the optimality of the computed solutions, i.e. independently from the floating-point rounding errors. Moreover, these solvers deal with a wide variety of mathematical operators. However, these solvers are not dedicated to quadratic optimization and do not exploit nonlinear convex relaxations in their framework. We present an interval branch-and-bound method that can efficiently solve quadratic optimization problems. At each node explored by the algorithm, our solver uses a quadratic convex relaxation which is as strong as a semi-definite programming relaxation, and a variable selection strategy dedicated to quadratic problems. The interval features can then propagate efficiently this information for contracting all variable domains. We also propose to make our algorithm rigorous by certifying firstly the convexity of the objective function of our relaxation, and secondly the validity of the lower bound calculated at each node. In the non-rigorous case, our experiments show significant speedups on general integer quadratic instances, and when reliability is required, our first results show that we are able to handle medium-sized instances in a reasonable running time.","PeriodicalId":15961,"journal":{"name":"Journal of Global Optimization","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139759499","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Efficiency conditions and duality for multiobjective semi-infinite programming problems on Hadamard manifolds 哈达玛流形上多目标半无限编程问题的效率条件和对偶性

IF 1.8 3区数学

Journal of Global Optimization Pub Date : 2024-01-31 DOI: 10.1007/s10898-024-01367-3

Balendu Bhooshan Upadhyay, Arnav Ghosh, Savin Treanţă

引用次数: 0