Prime-Number Parallel Solver for Engineering Design Optimization
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Solution Overview
Problem
Current parallel solvers for Engineering Design Optimization Problems (EDOPs) face challenges in effectively partitioning main programs into independent subprograms, leading to excessive communication time and difficulty in reaching optimal solutions due to random node generation and overlapping product values.
Innovation Solution
The method, referred to as PARA235, employs a prime-number-based approach to partition EDOPs into independent subprograms, utilizing available parallel processors to solve each subprogram independently, thereby reducing communication and overlapping product values, and automatically selecting the optimal solution.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If random node generation and conventional partitioning methods are used, then the main program can be divided into subprograms, but excessive communication time occurs and overlapping product values prevent optimal solutions
Solution Approach 1:
The patent divides the main program into N independent subprograms using prime number-based partitioning, where each subprogram is assigned to a separate processor. This segmentation eliminates the need for inter-processor communication during execution, directly resolving the contradiction by reducing communication time while maintaining solution optimization capability through independent parallel processing of disjoint variable sets.
2Measurement precision
If conventional partitioning methods are used, then the program can be processed in parallel, but overlapping product values occur across subprograms reducing solution quality
Solution Approach 1:
The patent employs asymmetric prime number-based partitioning where variables are distributed to subprograms based on their index modulo N, creating non-uniform but disjoint partitions. This asymmetric approach ensures that no two subprograms share the same product values, eliminating overlapping while maintaining manageable partitioning complexity through the mathematical properties of prime numbers.
Solution Approach 2:
The patent transforms the partitioning parameter from conventional sequential division to prime number-based modular arithmetic. By changing the partitioning parameter from a simple sequential assignment to a mathematically optimized prime-based assignment, the system achieves complete disjointness of product values across subprograms, improving solution optimality without significantly increasing partitioning complexity.
3Productivity
If more parallel processors are used, then computation burden is reduced, but coordination and solution integration become more complex
Solution Approach 1:
The patent extracts the coordination complexity by designing completely independent subprograms that each solve their own optimization problem using disjoint variable sets. Since no subprogram depends on results from others and no product values overlap, the system simply collects and compares final solutions without complex coordination, enabling scalable parallel processing where computation speed increases linearly with processor count while coordination remains trivial.
Data Source
AI summary
Received is a main program representing one Engineering Design Optimization Problem (EDOP), the EDOP including polynomial terms with product values. A number (N) of available parallel processors for parallel processing are identified. The main program is partitioned into N subprograms, N being a positive integer greater than one. The N subprograms have fewer overlapping product values between them compared to existing solutions, and the partitioning is prime-number based. Each of the available parallel processors then independently solve a unique subprogram of the N subprograms, resulting in N unique solutions. A best solution is automatically chosen from among the N unique solutions and the best solution is automatically applied to the EDOP.