A mathematical programming method in which a common decision space is defined by identifying decision variables, and a set of objective functions is developed as piecewise defined functions. Each objective function is dependent on at least one of the decision variables and corresponds to a goal. The objective function has a plurality of pieces, such that the objective function has only one piece for each combination of decision variables. A value function is developed in additive preference form based on weights and the objective functions. The value function is optimized by searching through the decision variable values to find the values of the decision variables that maximize the developed value function. An action dictated by the decision variable values can then be executed.

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> Method and apparatus for the automated detection and classification of defects in sewer pipes

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