Algorithms for hard quadratic combinatorial optimization problems and linkages with quantum bridge analytics

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The primary objective of the proposed research program is to develop efficient algorithms for solving a class of hard quadratic combinatorial optimization (QCOP) problems with applications in production, planning, communication, distribution, sequencing and scheduling, and resource allocation. An equally important objective is to train highly qualified graduate and undergraduate students, and post-doctoral fellows, fostering equity, diversity, and inclusion (EDI) considerations, who could apply cutting-edge techniques within complex optimization projects by enhancing existing procedures and developing viable alternatives. Dissemination of research results through conference presentations and publications in reputable journals are also part of the objectives. The primary focus of the algorithm design aspect of the project is aimed at developing algorithms to run on standard computers as well as bridging algorithms to run on hybrid hardware involving both standard and quantum inspired computers. Accomplishment of these long-term objectives translate into short-term goals of developing new theoretical results, intelligent application of existing results, new problem decomposition methods, clever reformulations, development of computer programs, and extensive computational and theoretical analysis of algorithms for specific problem classes identified. The investigators research experience in QCOP and results obtained in the past will be very useful in successfully completing this project. In particular, very large neighborhood search techniques developed by this investigator along with various collaborators and past research works on the quadratic unconstrained binary optimization problem (QUBO) and variants will be used in the design of algorithms. Some specific research problems include solving large scale QUBO, bipartite QUBO and other related optimization problems that fall under this general framework. The research program is expected to result in novel solution approaches exploiting recent developments in machine learning, and artificial intelligence and using technological developments in the emerging area of quantum computing and quantum bridge analytics, for solving problems of interest hitherto unsolved or for solving problems more efficiently and thereby making fundamental contributions to optimization modeling and solution approaches. Exploiting modern technological advancements and by harnessing theoretical and applied research, the proposed research work is expected to enhance the efficacy and uses of operations research methodologies for socio-economic developments within Canada and abroad. Several students with diverse backgrounds, emphasizing EDI considerations, will be employed in the project as research associates. These students will receive valuable research training in the areas of optimization modeling, design and analysis of algorithms, machine learning, computational testing of algorithms, and quantum bridge analytics.