Approximation for Batching via Priorities

We consider here the one-machine serial batching problem under weighted average completion. This problem is known to be $cal Ncal P$-hard and no good approximation algorithms are known. Batching has wide application in manufacturing, decision management, and scheduling in information technology. We give an approximation algorithm with approximation ratio of $2$; the algorithm is a priority algorithm, which batches jobs in decreasing order of priority. We also give a lower bound of $frac{2 +sqrt{6}}{4} approx 1.1124$ on the approximation ratio of any priority algorithm and conjecture that there is a priority algorithm which matches this bound. Adaptive algorithm experiments are used to support the conjecture. An easier problem is the list version of the problem where the order of the jobs is given. We give a new linear time algorithm for the list batching problem

Genetic algorithms using Galib

GAlib is a C++ library of genetic algorithm objects that was recently developed at the Massachusetts Institute of Technology. This thesis is to demonstrate its functionality and versatility for implementing haploid tripartite genetic algorithms; We first built a test bed in which GAlib could be used. To achieve this, we used GAlib to solve the Traveling Salesman Problem and implemented two-opt and simulated annealing for compariSon We then examined the use of genetic algorithms for finding loop invariants. We used GAlib successfully to build a model but results remain inconclusive; In our main thrust we applied genetic algorithms to train and develop neural networks. To develop neural network architectures we used two different methods of representing neural networks: connection matrices and graph-generation grammars. We were able to demonstrate that genetic algorithms are an effective tool for training networks as well as for finding network architectures

Evolutionary computing for routing and scheduling applications

Ph.DDOCTOR OF PHILOSOPH

Competitive genetic algorithms for the open-shop scheduling problem

International audienceFor more than two machines, and when preemption is forbidden, the computation of minimum makespan schedules for the open-shop problem is NP-hard. Compared to the flow-shop and the job-shop, the open-shop has free job routes which lead to a much larger solution space, to smaller gaps between the optimal makespan and the lower bounds, and to disappointing results for the algorithms based on the disjunctive graph model. For instance, the best existing branch and bound method cannot solve some 7 ×7 hard instances to optimality, and all published metaheuristics (working by reversing some disjunctions already fixed) do not better than some greedy or steepest-descent heuristics which need a much smaller computational effort. In this context, the intrinsic parallelism of genetic algorithms (GAs) seems well adapted, for detecting global optima disseminated among many quasi-optimal schedules. This paper presents several GAs for the open-shop problem. It is shown that even simple and fast versions can compete with the best known heuristics and metaheuristics, thanks to two key-features: a population in which each individual has a distinct makespan, and a special procedure which reorders every new chromosome. Using problem-specific heuristics, it is possible to design more powerful GAs which give excellent results, even on the hardest benchmarks of the literature: for instance, all hard open instances from Taillard are broken, except one for which the best known solution is improved

Evolutionary multi-objective optimization in scheduling problems

Ph.DDOCTOR OF PHILOSOPH