Abstract
This paper introduces a new hybrid algorithm for locating all solutions in multimodal optimization problems. This algorithm combines an adaptive sequential niche technique with deterministic local optimization to detect all extrema efficiently and reliably. A genetic element of the hybrid algorithm performs a global search while the deterministic local optimizer computes the precise coordinates of the extremum. Once an extremum is precisely located, a niche demarcating the area of attraction around the local minimum is recorded. The sequential process proceeds to search for additional extrema. Our novel method overcomes challenges to distinguish multiple extrema in problem-specific terrain by an automatic niche radius adjustment. Several comparative simulation experiments with previous niche algorithms demonstrate the novel algorithm's performance and reliability. We also present a difficult case study for solution multiplicity in catalytic pellets. We determine multiple solutions for distributed inversion problems.
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