Multi-Objective Optimization Calculation Device
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Solution Overview
Problem
Current methods for solving multi-objective optimization problems, such as the constraint method and linear weighted sum method, face challenges in determining appropriate constraints or weight coefficients, leading to difficulties in obtaining multiple Pareto solutions with different balances, especially when dealing with non-convex feasible solution sets.
Innovation Solution
A calculation device and method that calculates approximate Pareto solutions by generating different composite objective functions using varying weight patterns, predicting the increase in Pareto hypervolume, and iteratively updating candidate solutions using a solver device to select non-inferior solutions, thereby approximating Pareto solutions with a small amount of calculation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the constraint method is used to solve multi-objective optimization problems, then a solution optimizing the objective function under constraints can be obtained, but it is difficult to rationally determine the constraints and cannot obtain multiple Pareto solutions with different balances unless solved multiple times by changing constraints
Solution Approach 1:
The patent changes the parameter representation from constraints to weight coefficients. Instead of solving the same problem multiple times with different constraints, the system generates multiple composite objective functions by varying weight coefficients (w1, w2, ..., wM) for different objective functions. This allows obtaining multiple Pareto solutions in a single solving process by changing parameters (weights) rather than problem structure (constraints).
Solution Approach 2:
The patent creates a universal solving framework that handles multiple objectives simultaneously through a single composite objective function. The multi-objective optimization problem is transformed into a unified problem where F(x) = w1*f1(x) + w2*f2(x) + ... + wM*fM(x), allowing the same solver to generate diverse Pareto solutions by adjusting weights, rather than requiring separate solving processes for each objective balance.
2Adaptability or versatility
If the linear weighted sum method is used to calculate multiple Pareto solutions by changing weight coefficients, then multiple Pareto solutions with different balances can be obtained, but it is difficult to rationally determine the multiple weight coefficients and cannot obtain Pareto solutions for concave portions when the feasible solution set is non-convex
Solution Approach 1:
The patent performs preliminary action by pre-generating multiple candidate weight coefficient sets (w1, w2, ..., wM) before solving the optimization problem. Instead of arbitrarily choosing weights or requiring iterative adjustment, the system prepares a comprehensive set of weight combinations that systematically cover different objective balances, including those needed to reach concave portions of the Pareto front. This preliminary preparation eliminates the difficulty of determining appropriate weight coefficients.
Solution Approach 2:
The patent implements feedback by using the Pareto hypervolume as an evaluation metric to assess the quality and diversity of obtained Pareto solutions. The system calculates the hypervolume indicator to measure how well the obtained solutions cover the Pareto front, and uses this feedback to guide the selection and adjustment of weight coefficients, ensuring comprehensive coverage including concave portions that might be missed by simple weight variation.
3Measurement precision
If a multi-objective optimization solver is used to solve multi-objective optimization problems, then multiple Pareto solutions can be obtained, but the algorithm becomes complex and the amount of calculation becomes huge
Solution Approach 1:
The patent substitutes a complex multi-objective optimization solver with a simpler single-objective optimization solver. By transforming the multi-objective problem into a single composite objective function F(x) = w1*f1(x) + w2*f2(x) + ... + wM*fM(x), the system replaces the need for sophisticated multi-objective algorithms with standard single-objective optimization techniques, dramatically reducing computational complexity while maintaining the ability to obtain accurate Pareto solutions through weight coefficient variation.
Data Source
AI summary
A calculation device includes a prediction unit, a selection unit, an update unit, a repetitive control unit, and an output unit. The prediction unit performs, for each weight-pattern, predicting the amount of increase in Pareto hypervolume by using a corresponding weight-pattern. The selection unit performs selecting a maximum weight-pattern with the largest amount of increase. The update unit performs updating a candidate solution set by acquiring, from a solver device, multiple solutions in a problem of minimizing a composite objective function being a linear weighted sum of multiple objective functions and multiple weight coefficients represented by the maximum weight-pattern, and adding the acquired multiple solutions to the candidate solution set. The repetitive control unit performs repeating the prediction, the selection, and the update. The output unit outputs a set including a non-inferior solution in the candidate solution set as an approximate Pareto solution set.