Scale-Adaptive Subspace-Based Multiform Optimization for Large-Scale Optimization Problems

With the increasing size of optimization problems in various scientific and engineering fields, finding promising solutions for these large-scale optimization problems has become increasingly challenging. Dimension reduction-based evolutionary algorithms have emerged as one of the most efficient approaches to tackle these challenges. However, they still face difficulties in constructing appropriate subspaces and preserving the global optimum within those subspaces. To overcome these challenges, a multiform optimization framework with scale-adaptive subspace, called MFO-SAS, is proposed for large-scale optimization by taking full advantage of the subspace-assisted and multitasking mechanisms. To address the first challenge, a scale-adaptive switch strategy is designed to switch the subspaces with different scales at different optimization stages, enabling efficient assistance of the optimization processes for the original problem with appropriate subspaces. To tackle the second challenge, a multiform optimization paradigm is adopted to conduct the simultaneous search over both the original problem space and the constructed subspaces in a multitasking scenario, thus facilitating the utilization of the search experiences from different problem spaces. Consequently, the MFO-SAS framework effectively leverages valuable knowledge obtained from different spaces to guide the search and dynamically balances the representation accuracy of the subspace with the computational cost of subspace search. Experimental results on the large-scale benchmark problems demonstrate the superiority of MFO-SAS over several state-of-the-art algorithms.