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Peak and valley detection in multimodal functions by means of 3D normal metadata

A novel approach for detecting multiple optimal and suboptimal solutions in multimodal function optimisation problems is proposed in this paper. A peak and valley detecting algorithm utilising 3D normal metadata will be presented and tested against several multimodal functions in this paper. The peak and valley detection method by means three dimensional (3D) normal metadata presents the multimodal function as a 3D mesh in which the normals are calculated from the triangles that constitute the 3D mesh. The set of normals forms the metadata from which the algorithm determines if a region is an optimal region. Peak (maximum) and valley (minimum) regions are detected by determining the angle between the normal and a unit vector. A line intersecting algorithm is then used to determine if a region is either convex (i.e. a peak) or concave (i.e. a valley).