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Global Optimization Algorithm for Minimizing Linear Fractional Programming 认领 引用
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作者 ZHAO Peng SHEN Pei-ping ZHONG Zhe-wei 《Chinese Quarterly Journal of Mathematics》 2026年第1期50-59,共10页
In this paper,we study a class of Linear Fractional Programming on a nonempty bounded set,called the Problem(LFP),and design a branch and bound algorithm to find the global optimal solution of the problem(LFP).First,w... In this paper,we study a class of Linear Fractional Programming on a nonempty bounded set,called the Problem(LFP),and design a branch and bound algorithm to find the global optimal solution of the problem(LFP).First,we convert the problem(LFP)to the equivalent problem(EP2).Secondly,by applying the linear relaxation technique to the problem(EP2),the linear relaxation programming problem(LRP2Y)was obtained.Then,the overall framework of the algorithm is given,and the convergence and complexity of the algorithm are analyzed.Finally,experimental results are listed to illustrate the effectiveness of the algorithm. 展开更多
关键词 Global optimization Linear Fractional Programming Branch and bound algorithm Linear relaxation
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Cat Swarm Algorithm Generated Based on Genetic Programming Framework Applied in Digital Watermarking 认领 引用 被引量:1
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作者 Shu-Chuan Chu Libin Fu +2 位作者 Jeng-Shyang Pan Xingsi Xue Min Liu 《Computers, Materials & Continua》 SCIE EI 2025年第5期3135-3163,共29页
Evolutionary algorithms have been extensively utilized in practical applications.However,manually designed population updating formulas are inherently prone to the subjective influence of the designer.Genetic programm... Evolutionary algorithms have been extensively utilized in practical applications.However,manually designed population updating formulas are inherently prone to the subjective influence of the designer.Genetic programming(GP),characterized by its tree-based solution structure,is a widely adopted technique for optimizing the structure of mathematical models tailored to real-world problems.This paper introduces a GP-based framework(GPEAs)for the autonomous generation of update formulas,aiming to reduce human intervention.Partial modifications to tree-based GP have been instigated,encompassing adjustments to its initialization process and fundamental update operations such as crossover and mutation within the algorithm.By designing suitable function sets and terminal sets tailored to the selected evolutionary algorithm,and ultimately derive an improved update formula.The Cat Swarm Optimization Algorithm(CSO)is chosen as a case study,and the GP-EAs is employed to regenerate the speed update formulas of the CSO.To validate the feasibility of the GP-EAs,the comprehensive performance of the enhanced algorithm(GP-CSO)was evaluated on the CEC2017 benchmark suite.Furthermore,GP-CSO is applied to deduce suitable embedding factors,thereby improving the robustness of the digital watermarking process.The experimental results indicate that the update formulas generated through training with GP-EAs possess excellent performance scalability and practical application proficiency. 展开更多
关键词 Cat swarm algorithm genetic programming digital watermarking update mode mode generation framework
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From recursion to tabulation:Rethinking how we teach dynamic programming 认领 引用
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作者 Jiang Long 《计算机教育》 2026年第6期302-311,共10页
This paper proposes an intuitive,modular teaching framework for dynamic programming(DP).Beginning with the fundamental concept of recursion,the framework leverages dependency graphs to visually illustrate structural r... This paper proposes an intuitive,modular teaching framework for dynamic programming(DP).Beginning with the fundamental concept of recursion,the framework leverages dependency graphs to visually illustrate structural relationships among subproblems.This visual approach helps students intuitively grasp the underlying logic of tabulation,enabling them to independently determine correct tabulation orders.The plug-and-play design significantly reduces the barrier to learning,while strengthening students'analytical thinking and problem-solving skills.The effectiveness of this method is demonstrated through classroom application using classic examples such as the longest common subsequence(LCS),matrix chain multiplication(MCM),and rod cutting problems. 展开更多
关键词 Dynamic programming Plug-and-play framework Algorithm pedagogy Computer science education
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Improved genetic algorithm for nonlinear programming problems 认领 引用 被引量:10
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作者 Kezong Tang Jingyu Yang +1 位作者 Haiyan Chen Shang Gao 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2011年第3期540-546,共7页
An improved genetic algorithm(IGA) based on a novel selection strategy to handle nonlinear programming problems is proposed.Each individual in selection process is represented as a three-dimensional feature vector w... An improved genetic algorithm(IGA) based on a novel selection strategy to handle nonlinear programming problems is proposed.Each individual in selection process is represented as a three-dimensional feature vector which is composed of objective function value,the degree of constraints violations and the number of constraints violations.It is easy to distinguish excellent individuals from general individuals by using an individuals' feature vector.Additionally,a local search(LS) process is incorporated into selection operation so as to find feasible solutions located in the neighboring areas of some infeasible solutions.The combination of IGA and LS should offer the advantage of both the quality of solutions and diversity of solutions.Experimental results over a set of benchmark problems demonstrate that IGA has better performance than other algorithms. 展开更多
关键词 genetic algorithm(GA) nonlinear programming problem constraint handling non-dominated solution optimization problem.
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Automatic Algorithm Programming Model Based on the Improved Morgan's Refinement Calculus 认领 引用 被引量:7
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作者 ZUO Zhengkang HU Ying +2 位作者 HUANG Qing WANG Yuan WANG Changjing 《Wuhan University Journal of Natural Sciences》 CAS CSCD 2022年第5期405-414,共10页
The automatic algorithm programming model can increase the dependability and efficiency of algorithm program development,including specification generation,program refinement,and formal verification.However,the existi... The automatic algorithm programming model can increase the dependability and efficiency of algorithm program development,including specification generation,program refinement,and formal verification.However,the existing model has two flaws:incompleteness of program refinement and inadequate automation of formal verification.This paper proposes an automatic algorithm programming model based on the improved Morgan’s refinement calculus.It extends the Morgan’s refinement calculus rules and designs the C++generation system for realizing the complete process of refinement.Meanwhile,the automation tools VCG(Verification Condition Generator)and Isabelle are used to improve the automation of formal verification.An example of a stock’s maximum income demonstrates the effectiveness of the proposed model.Furthermore,the proposed model has some relevance for automatic software generation. 展开更多
关键词 automatic algorithm programming model program refinement VCG Isabelle Morgan’s refinement calculus
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Solution for integer linear bilevel programming problems using orthogonal genetic algorithm 认领 引用 被引量:10
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作者 Hong Li Li Zhang Yongchang Jiao 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2014年第3期443-451,共9页
An integer linear bilevel programming problem is firstly transformed into a binary linear bilevel programming problem, and then converted into a single-level binary implicit programming. An orthogonal genetic algorith... An integer linear bilevel programming problem is firstly transformed into a binary linear bilevel programming problem, and then converted into a single-level binary implicit programming. An orthogonal genetic algorithm is developed for solving the binary linear implicit programming problem based on the orthogonal design. The orthogonal design with the factor analysis, an experimental design method is applied to the genetic algorithm to make the algorithm more robust, statistical y sound and quickly convergent. A crossover operator formed by the orthogonal array and the factor analysis is presented. First, this crossover operator can generate a smal but representative sample of points as offspring. After al of the better genes of these offspring are selected, a best combination among these offspring is then generated. The simulation results show the effectiveness of the proposed algorithm. 展开更多
关键词 integer linear bilevel programming problem integer optimization genetic algorithm orthogonal experiment design
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Orthogonal genetic algorithm for solving quadratic bilevel programming problems 认领 引用 被引量:4
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作者 Hong Li Yongchang Jiao Li Zhang 《Journal of Systems Engineering and Electronics》 SCIE EI 2010年第5期763-770,共8页
A quadratic bilevel programming problem is transformed into a single level complementarity slackness problem by applying Karush-Kuhn-Tucker(KKT) conditions.To cope with the complementarity constraints,a binary encod... A quadratic bilevel programming problem is transformed into a single level complementarity slackness problem by applying Karush-Kuhn-Tucker(KKT) conditions.To cope with the complementarity constraints,a binary encoding scheme is adopted for KKT multipliers,and then the complementarity slackness problem is simplified to successive quadratic programming problems,which can be solved by many algorithms available.Based on 0-1 binary encoding,an orthogonal genetic algorithm,in which the orthogonal experimental design with both two-level orthogonal array and factor analysis is used as crossover operator,is proposed.Numerical experiments on 10 benchmark examples show that the orthogonal genetic algorithm can find global optimal solutions of quadratic bilevel programming problems with high accuracy in a small number of iterations. 展开更多
关键词 orthogonal genetic algorithm quadratic bilevel programming problem Karush-Kuhn-Tucker conditions orthogonal experimental design global optimal solution.
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A POLYNOMIAL PREDICTOR-CORRECTOR INTERIOR-POINT ALGORITHM FOR CONVEX QUADRATIC PROGRAMMING 认领 引用 被引量:6
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作者 余谦 黄崇超 江燕 《Acta Mathematica Scientia》 SCIE 2006年第2期265-270,共6页
This article presents a polynomial predictor-corrector interior-point algorithm for convex quadratic programming based on a modified predictor-corrector interior-point algorithm. In this algorithm, there is only one c... This article presents a polynomial predictor-corrector interior-point algorithm for convex quadratic programming based on a modified predictor-corrector interior-point algorithm. In this algorithm, there is only one corrector step after each predictor step, where Step 2 is a predictor step and Step 4 is a corrector step in the algorithm. In the algorithm, the predictor step decreases the dual gap as much as possible in a wider neighborhood of the central path and the corrector step draws iteration points back to a narrower neighborhood and make a reduction for the dual gap. It is shown that the algorithm has O(√nL) iteration complexity which is the best result for convex quadratic programming so far. 展开更多
关键词 Convex quadratic programming predictor-corrector interior-point algorithm
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Genetic Algorithm for Solving Quadratic Bilevel Programming Problem 认领 引用 被引量:1
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作者 WANG Guangmin WAN Zhongping +1 位作者 WANG Xianjiai FANG Debin 《Wuhan University Journal of Natural Sciences》 CAS 2007年第3期421-425,共5页
By applying Kuhn-Tucker condition the quadratic bilevel programming, a class of bilevel programming, is transformed into a single level programming problem, which can be simplified by some rule. So we can search the o... By applying Kuhn-Tucker condition the quadratic bilevel programming, a class of bilevel programming, is transformed into a single level programming problem, which can be simplified by some rule. So we can search the optimal solution in the feasible region, hence reduce greatly the searching space. Numerical experiments on several literature problems show that the new algorithm is both feasible and effective in practice. 展开更多
关键词 quadratic bilevel programming genetic algorithm optimal solution
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An adaptive genetic algorithm for solving bilevel linear programming problem 认领 引用 被引量:2
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作者 王广民 王先甲 +1 位作者 万仲平 贾世会 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2007年第12期1605-1612,共8页
Bilevel linear programming, which consists of the objective functions of the upper level and lower level, is a useful tool for modeling decentralized decision problems. Various methods are proposed for solving this pr... Bilevel linear programming, which consists of the objective functions of the upper level and lower level, is a useful tool for modeling decentralized decision problems. Various methods are proposed for solving this problem. Of all the algorithms, the ge- netic algorithm is an alternative to conventional approaches to find the solution of the bilevel linear programming. In this paper, we describe an adaptive genetic algorithm for solving the bilevel linear programming problem to overcome the difficulty of determining the probabilities of crossover and mutation. In addition, some techniques are adopted not only to deal with the difficulty that most of the chromosomes maybe infeasible in solving constrained optimization problem with genetic algorithm but also to improve the efficiency of the algorithm. The performance of this proposed algorithm is illustrated by the examples from references. 展开更多
关键词 bilevel linear programming genetic algorithm fitness value adaptive operator probabilities crossover and mutation
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A Branch and Bound-Based Algorithm for the Weak Linear Bilevel Programming Problems 认领 引用 被引量:1
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作者 LIU June HONG Yunfei ZHENG Yue 《Wuhan University Journal of Natural Sciences》 CAS CSCD 2018年第6期480-486,共7页
Most real-world optimization problems are hierarchical involving non-cooperative objectives. Many of these problems can be formulated in terms of the first(upper level) objective function being minimized over the so... Most real-world optimization problems are hierarchical involving non-cooperative objectives. Many of these problems can be formulated in terms of the first(upper level) objective function being minimized over the solution set mapping of the second(lower level) optimization problem. Often the upper level decision maker is risk-averse. The resulting class of problem is named weak bilevel programming problem. This paper presents a new algorithm which embeds a penalty function method into a branch and bound algorithm to deal with a weak linear bilevel programming problem. An example illustrates the feasibility of the proposed algorithm. 展开更多
关键词 bilevel programming penalty function branch andbound algorithm
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Random Fuzzy Chance-constrained Programming Based on Adaptive Chaos Quantum Honey Bee Algorithm and Robustness Analysis 认领 引用 被引量:5
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作者 Han Xue Xun Li Hong-Xu Ma 《International Journal of Automation and computing》 2010年第1期115-122,共8页
This paper proposes an adaptive chaos quantum honey bee algorithm(CQHBA)for solving chance-constrained program-ming in random fuzzy environment based on random fuzzy simulations.Random fuzzy simulation is designed to ... This paper proposes an adaptive chaos quantum honey bee algorithm(CQHBA)for solving chance-constrained program-ming in random fuzzy environment based on random fuzzy simulations.Random fuzzy simulation is designed to estimate the chance of a random fuzzy event and the optimistic value to a random fuzzy variable.In CQHBA,each bee carries a group of quantum bits representing a solution.Chaos optimization searches space around the selected best-so-far food source.In the marriage process,random interferential discrete quantum crossover is done between selected drones and the queen.Gaussian quantum mutation is used to keep the diversity of whole population.New methods of computing quantum rotation angles are designed based on grads.A proof of con-vergence for CQHBA is developed and a theoretical analysis of the computational overhead for the algorithm is presented.Numerical examples are presented to demonstrate its superiority in robustness and stability,efficiency of computational complexity,success rate,and accuracy of solution quality.CQHBA is manifested to be highly robust under various conditions and capable of handling most random fuzzy programmings with any parameter settings,variable initializations,system tolerance and confidence level,perturbations,and noises. 展开更多
关键词 Honey bee algorithm random fuzzy programming quantum computation chaos optimization robustness
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Hierarchical On-line Scheduling of Multiproduct Batch Plants with a Combined Approach of Mathematical Programming and Genetic Algorithm 认领 引用 被引量:1
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作者 陈理 王克峰 +1 位作者 徐霄羽 姚平经 《Chinese Journal of Chemical Engineering》 SCIE EI CAS 2004年第1期78-84,共7页
In this contribution we present an online scheduling algorithm for a real world multiproduct batch plant. The overall mixed integer nonlinear programming (MINLP) problem is hierarchically structured into a mixed integ... In this contribution we present an online scheduling algorithm for a real world multiproduct batch plant. The overall mixed integer nonlinear programming (MINLP) problem is hierarchically structured into a mixed integer linear programming (MILP) problem first and then a reduced dimensional MINLP problem, which are optimized by mathematical programming (MP) and genetic algorithm (GA) respectively. The basis idea relies on combining MP with GA to exploit their complementary capacity. The key features of the hierarchical model are explained and illustrated with some real world cases from the multiproduct batch plants. 展开更多
关键词 online scheduling multiproduct batch plant mixed integer nonlinear programming mathematical programming genetic algorithm
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Two new predictor-corrector algorithms for second-order cone programming 认领 引用 被引量:1
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作者 曾友芳 白延琴 +1 位作者 简金宝 唐春明 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2011年第4期521-532,共12页
Based on the ideas of infeasible interior-point methods and predictor-corrector algorithms, two interior-point predictor-corrector algorithms for the second-order cone programming (SOCP) are presented. The two algor... Based on the ideas of infeasible interior-point methods and predictor-corrector algorithms, two interior-point predictor-corrector algorithms for the second-order cone programming (SOCP) are presented. The two algorithms use the Newton direction and the Euler direction as the predictor directions, respectively. The corrector directions belong to the category of the Alizadeh-Haeberly-Overton (AHO) directions. These algorithms are suitable to the cases of feasible and infeasible interior iterative points. A simpler neighborhood of the central path for the SOCP is proposed, which is the pivotal difference from other interior-point predictor-corrector algorithms. Under some assumptions, the algorithms possess the global, linear, and quadratic convergence. The complexity bound O(rln(εo/ε)) is obtained, where r denotes the number of the second-order cones in the SOCP problem. The numerical results show that the proposed algorithms are effective. 展开更多
关键词 second-order cone programming infeasible interior-point algorithm predictor-corrector algorithm global convergence complexity analysis
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Exponential distribution-based genetic algorithm for solving mixed-integer bilevel programming problems 认领 引用 被引量:4
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作者 Li Hecheng Wang Yuping 《Journal of Systems Engineering and Electronics》 SCIE EI 2008年第6期1157-1164,共8页
Two classes of mixed-integer nonlinear bilevel programming problems are discussed. One is that the follower's functions are separable with respect to the follower's variables, and the other is that the follower's f... Two classes of mixed-integer nonlinear bilevel programming problems are discussed. One is that the follower's functions are separable with respect to the follower's variables, and the other is that the follower's functions are convex if the follower's variables are not restricted to integers. A genetic algorithm based on an exponential distribution is proposed for the aforementioned problems. First, for each fixed leader's variable x, it is proved that the optimal solution y of the follower's mixed-integer programming can be obtained by solving associated relaxed problems, and according to the convexity of the functions involved, a simplified branch and bound approach is given to solve the follower's programming for the second class of problems. Furthermore, based on an exponential distribution with a parameter λ, a new crossover operator is designed in which the best individuals are used to generate better offspring of crossover. The simulation results illustrate that the proposed algorithm is efficient and robust. 展开更多
关键词 mixed-integer nonlinear bilevel programming genetic algorithm exponential distribution optimalsolutions
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Smoothing Newton Algorithm for Linear Programming over Symmetric Cones 认领 引用 被引量:3
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作者 刘晓红 倪铁 《Transactions of Tianjin University》 EI CAS 2009年第3期216-221,共6页
By using the theory of Euclidean Jordan algebras,based on a new class of smoothing functions,the QiSun-Zhou's smoothing Newton algorithm is extended to solve linear programming over symmetric cones(SCLP).The algor... By using the theory of Euclidean Jordan algebras,based on a new class of smoothing functions,the QiSun-Zhou's smoothing Newton algorithm is extended to solve linear programming over symmetric cones(SCLP).The algorithm is globally convergent under suitable assumptions. 展开更多
关键词 linear programming symmetric cone Euclidean Jordan algebra smoothing algorithm
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Gaining-Sharing Knowledge Based Algorithm for Solving Stochastic Programming Problems 认领 引用 被引量:1
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作者 Prachi Agrawal Khalid Alnowibet Ali Wagdy Mohamed 《Computers, Materials & Continua》 SCIE EI 2022年第5期2847-2868,共22页
This paper presents a novel application of metaheuristic algorithmsfor solving stochastic programming problems using a recently developed gaining sharing knowledge based optimization (GSK) algorithm. The algorithmis b... This paper presents a novel application of metaheuristic algorithmsfor solving stochastic programming problems using a recently developed gaining sharing knowledge based optimization (GSK) algorithm. The algorithmis based on human behavior in which people gain and share their knowledgewith others. Different types of stochastic fractional programming problemsare considered in this study. The augmented Lagrangian method (ALM)is used to handle these constrained optimization problems by convertingthem into unconstrained optimization problems. Three examples from theliterature are considered and transformed into their deterministic form usingthe chance-constrained technique. The transformed problems are solved usingGSK algorithm and the results are compared with eight other state-of-the-artmetaheuristic algorithms. The obtained results are also compared with theoptimal global solution and the results quoted in the literature. To investigatethe performance of the GSK algorithm on a real-world problem, a solidstochastic fixed charge transportation problem is examined, in which theparameters of the problem are considered as random variables. The obtainedresults show that the GSK algorithm outperforms other algorithms in termsof convergence, robustness, computational time, and quality of obtainedsolutions. 展开更多
关键词 Gaining-sharing knowledge based algorithm metaheuristic algorithms stochastic programming stochastic transportation problem
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Discrete differential evolution algorithm for integer linear bilevel programming problems 认领 引用 被引量:1
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作者 Hong Li Li Zhang Yongchang Jiao 《Journal of Systems Engineering and Electronics》 SCIE CSCD 2016年第4期912-919,共8页
A discrete differential evolution algorithm combined with the branch and bound method is developed to solve the integer linear bilevel programming problems, in which both upper level and lower level variables are forc... A discrete differential evolution algorithm combined with the branch and bound method is developed to solve the integer linear bilevel programming problems, in which both upper level and lower level variables are forced to be integer. An integer coding for upper level variables is adopted, and then a discrete differential evolution algorithm with an improved feasibility-based comparison is developed to directly explore the integer solution at the upper level. For a given upper level integer variable, the lower level integer programming problem is solved by the existing branch and bound algorithm to obtain the optimal integer solution at the lower level. In the same framework of the algorithm, two other constraint handling methods, i.e. the penalty function method and the feasibility-based comparison method are also tested. The experimental results demonstrate that the discrete differential evolution algorithm with different constraint handling methods is effective in finding the global optimal integer solutions, but the improved constraint handling method performs better than two compared constraint handling methods. 展开更多
关键词 discrete linear bilevel programming problem discrete differential evolution constraint handling method branch and bound algorithm
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Web mining based on chaotic social evolutionary programming algorithm 认领 引用 被引量:1
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作者 Xie Bin 《Journal of Systems Engineering and Electronics》 SCIE EI 2008年第6期1272-1276,共5页
With an aim to the fact that the K-means clustering algorithm usually ends in local optimization and is hard to harvest global optimization, a new web clustering method is presented based on the chaotic social evoluti... With an aim to the fact that the K-means clustering algorithm usually ends in local optimization and is hard to harvest global optimization, a new web clustering method is presented based on the chaotic social evolutionary programming (CSEP) algorithm. This method brings up the manner of that a cognitive agent inherits a paradigm in clustering to enable the cognitive agent to acquire a chaotic mutation operator in the betrayal. As proven in the experiment, this method can not only effectively increase web clustering efficiency, but it can also practically improve the precision of web clustering. 展开更多
关键词 web clustering chaotic social evolutionary programming K-means algorithm
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A hybrid genetic algorithm to the program optimization model based on a heterogeneous network 认领 引用 被引量:2
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作者 CHEN Hang DOU Yajie +3 位作者 CHEN Ziyi JIA Qingyang ZHU Chen CHEN Haoxuan 《Journal of Systems Engineering and Electronics》 SCIE CSCD 2025年第4期994-1005,共12页
Project construction and development are an impor-tant part of future army designs.In today’s world,intelligent war-fare and joint operations have become the dominant develop-ments in warfare,so the construction and ... Project construction and development are an impor-tant part of future army designs.In today’s world,intelligent war-fare and joint operations have become the dominant develop-ments in warfare,so the construction and development of the army need top-down,top-level design,and comprehensive plan-ning.The traditional project development model is no longer suf-ficient to meet the army’s complex capability requirements.Projects in various fields need to be developed and coordinated to form a joint force and improve the army’s combat effective-ness.At the same time,when a program consists of large-scale project data,the effectiveness of the traditional,precise mathe-matical planning method is greatly reduced because it is time-consuming,costly,and impractical.To solve above problems,this paper proposes a multi-stage program optimization model based on a heterogeneous network and hybrid genetic algo-rithm and verifies the effectiveness and feasibility of the model and algorithm through an example.The results show that the hybrid algorithm proposed in this paper is better than the exist-ing meta-heuristic algorithm. 展开更多
关键词 program optimization heterogeneous network genetic algorithm portfolio selection.
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