Fast divide-and-conquer algorithms for preemptive scheduling problems with controllable processing times – A polymatroid optimization approach

We consider a variety of preemptive scheduling problems with controllable processing times on a single machine and on identical/uniform parallel machines, where the objective is to minimize the total compression cost. In this paper, we propose fast divide-and-conquer algorithms for these scheduling problems. Our approach is based on the observation that each scheduling problem we discuss can be formulated as a polymatroid optimization problem. We develop a novel divide-and-conquer technique for the polymatroid optimization problem and then apply it to each scheduling problem. We show that each scheduling problem can be solved in O(Tfeas(n) log n) time by using our divide-and-conquer technique, where n is the number of jobs and Tfeas(n) denotes the time complexity of the corresponding feasible scheduling problem with n jobs. This approach yields faster algorithms for most of the scheduling problems discussed in this paper

Preemptive Online Scheduling: Optimal Algorithms for All Speeds

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Harmony Search Algorithms in Structural Engineering

Harmony search method is widely applied in structural design optimization since its emergence. These applications have shown that harmony search algorithm is robust, effective and reliable optimization method. Within recent years several enhancements are suggested to improve the performance of the algorithm. Among these Mandavi has presented two versions of harmony search methods. He named these as improved harmony search method and global best harmony search method. Saka and Hasancebi (2009) have suggested adaptive harmony search where the harmony search parameters are adjusted automatically during design iterations. Coelho has proposed improved harmony search method. He suggested an expression for one of the parameters of standard harmony search method. In this chapter, the optimum design problem of steel space frames is formulated according to the provisions of LRFD-AISC (Load and Resistance Factor Design-American Institute of Steel Corporation): The weight of the steel frame is taken as the objective function to be minimized. Seven different structural optimization algorithms are developed each of which are based on one of the above mentioned versions of harmony search method. Three real size steel frames are designed using each of these algorithms. The optimum designs obtained by these techniques are compared and performance of each version is evaluated