A Lagrangian relaxation(LR) approach was presented which is with machine capacity relaxation and operation precedence relaxation for solving a flexible job shop(FJS) scheduling problem from the steelmaking-refining-co...A Lagrangian relaxation(LR) approach was presented which is with machine capacity relaxation and operation precedence relaxation for solving a flexible job shop(FJS) scheduling problem from the steelmaking-refining-continuous casting process. Unlike the full optimization of LR problems in traditional LR approaches, the machine capacity relaxation is optimized asymptotically, while the precedence relaxation is optimized approximately due to the NP-hard nature of its LR problem. Because the standard subgradient algorithm(SSA) cannot solve the Lagrangian dual(LD) problem within the partial optimization of LR problem, an effective deflected-conditional approximate subgradient level algorithm(DCASLA) was developed, named as Lagrangian relaxation level approach. The efficiency of the DCASLA is enhanced by a deflected-conditional epsilon-subgradient to weaken the possible zigzagging phenomena. Computational results and comparisons show that the proposed methods improve significantly the efficiency of the LR approach and the DCASLA adopting capacity relaxation strategy performs best among eight methods in terms of solution quality and running time.展开更多
Unit commitment (UC) is one of the most important aspect of power generation in the world today. Though, there is no method to find the exact optimized solution, there exists several meta-heuristic algorithms to det...Unit commitment (UC) is one of the most important aspect of power generation in the world today. Though, there is no method to find the exact optimized solution, there exists several meta-heuristic algorithms to determine the close to exact solution. This paper proposes a novel solution to effectively determine UC and generation cost using the technique of invasive weed optimization (IWO). The existing technique distributes the load demand among all the generating units. The method proposed here utilizes the output of UC obtained by using the Lagrangian relaxation (LR) method and calculates the required generation from only the plants that are ON discarding the OFF generator units and thereby giving a faster and more accurate response. Moreover, the results show the comparison between the LR-particle swarm optimization (PSO) and LR-IWO, and prove that the cost of generation for a 4 unit, 8 hour schedule is much less in the case of IWO when compared to PSO.展开更多
基金Projects(51435009,51575212,61573249,61371200)supported by the National Natural Science Foundation of ChinaProjects(2015T80798,2014M552040,2014M561250,2015M571328)supported by Postdoctoral Science Foundation of ChinaProject(L2015372)supported by Liaoning Province Education Administration,China
文摘A Lagrangian relaxation(LR) approach was presented which is with machine capacity relaxation and operation precedence relaxation for solving a flexible job shop(FJS) scheduling problem from the steelmaking-refining-continuous casting process. Unlike the full optimization of LR problems in traditional LR approaches, the machine capacity relaxation is optimized asymptotically, while the precedence relaxation is optimized approximately due to the NP-hard nature of its LR problem. Because the standard subgradient algorithm(SSA) cannot solve the Lagrangian dual(LD) problem within the partial optimization of LR problem, an effective deflected-conditional approximate subgradient level algorithm(DCASLA) was developed, named as Lagrangian relaxation level approach. The efficiency of the DCASLA is enhanced by a deflected-conditional epsilon-subgradient to weaken the possible zigzagging phenomena. Computational results and comparisons show that the proposed methods improve significantly the efficiency of the LR approach and the DCASLA adopting capacity relaxation strategy performs best among eight methods in terms of solution quality and running time.
文摘Unit commitment (UC) is one of the most important aspect of power generation in the world today. Though, there is no method to find the exact optimized solution, there exists several meta-heuristic algorithms to determine the close to exact solution. This paper proposes a novel solution to effectively determine UC and generation cost using the technique of invasive weed optimization (IWO). The existing technique distributes the load demand among all the generating units. The method proposed here utilizes the output of UC obtained by using the Lagrangian relaxation (LR) method and calculates the required generation from only the plants that are ON discarding the OFF generator units and thereby giving a faster and more accurate response. Moreover, the results show the comparison between the LR-particle swarm optimization (PSO) and LR-IWO, and prove that the cost of generation for a 4 unit, 8 hour schedule is much less in the case of IWO when compared to PSO.