Dynamic Programming Optimization for Combined Objective Functions
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Conventional dynamic programming methods are inadequate for calculating solutions for optimization problems involving the combination of two objective functions, as they cannot simultaneously satisfy the constraint conditions of multiple objective functions.
Innovation Solution
An apparatus and method that acquire and select solutions for a third objective function by optimizing a combination of first and second objective functions, using dynamic programming to calculate solution candidates and update constraints until no further solutions optimize the second objective function, thereby efficiently solving the optimization problem.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If dynamic programming is used to solve optimization problems with a single objective function, then the solution can be calculated efficiently, but the method cannot handle objective functions formed by combining two different types of objective functions
Solution Approach 1:
The patent divides the optimization problem into multiple independent parts by separating the objective functions into first and second objective functions, each with their own constraints. This segmentation allows dynamic programming to be applied to each objective function independently, overcoming the limitation of handling combined objective functions while maintaining calculation efficiency.
Solution Approach 2:
The patent introduces a new dimension by using constraint values from the first objective function as parameters for the second objective function optimization. This dimensional extension enables the system to handle combined objective functions by transforming the problem into a multi-dimensional search space where dynamic programming can operate effectively.
2Device complexity
If conventional dynamic programming is applied to combined objective functions, then the method remains simple, but it cannot simultaneously satisfy constraint conditions of multiple objective functions
Solution Approach 1:
The patent performs preliminary optimization of the first objective function to obtain constraint values before optimizing the second objective function. This preliminary action ensures that the constraints from the first objective function are satisfied before introducing the second objective function, thereby maintaining reliability of constraint satisfaction while keeping the method relatively simple.
Solution Approach 2:
The patent uses constraint values as intermediary elements that link the two objective functions. These constraint values act as mediators that allow the system to satisfy the constraints of the first objective function while optimizing the second objective function, ensuring reliable constraint satisfaction without requiring a completely complex method.
3Measurement precision
If iterative optimization is performed to handle multiple objective functions, then the solution accuracy improves, but the computational time and cost increase
Solution Approach 1:
The patent applies partial optimization by focusing on optimizing one objective function at a time with its specific constraints, rather than simultaneously optimizing all objective functions. This partial action approach achieves sufficient solution accuracy for each objective function while reducing the overall computational time and cost compared to simultaneous optimization.
Solution Approach 2:
The patent changes parameters by using constraint values from the first objective function as fixed parameters for the second objective function optimization. This parameter change strategy allows the system to achieve high solution accuracy by systematically varying constraints while reducing computational time through structured optimization steps rather than exhaustive search.
4Loss of energy
If stored objective function values are used to reduce computation, then computational cost decreases, but the system complexity increases
Solution Approach 1:
The patent uses stored objective function values as copies of computation results from previous steps. By storing and reusing these values, the system reduces computational cost by avoiding redundant calculations. The copying approach is implemented through a straightforward storage mechanism that does not significantly increase system complexity, making it an efficient way to reduce energy consumption.
Data Source
AI summary
Provided is an apparatus comprising a processor and one or more computer readable mediums collectively including instructions that, when executed by the processor, cause the processor to: acquire a candidate for a solution of an optimization problem for optimizing a third objective function based on a first objective function and a second objective function; obtain, as another candidate for the solution of the optimization problem, a solution that optimizes the second objective function under a constraint corresponding to a value of the first objective function for the acquired candidate; and select the solution of the optimization problem from among the plurality of candidates for the solution of the optimization problem. Also provided as the first aspect are a method and non-transitory computer readable storage medium.