Symmetry-Guided Neural Approximation and Convolutional Non-Dominated Sorting on Synthetic Two-Objective Benchmarks Toward Option-Pricing Model Research in Financial Mathematics and Quantitative Economic Analysis

Two-objective optimization requires both reliable front approximation and explainable non-dominated extraction. This study develops a theoretical and computational method that maps sampled objective vectors to rasterized objective-space images and processes their Pareto structure through supervised neural approximation, a deterministic convolutional extractor, and exploratory reinforcement search. Network I reconstructs a high-density sampled occupancy image from sparse samples, whereas Network II approximates the sampled Pareto-front boundary. The principal algorithmic contribution is a fixed cross-correlation kernel derived from the two-objective dominance quadrant and coupled with a cell archive that preserves original vectors and resolves raster collisions through exact dominance checks. Under the stated coordinate convention, central inversion relates the dominating and dominated displacement quadrants, translation-equivariant cross-correlation applies the same local relation across the grid, and minimization selects only the improvement-directed boundary. Experiments on SCH, FON, POL, KUR, and ZDT synthetic benchmarks assess front-geometry recovery and deterministic extraction on grids from 127 × 127 to 2048 × 2048; the reinforcement-learning results on SCH are interpreted as exploratory feasibility evidence. The present evidence is therefore confined to synthetic benchmarks. The method provides a benchmark-based methodological foundation for future multi-criterion model-selection and calibration research, including option-pricing model research in financial mathematics and quantitative economic analysis.