1. the complete title of one (or more) paper(s) published in the open literature describing the work that the author claims describes a human-competitive result; Discovering Numerous Strassen's Equivalent Equations Using a Simple Micro Multimodal GA: Evolution in Action
2. the name, complete physical mailing address, e-mail address, and phone number of EACH author of EACH paper(s);
Azam Asilian Bidgoli, 76-1760 Simcoe St. N., Oshawa, ON L1G 0C3, Canada, Email: azam.asilianbidgoli@uoit.ca, Phone number: (+1) 365-688-6288
Steven Trumble, 2000 Simcoe St N, Oshawa, ON L1G 0C5, Canada, Email: steven.trumble@ontariotechu.net
Shahryar Rahnamayan, 60 Burnaby Blvd, Toronto, ON M5N 1G4, Canada, Email: shahryar.rahnamayan@uoit.ca, Phone number: (+1) 905-449-5026
3. the name of the corresponding author (i.e., the author to whom notices will be sent concerning the competition); Azam Asilian Bidgoli
4. the abstract of the paper(s); Solving real-world complex optimization problems using simple metaheuristic algorithms is a challenging but attractive task. Making matrix multiplication efficient is one of the interesting problems. This time-consuming algebraic operation is required in many applications in science and engineering, thus reducing its complexity targets more efficient computation. In fact, many of practical and theatrical complicated calculations can be modeled efficiently as matrix-based operations, therefore matrix multiplication is computationally expansive operator among all others. In this paper, a simple metaheuristic method based on Micro Genetic Algorithm is proposed to find Strassen's equivalent solutions which is an algebraic method to compute the product of two matrices with minimal number of multiplications. Since there are numerous optimal solutions, the modeled problem is a large-scale and highly multi-modal optimization problem. The proposed method could find more than 160,000 valid solutions with same complexity as Strassen's in a large-scale search space. Among all discovered solutions found using the proposed method, there are 701 distinct solutions which is the maximum number of discovered Strassen's equivalent solutions to the best of our knowledge. The proposed algorithm is simple but very efficient to find more and more solutions, in fact, that is a great demonstration of ‘evolution in action’ to tackle real-world complex problems like the current one, which just one set of its equations has been discovered by the Germen mathematicians and has remained mysterious for more than 50 years.
5. a list containing one or more of the eight letters (A, B, C, D, E, F, G, or H) that correspond to the criteria (see above) that the author claims that the work satisfies;
(B) The result is equal to or better than a result that was accepted as a new scientific result at the time when it was published in a peer-reviewed scientific journal.
(E) The result is equal to or better than the most recent human-created solution to a long-standing problem for which there has been a succession of increasingly better human-created solutions.
6. a statement stating why the result satisfies the criteria that the contestant claims (see examples of statements of human-competitiveness as a guide to aid in constructing this part of the submission);
(B) The result is equal to or better than a result that was accepted as a new scientific result at the time when it was published in a peer-reviewed scientific journal. As a new scientific discovery in mathematic, Strassen algorithm which decreases the number of multiplications using a smart technique proposed by Arnold Schonhage and Volker Strassen in 1971. One form of equation combinations was presented by this solution, however there are namouras Strassen’s equivalent solutions for matrix multiplication. GA algorithm accordingly can discover as many as possible valid solutions.
(E) The result is equal to or better than the most recent human-created solution to a long-standing problem for which there has been a succession of increasingly better human-created solutions.
The proposed approach provides an effective solution for the challenging problem of finding Strassen’s equivalent solutions which is an algebraic method to compute the product of two matrices with minimal number of multiplications. However, searching for the optimal combining equations in an extremely large-scale space is very crucial. In this study, a simple metaheuristic method based on Micro Genetic Algorithm is proposed to tackle this large-scale problem. Since there are numerous optimal solutions, finding all of them by human is almost impossible, whereas by GA, more than 160,000 valid solutions with same complexity as Strassen’s have been discovered.
7. a full citation of the paper (that is, author names; title, publication date; name of journal, conference, or book in which article appeared; name of editors, if applicable, of the journal or edited book; publisher name; publisher city; page numbers, if applicable); A. A. Bidgoli, S. Trumble and S. Rahnamayan, "Discovering Numerous Strassen’s Equivalent Equations Using a Simple Micro Multimodal GA: Evolution in Action," 2020 IEEE Congress on Evolutionary Computation (CEC), 2020, pp. 1-8, doi: 10.1109/CEC48606.2020.9185609.
8. a statement either that "any prize money, if any, is to be divided equally among the co-authors" OR a specific percentage breakdown as to how the prize money, if any, is to be divided among the co-authors; Any prize money, if any, is to be divided equally among the co-authors Azam Asilian Bidgoli, Steven Trumble, and Shahryar Rahnamayan.
9. a statement stating why the authors expect that their entry would be the "best,"
We believe that our work could qualify as the best for the following reasons:
• Our work solves effectively one of the most challenging real-world problem, known as finding Strassen’s equivalent solutions for matrix multiplication.
• Making Matrix multiplication as a time-consuming algebraic operation efficient has a huge impact in many applications in science and engineering, because reducing its complexity targets more efficient computation.
• The results obtained by the proposed GA approach has been published in a high-impact conference in the field of evolutionary computation.
• The proposed GA approach can find more than 160K solutions for the matrix multiplication of size 2 × 2 which is not possible by human.
• The proposed methodology showed for the first time that GA can be effectively employed for the discovering this much various solutions in a large-scale optimization problem for matrix multiplication.
• Using 701 unique solutions discovered by the proposed algorithm, more than 57 billion solutions can be generated which are a small portion of very large-scale exhaustive search possibilities.
10. An indication of the general type of genetic or evolutionary computation used, such as GA (genetic algorithms), GP (genetic programming), ES (evolution strategies), EP (evolutionary programming), LCS (learning classifier systems), GI (genetic improvement), GE (grammatical evolution), GEP (gene expression programming), DE (differential evolution), etc.
GA (Genetic Algorithm)
11. The date of publication of each paper. If the date of publication is not on or before the deadline for submission, but instead, the paper has been unconditionally accepted for publication and is “in press” by the deadline for this competition, the entry must include a copy of the documentation establishing that the paper meets the "in press" requirement. 03 September 2020