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A method for enumerating pairwise compatibility graphs with a given number of vertices

DISCRETE APPLIED MATHEMATICS 2021年 303卷 171-185页

作者： Azam, Naveed Ahmed Shurbevski, Aleksandar Nagamochi, Hiroshi Kyoto Univ Dept Appl Math & Phys Kyoto Japan

Azam et al. (2018) proposed a method to enumerate all pairwise compatibility graphs (PCGs) with a given number n of vertices. For a tuple (G, T, sigma, lambda) of a graph G with n vertices and a tree T with n leaves, a bijection sigma between the vertices in G and the leaves in T, and a bi-partition lambda of the set of non-adjacent vertex pairs in G, they formulated two linear programs, LP(G, T, sigma, lambda) and DLP(G, T, sigma, lambda) such that: exactly one of them is feasible;and G is a PCG if and only if LP(G, T, sigma, lambda) is feasible for some tuple (G, T, sigma, lambda). To reduce the number of graphs G with n vertices (resp., tuples) for which the LPs are solved, they excluded PCGs by heuristically generating PCGs (resp., some tuples that contain a sub-tuple (G', T', sigma', lambda') for n = 4 whose LP(G', T', sigma', lambda') is infeasible). This paper proposes two improvements in the method: derive a sufficient condition for a graph to be a PCG for a given tree in order to exclude more PCGs;and characterize all sub-tuples (G', T', sigma', lambda') for n = 4 for which LP(G', T', sigma', lambda') is infeasible, and enumerate tuples that contain no such sub-tuples by a branch-and-bound algorithm. Experimental results show that our method more efficiently enumerated all PCGs for n = 8. (C) 2020 Elsevier B.V. All rights reserved.

关键词： Pairwise compatibility graph linear programming Gale's theorem Branch-and-bound algorithm Graph isomorphism

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An Adaptive Mechanism With Cooperative Coevolution and Covariance for Differential Evolution

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IEEE ACCESS 2021年 9卷 99890-99904页

作者： Wang, Bin Ren, Lu Prado, Juan Diego He, Wenjuan Jin, Haiyan Jiang, Qiaoyong Wang, Xiaofan Xian Univ Technol Fac Comp Sci & Engn Xian 710048 Peoples R China Shaanxi Key Lab Network Comp & Secur Technol Xian 710048 Peoples R China

Differential evolution (DE) is an evolutionary algorithm widely used to solve optimization problems with different characteristics in fields where actions and decisions depend on numerical data such as engineering, economics, and logistics. In this paper, an adaptive differential evolution mechanism with cooperative co-evolution and covariance (A-CC/COV-DE) is proposed to overcome the low efficiency of differential evolution when solving large-scale numerical optimization problems, especially when the correlation between the variables of the problem is unknown. An unknown correlation of variables hinders DE from achieving an optimal search process since different types of correlations ideally require distinct optimization strategies. According to the separability of variables, the appropriate evolutionary strategy is selected adaptively. For separable functions, cooperative coevolution is adopted. After using extended differential grouping to split the problem, the sub-components are optimized by differential evolution. This reduces the dimensionality and complexity of the problem, improving its convergence speed and global search ability. For non-separable functions, a covariance matrix is calculated, and then the eigenvector is used to rotate the coordinate system. This leads to eliminate the correlation between variables and improve the search efficiency of differential evolution. We evaluated the performance of A-CC/COV-DE on the CEC 2014 test suite and compared it with state-of-the-art differential evolution algorithms. The experimental results show that our proposal is quite competitive with recent algorithms.

关键词： Optimization Correlation linear programming Licenses Covariance matrices Sun Sociology Cooperative coevolution covariance differential evolution adaptive mechanism

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Randomized Greedy Sensor Selection: Leveraging Weak Submodularity

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2021年第1期66卷 199-212页

作者： Hashemi, Abolfazl Ghasemi, Mahsa Vikalo, Haris Topcu, Ufuk Univ Texas Austin Dept Elect & Comp Engn Austin TX 78712 USA Univ Texas Austin Dept Mech Engn Austin TX 78712 USA Univ Texas Austin Dept Aerosp Engn & Engn Mech Austin TX 78712 USA

We study the problem of estimating a random process from the observations collected by a network of sensors that operate under resource constraints. When the dynamics of the process and sensor observations are described by a state-space model and the resource are unlimited, the conventional Kalman filter provides the minimum mean square error (MMSE) estimates. However, at any given time, restrictions on the available communications bandwidth and computational capabilities and/or power impose a limitation on the number of network nodes, whose observations can be used to compute the estimates. We formulate the problem of selecting the most informative subset of the sensors as a combinatorial problem of maximizing a monotone set function under a uniform matroid constraint. For the MMSE estimation criterion, we show that the maximum elementwise curvature of the objective function satisfies a certain upper-bound constraint and is, therefore, weak submodular. Building upon the work of Mirzasoleiman et al. on submodular maximization, we develop an efficient randomized greedy algorithm for sensor selection and establish guarantees on the estimator's performance in this setting. Extensive simulation results demonstrate the efficacy of the randomized greedy algorithm compared to state-of-the-art greedy and semidefinite programming relaxation methods.

关键词： Greedy algorithms Covariance matrices Kalman filters Radar tracking linear programming Mean square error methods Noise measurement Kalman filtering sensor networks sensor selection weak submodularity

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ImpSuic: A quality updating rule in mixing coins with maximum utilities

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INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS 2021年第3期36卷 1182-1198页

作者： Yu, Xinying Wang, Zhaojie Wang, Yilei Li, Fengyin Li, Tao Chen, Yuling Tian, Youliang Yu, Xiaomei Qufu Normal Univ Sch Comp Sci Rizhao 276826 Peoples R China Guizhou Univ Coll Comp Sci & Technol Guiyang Peoples R China Guizhou Univ State Key Lab Publ Big Data Guiyang Peoples R China Shandong Normal Univ Sch Informat Sci & Engn Jinan Peoples R China

vMixing coins strategy can realize the anonymity of user information, thereby protecting the user's privacy. Ideally, the blacklist is public information and all bad coins are recorded in it. However, due to the failure of some bad coins to be registered in the blacklist in time, users can only obtain part of the blacklist information, which allows illegal criminals to take advantage of it. How to prevent illegal activities under the partial information blacklist and how to design coins' quality updating rule rationally have become open issues in mixing coins. The updating rule of coins' quality in mixing is addressed since illegal criminals may carry out illegal activities, for example, money laundering. ImpSuic, an improved suicide strategy, is proposed as a new quality updating rule. The intuition is: all coins of the one who has the highest bad coins according to the blacklist, are recorded as bad coins. On the other hand, the coins' quality of others remain unchanged. Besides, linear programming is introduced into ImpSuic strategy to predict the maximum utility after mixing coins, which facilitates users to make reasonable decisions before mixing coins. Simulation results show that the quality updating rule in ImpSuic strategy can preserve users' privacy and antimoney launder.

关键词： blacklist ImpSuic strategy linear programming maximum utility mixing coins

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Partial Evaluation and Efficient Discarding for the Maximal Covering Location Problem

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IEEE ACCESS 2021年 9卷 20542-20556页

作者： Porras, Cynthia Fajardo, Jenny Rosete, Alejandro Masegosa, Antonio D. Univ Tecnol La Habana Jose Antonio Echeverr Dept Inteligencia Articial & Infraestruct Sistema Fac Informat Havana 11500 Cuba Univ Deusto Deusto Inst Technol Bilbao 48007 Spain Ikerbasque Basque Fdn Sci Bilbao 48011 Spain

The maximal covering location problem attempts to locate a limited number of facilities in order to maximize the coverage over a set of demand nodes. This problem is NP-Hard and it has been often addressed by using metaheuristics, where the execution time directly depends on the number of evaluations of the objective function. In this article, the principles of efficient discarding and partial evaluation are applied to obtain more efficient versions of the objective function of this problem, i.e. not-approximate surrogate objective functions. An experimental study is presented to compare the surrogate functions in terms of number of distance comparisons and runtime. The results show that (on average) the best surrogate function is more than 5 times faster than the original function in general, and more than 8 times faster in the largest instances. This proposal allows for a more efficient metaheuristic solution based on swap operators.

关键词： linear programming Complexity theory Approximation algorithms Licenses Indexes Computational efficiency Time complexity Efficient discarding partial evaluation maximal covering location problem objective function

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Stabilization of Enforced Positive Switched linear Systems with Bounded Controls

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INTERNATIONAL JOURNAL OF CONTROL AUTOMATION AND SYSTEMS 2021年第2期19卷 607-617页

作者： Liu, Jinjin Henan Univ Econ & Law Dept Math & Informat Sci Zhengzhou 450046 Peoples R China

This paper is concerned with the controller synthesis issue for enforced positive switched linear systems via output feedback. First, the stabilization problem is studied with output feedback under average dwell time switching signal, and the controllers we proposed guarantee stability and positivity of the closed-loop systems. Second, the output feedback stabilization issue is investigated by introducing special form of diagonal matrices, and the constraints on states and control inputs are solved based on limited initial conditions. Then, the derived conditions are described via linear programming, also extending the theoretical findings to constrained output issue. Finally, the simulation results demonstrate the feasibility of the control strategy.

关键词： Bounded control linear programming output feedback positive system switched linear systems

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Correlation Clustering in Data Streams

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ALGORITHMICA 2021年第7期83卷 1980-2017页

作者： Ahn, Kook Jin Cormode, Graham Guha, Sudipto McGregor, Andrew Wirth, Anthony Univ Penn Philadelphia PA 19104 USA Univ Warwick Coventry W Midlands England Univ Massachusetts Amherst MA 01003 USA Univ Melbourne Sch Comp & Informat Syst Parkville Vic Australia

Clustering is a fundamental tool for analyzing large data sets. A rich body of work has been devoted to designing data-stream algorithms for the relevant optimization problems such as k-center, k-median, and k-means. Such algorithms need to be both time and and space efficient. In this paper, we address the problem of correlation clustering in the dynamic data stream model. The stream consists of updates to the edge weights of a graph on n nodes and the goal is to find a node-partition such that the end-points of negative-weight edges are typically in different clusters whereas the end-points of positive-weight edges are typically in the same cluster. We present polynomial-time, O(n center dot polylogn)-space approximation algorithms for natural problems that arise. We first develop data structures based on linear sketches that allow the "quality" of a given node-partition to be measured. We then combine these data structures with convex programming and sampling techniques to solve the relevant approximation problem. Unfortunately, the standard LP and SDP formulations are not obviously solvable in O(n center dot polylogn)-space. Our work presents space-efficient algorithms for the convex programming required, as well as approaches to reduce the adaptivity of the sampling.

关键词： Correlation clustering Data streams linear sketches linear programming

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Fixed-Time Stable Gradient Flows: Applications to Continuous-Time Optimization

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2021年第5期66卷 2002-2015页

作者： Garg, Kunal Panagou, Dimitra Univ Michigan Dept Aerosp Engn Ann Arbor MI 48109 USA

Continuous-time optimization is currently an active field of research in optimization theory;prior work in this area has yielded useful insights and elegant methods for proving stability and convergence properties of the continuous-time optimization algorithms. This article proposes novel gradient-flow schemes that yield convergence to the optimal point of a convex optimization problem within a fixed time from any given initial condition for unconstrained optimization, constrained optimization, and min-max problems. It is shown that the solution of the modified gradient-flow dynamics exists and is unique under certain regularity conditions on the objective function, while fixed-time convergence to the optimal point is shown via Lyapunov-based analysis. The application of the modified gradient flow to unconstrained optimization problems is studied under the assumption of gradient dominance, a relaxation of strong convexity. Then, a modified Newton's method is presented that exhibits fixed-time convergence under some mild conditions on the objective function. Building upon this method, a novel technique for solving convex optimization problems with linear equality constraints that yields convergence to the optimal point in fixed time is developed. Finally, the general min-max problem is considered, and a modified saddle-point dynamics to obtain the optimal solution in fixed time is developed.

关键词： Optimization Convergence linear programming Convex functions Stability analysis Heuristic algorithms Newton method Finite and fixed-time stability nonlinear systems optimization

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A Functional Clipping Approach for Policy Optimization Algorithms

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IEEE ACCESS 2021年 9卷 96056-96063页

作者： Zhu, Wangshu Rosendo, Andre Shanghai Tech Univ Sch Informat Sci & Technol Dept Comp Sci Living Machines Labs Shanghai 201210 Peoples R China

Proximal policy optimization (PPO) has yielded state-of-the-art results in policy search, a subfield of reinforcement learning, with one of its key points being the use of a surrogate objective function to restrict the step size at each policy update. Although such restriction is helpful, the algorithm still suffers from performance instability and optimization inefficiency from the sudden flattening of the curve. To address this issue we present a novel functional clipping policy optimization algorithm, named Proximal Policy Optimization Smoothed Algorithm (PPOS), and its critical improvement is the use of a functional clipping method instead of a flat clipping method. We compare our approach with PPO and PPORB, which adopts a rollback clipping method, and prove that our approach can conduct more accurate updates than other PPO methods. We show that it outperforms the latest PPO variants on both performance and stability in challenging continuous control tasks. Moreover, we provide an instructive guideline for tuning the main hyperparameter in our algorithm.

关键词： Optimization Task analysis Reinforcement learning Search problems linear programming Licenses Tuning Machine learning robot control deep reinforcement learning policy search algorithm

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A Comprehensive Review on NSGA-II for Multi-Objective Combinatorial Optimization Problems

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IEEE ACCESS 2021年 9卷 57757-57791页

作者： Verma, Shanu Pant, Millie Snasel, Vaclav Indian Inst Technol Roorkee Dept Appl Sci & Engn Roorkee 247667 Uttar Pradesh India VSB Tech Univ Ostrava Dept Comp Sci Ostrava 70800 Czech Republic

This paper provides an extensive review of the popular multi-objective optimization algorithm NSGA-II for selected combinatorial optimization problems viz. assignment problem, allocation problem, travelling salesman problem, vehicle routing problem, scheduling problem, and knapsack problem. It is identified that based on the manner in which NSGA-II has been implemented for solving the aforementioned group of problems, there can be three categories: Conventional NSGA-II, where the authors have implemented the basic version of NSGA-II, without making any changes in the operators;the second one is Modified NSGA-II, where the researchers have implemented NSGA-II after making some changes into it and finally, Hybrid NSGA-II variants, where the researchers have hybridized the conventional and modified NSGA-II with some other technique. The article analyses the modifications in NSGA-II and also discusses the various performance assessment techniques used by the researchers, i.e., test instances, performance metrics, statistical tests, case studies, benchmarking with other state-of-the-art algorithms. Additionally, the paper also provides a brief bibliometric analysis based on the work done in this study.

关键词： Optimization Statistics Sociology Sorting Resource management linear programming Genetic algorithms NSGA-II combinatorial optimization multi-objective optimization genetic algorithms

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