Abstract. Solutions calculated by Evolutionary Algorithms have come to surpass exact methods for solving various problems. The Rubik's Cube multiobjective optimization problem is one such area. In this work we present an evolutionary approach to solve the Rubik's Cube with a low number of moves by building upon the classic Thistlethwaite's approach. We provide a group theoretic analysis of the subproblem complexity induced by Thistlethwaite's group transitions and design an Evolutionary Algorithm from the ground up including detailed derivation of our custom fitness functions. The implementation resulting from these observations is thoroughly tested for integrity and random scrambles, revealing performance that is competitive with exact methods without the need for pre-calculated lookup-tables.

In nature, building block-based biopolymers can adapt to functional and environmental demands by recombination and mutation of the monomer sequence. We present here an analogous, artificial evolutionary optimization process which we have applied to improve the functionality of cell-penetrating peptide molecules. The “evolution” consisted of repeated rounds of in silico peptide sequence alterations using a genetic algorithm followed by in vitro peptide synthesis, experimental analysis, and ranking according to their “fitness” (i.e., their ability to carry the cargo carboxyfluorescein into cultured cells). The genetic algorithm-based optimization method was customized and adapted from former successful applications in the lab to realize an early convergence and a minimum number of in vitro and in silico processing steps by configured settings derived from empirical in silico simulation. We started out with 20 “lead peptides” which we had previously identified as top performers regarding their ability to enter cultured cells. Ten breeding rounds comprising 240 peptides each yielded a peptide population of which the top 10 candidates displayed a 6-fold (median values) increase in its cell-penetration capability compared with the top 10 lead peptides, and two consensus sequences emerged which represent local fitness optima. In addition, the cell-penetrating potential could be proven independently of the carboxyfluorescein cargo in an alternative setting. Our results demonstrate that we have established a powerful optimization technology that can be used to further improve peptides with known functionality and adapt them to specific applications.

Abstract. Solutions calculated by Evolutionary Algorithms have come to surpass exact methods for solving various problems. The Rubik's Cube multiobjective optimization problem is one such area. In this paper we design, benchmark and compare two different evolutionary approaches to solve the Rubik's Cube. One is based on the work of Michael Herdy using predefined swapping and flipping algorithms, the other adapting the Thistlethwaite Algorithm. The latter is based on group theory, transforming the problem of solving the Cube into four subproblems. We give detailed information about realizing those Evolutionary Algorithms regarding selection method, fitness function and mutation operators. Finally, both methods are benchmarked and compared to enable an interesting view of solution space size and exploration/exploitation in regard to the Rubik's Cube.

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