NP-hard optimization problems are computationally challenging tasks that require significant resources to solve, particularly as problem sizes increase. In this paper, we introduce a novel framework, GiraDP, which converts dynamic programming problems into graphs and solves these Large-scale graphs efficiently. GiraDP addresses NP-hard optimization problems by leveraging advanced graph processing techniques. The framework utilizes Giraph and Hadoop in its architecture to manage extensive datasets and complex computations. It generates input data for Giraph and identifies active vertices that correspond to sub-problems within the Larger problem. Our experiments include scenarios with 20, 40, and 60 items, across varying knapsack capacities. The results indicate that while the serial algorithm performs best at low capacities, it fails to handle Larger instances due to memory limitations, resulting in heap space errors. In contrast, GiraDP demonstrates superior efficiency and scalability for high capacities and Large item sets. The MPI-based approach also shows improved performance over the serial algorithm for Larger problems, although it does not match the efficiency of GiraDP. These findings underscore the importance of distributed computing solutions for Large-scale optimization problems

Direct drive permanent magnet synchronous generators have numerous advantages such as improved reliability, low maintenance, long life, and developed performance characteristics. Focus of this paper is on the development of a step-by-step method for the design of a permanent magnet synchronous generator. Then the winding function method is used to model the generator and to analytically calculate its output characteristics. The analytical results of the designed generator are evaluated with the finite element analysis (FEA) results and it is demonstrated that the achieved results from both methods are well matched with the experimental measurements of the Northern Power direct-drive generator. The sensitivity analysis and the optimization based on the genetic algorithm are used to achieve an optimum generator. The optimization goal is obtaining higher efficiency and power factor with lower required permanent magnet (PM) volume and voltage regulation for the optimum machine compared to the initial design. In addition, the calculation of the voltage total harmonic distortion (THD) is presented and the optimum skew angle for the optimum generator is computed to reduce the voltage THD.

Optimal design of Large-scale structures is a rather difficult task and the computational efficiency of the currently available methods needs to be improved. In view of this, the paper presents a modified Charged System Search (CSS) algorithm. The new methodology is based on the combination of CSS and Particle Swarm Optimizer. In addition, in order to improve optimization search, the sequence of tasks entailed by the optimization process is changed so that the updating of the design variables can directly be performed after each movement. In this way, the new method acts as a single-agent algorithm while preserving the positive characteristics of its original multi-agent formulation.

This paper proposes a refined version of particle swarm optimization technique for the optimum design of steel structures. Swarm is composed of a number of particles and each particle in the swarm represents a candidate solution of the optimum design problem. Design constraints in accordance with ASD-AISC (Allowable Stress Design Code of American Institute of Steel Institution) are imposed by the particle swarm optimization based optimum design algorithm developed. A constraint handling method called the 'penalty function method' is introduced to maintain acceptable solutions. The refined version of the particle swarm optimization algorithm proposed in this paper is easy to implement and the results and convergence performance are better than the simple particle swarm optimization algorithm and some other meta-heuristic optimization techniques. The effect of different inertia weight parameters in finding the optimum design is also tested in two numerical examples.