Algorithms for some hard discrete nonlinear optimization problems and applications

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The primary objective of the proposed research program is to develop efficient algorithms for solving fundamental hard discrete optimization problems with applications in the areas of production, planning, distribution, scheduling, communication etc. An equally important objective is to train highly qualified graduate and undergraduate students and postdoctoral fellows who could apply cutting-edge algorithmic and modeling techniques to solve complex optimization projects and develop viable alternative solution approaches that improve solution quality and running time. Dissemination of research results through conference presentations and publications in reputable journals are also part of the objectives.***Accomplishment of these objectives necessitate development of new theoretical results, intelligent application of existing results, development of computer programs, and extensive experimental and theoretical analysis of algorithms. This investigator's research experience and results obtained in the past will be very useful in completing the project. In particular, domination analysis of heuristics and very large scale neighborhood search techniques developed by our research group and others will be vital algorithm design tools in the research project. The proposed research work includes, among others, solving large scale discrete optimization problems with nonlinear objective functions. Special emphasis will be given to quadratic, bilinear, and fractional objectives and applications where feasible solutions are special graph theoretic structures and/or discrete points within polyhedral sets. Variations of the binary quadratic programming problem, algorithms that uses fixed size unconstrained binary quadratic programs within a quantum computing-like framework, enhancements to variable neighborhood search algorithms, analysis of algorithms for 0-1 fractional programming problems involving ratios of linear or quadratic functions are some of the specific topics considered in this project.  We will also investigate more general nonlinear integer programs, a class of discrete optimization problems that has considerable modeling flexibility, yet relatively little algorithmic advancements have been reported in literature.***The research is expected to result in novel solution approaches for problems of interest hitherto unsolved or for  solving problems more efficiently and thereby making fundamental contributions to optimization modeling and solution approaches that harness theoretical and applied research. The outcome of the research work is expected to enhance the efficacy and uses of operations research methodologies for socioeconomic developments within Canada and abroad. Further, graduate and undergraduate students and postdoctoral fellows employed in the project will receive valuable research training in operations research.**