Faster Algorithms for Semi-Matching Problems

We consider the problem of finding \textit{semi-matching} in bipartite graphs which is also extensively studied under various names in the scheduling literature. We give faster algorithms for both weighted and unweighted case. For the weighted case, we give an $O(nm\log n)$-time algorithm, where $n$ is the number of vertices and $m$ is the number of edges, by exploiting the geometric structure of the problem. This improves the classical $O(n^3)$ algorithms by Horn [Operations Research 1973] and Bruno, Coffman and Sethi [Communications of the ACM 1974]. For the unweighted case, the bound could be improved even further. We give a simple divide-and-conquer algorithm which runs in $O(\sqrt{n}m\log n)$ time, improving two previous $O(nm)$-time algorithms by Abraham [MSc thesis, University of Glasgow 2003] and Harvey, Ladner, Lov\'asz and Tamir [WADS 2003 and Journal of Algorithms 2006]. We also extend this algorithm to solve the \textit{Balance Edge Cover} problem in $O(\sqrt{n}m\log n)$ time, improving the previous $O(nm)$-time algorithm by Harada, Ono, Sadakane and Yamashita [ISAAC 2008].Comment: ICALP 201

Research on the time optimization model algorithm of Customer Collaborative Product Innovation

Purpose: To improve the efficiency of information sharing among the innovation agents of customer collaborative product innovation and shorten the product design cycle, an improved genetic annealing algorithm of the time optimization was presented. Design/methodology/approach: Based on the analysis of the objective relationship between the design tasks, the paper takes job shop problems for machining model and proposes the improved genetic algorithm to solve the problems, which is based on the niche technology and thus a better product collaborative innovation design time schedule is got to improve the efficiency. Finally, through the collaborative innovation design of a certain type of mobile phone, the proposed model and method were verified to be correct and effective. Findings and Originality/value: An algorithm with obvious advantages in terms of searching capability and optimization efficiency of customer collaborative product innovation was proposed. According to the defects of the traditional genetic annealing algorithm, the niche genetic annealing algorithm was presented. Firstly, it avoided the effective gene deletions at the early search stage and guaranteed the diversity of solution; Secondly, adaptive double point crossover and swap mutation strategy were introduced to overcome the defects of long solving process and easily converging local minimum value due to the fixed crossover and mutation probability; Thirdly, elite reserved strategy was imported that optimal solution missing was avoided effectively and evolution speed was accelerated. Originality/value: Firstly, the improved genetic simulated annealing algorithm overcomes some defects such as effective gene easily lost in early search. It is helpful to shorten the calculation process and improve the accuracy of the convergence value. Moreover, it speeds up the evolution and ensures the reliability of the optimal solution. Meanwhile, it has obvious advantages in efficiency of information sharing among the innovation agents of customer collaborative product innovation. So, the product design cycle could be shortened.Peer Reviewe

Swarm lexicographic goal programming for fuzzy open shop scheduling

In this work we consider a multiobjective open shop scheduling problem with uncertain processing times and flexible due dates, both modelled using fuzzy sets. We adopt a goal programming model based on lexicographic multiobjective optimisation of both makespan and due-date satisfaction and propose a particle swarm algorithm to solve the resulting problem. We present experimental results which show that this multiobjective approach achieves as good results as single-objective algorithms for the objective with the highest priority, while greatly improving on the second objectiv