Angle modulated population based algorithms to solve binary problems (original) (raw)
Recently, continuous-valued optimization problems have received a great amount of focus, resulting in optimization algorithms which are very efficient within the continuousvalued space. Many optimization problems are, however, defined within the binaryvalued problem space. These continuous-valued optimization algorithms can not operate directly on a binary-valued problem representation, without algorithm adaptations because the mathematics used within these algorithms generally fails within a binary problem space. Unfortunately, such adaptations may alter the behavior of the algorithm, potentially degrading the performance of the original continuous-valued optimization algorithm. Additionally, binary representations present complications with respect to increasing problem dimensionality, interdependencies between dimensions, and a loss of precision. This research investigates the possiblity of applying continuous-valued optimization algorithms to solve binary-valued problems, without requiring algorithm adaptation. This is achieved through the application of a mapping technique, known as angle modulation. Angle modulation effectively addresses most of the problems associated with the use of a binary representation by abstracting a binary problem into a four-dimensional continuous-valued space, from which a binary solution is then obtained. The abstraction is obtained as a bit-generating function produced by a continuous-vaued algorithm. A binary solution is then obtained by sampling the bit-generating function. This thesis proposes a number of population-based angle-modulated continuousvalued algorithms to solve binary-valued problems. These algorithms are then compared to binary algorithm counterparts, using a suite of benchmark functions. Empirical analysis will show that the angle-modulated continuous-valued algorithms are viable alternatives to binary optimization algorithms.
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