Equivalent simplification is an effective method for solving large-scale complex problems. In this paper, the authors simplify a classic project scheduling problem, which is the nonlinear continuous time-cost tradeoff...Equivalent simplification is an effective method for solving large-scale complex problems. In this paper, the authors simplify a classic project scheduling problem, which is the nonlinear continuous time-cost tradeoff problem(TCTP). Simplifying TCTP is a simple path problem in a critical path method(CPM) network. The authors transform TCTP into a simple activity float problem and design a complex polynomial algorithm for its solution. First, the authors discover relationships between activity floats and path lengths by studying activity floats from the perspective of path instead of time.Second, the authors perform simplification and improve the efficiency and accuracy of the solution by deleting redundant activities and narrowing the duration intervals of non-redundant activities. Finally,the authors compare our method with current methods. The relationships between activity floats and path lengths provide new approaches for other path and correlative project problems.展开更多
Based on the two-list algorithm and the parallel three-list algorithm, an improved parallel three-list algorithm for knapsack problem is proposed, in which the method of divide and conquer, and parallel merging withou...Based on the two-list algorithm and the parallel three-list algorithm, an improved parallel three-list algorithm for knapsack problem is proposed, in which the method of divide and conquer, and parallel merging without memory conflicts are adopted. To find a solution for the n-element knapsack problem, the proposed algorithm needs O（2^3n/8） time when O（2^3n/8） shared memory units and O（2^n/4） processors are available. The comparisons between the proposed algorithm and 10 existing algorithms show that the improved parallel three-fist algorithm is the first exclusive-read exclusive-write （EREW） parallel algorithm that can solve the knapsack instances in less than O（2^n/2） time when the available hardware resource is smaller than O（2^n/2） , and hence is an improved result over the past researches.展开更多
Job-shop scheduling problem with discretely controllable processing times (JSP-DCPT) is modeled based on the disjunctive graph, and the formulation of JSP-DCPT is presented. A three-step decomposition approach is prop...Job-shop scheduling problem with discretely controllable processing times (JSP-DCPT) is modeled based on the disjunctive graph, and the formulation of JSP-DCPT is presented. A three-step decomposition approach is proposed so that JSP-DCPT can be handled by solving a job-shop scheduling problem (JSP) and a series of discrete time-cost tradeoff problems. To simplify the decomposition approach, the time-cost phase plane is introduced to describe tradeoffs of the discrete time-cost tradeoff problem, and an extreme mode-based set dominant theory is elaborated so that an upper bound is determined to cut discrete time-cost tradeoff problems generated by using the proposed decomposition approach. An extreme mode-based set dominant decomposition algorithm (EMSDDA) is then proposed. Experimental simulations for instance JSPDCPT_FT10, which is designed based on a JSP benchmark FT10, demonstrate the effectiveness of the proposed theory and the decomposition approach.展开更多
基金supported by the Science and Technology Foundation of Jiangxi Provincial Department of Education in China under Grant No.GJJ161114the Natural Science Foundation of China under Grant No.71271081the Soft Science Research Base of Water Security and Sustainable Development of Jiangxi Province in China
文摘Equivalent simplification is an effective method for solving large-scale complex problems. In this paper, the authors simplify a classic project scheduling problem, which is the nonlinear continuous time-cost tradeoff problem(TCTP). Simplifying TCTP is a simple path problem in a critical path method(CPM) network. The authors transform TCTP into a simple activity float problem and design a complex polynomial algorithm for its solution. First, the authors discover relationships between activity floats and path lengths by studying activity floats from the perspective of path instead of time.Second, the authors perform simplification and improve the efficiency and accuracy of the solution by deleting redundant activities and narrowing the duration intervals of non-redundant activities. Finally,the authors compare our method with current methods. The relationships between activity floats and path lengths provide new approaches for other path and correlative project problems.
文摘Based on the two-list algorithm and the parallel three-list algorithm, an improved parallel three-list algorithm for knapsack problem is proposed, in which the method of divide and conquer, and parallel merging without memory conflicts are adopted. To find a solution for the n-element knapsack problem, the proposed algorithm needs O（2^3n/8） time when O（2^3n/8） shared memory units and O（2^n/4） processors are available. The comparisons between the proposed algorithm and 10 existing algorithms show that the improved parallel three-fist algorithm is the first exclusive-read exclusive-write （EREW） parallel algorithm that can solve the knapsack instances in less than O（2^n/2） time when the available hardware resource is smaller than O（2^n/2） , and hence is an improved result over the past researches.
基金supported by the National Natural Science Foundation of China (Grant Nos. 51075337, 50705076, 50705077)the Natural Sci-ence Basic Research Plan in Shaanxi Province of China (Grant No. 2009JQ9002)
文摘Job-shop scheduling problem with discretely controllable processing times (JSP-DCPT) is modeled based on the disjunctive graph, and the formulation of JSP-DCPT is presented. A three-step decomposition approach is proposed so that JSP-DCPT can be handled by solving a job-shop scheduling problem (JSP) and a series of discrete time-cost tradeoff problems. To simplify the decomposition approach, the time-cost phase plane is introduced to describe tradeoffs of the discrete time-cost tradeoff problem, and an extreme mode-based set dominant theory is elaborated so that an upper bound is determined to cut discrete time-cost tradeoff problems generated by using the proposed decomposition approach. An extreme mode-based set dominant decomposition algorithm (EMSDDA) is then proposed. Experimental simulations for instance JSPDCPT_FT10, which is designed based on a JSP benchmark FT10, demonstrate the effectiveness of the proposed theory and the decomposition approach.
