Watson, Richard A. “Problem Decomposition and Multi-Objective Optimization.” In PPSN/SAB Workshop on Multiobjective Problem Solving from Nature (MPSN) . 2000.
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Divide and conquer techniques in problem solving are familiar and intuitive; first find the solution to sub-problems and then re-use these to find solutions to the whole problem. For example, we may decompose the problem of designing a vehicle into designing the engine and designing the body. It is acknowledged that most real-world problems (vehicles included) do not decompose neatly into separable sub-problems. For example, the optimal properties of a drive system have dependencies with the passenger capacity. Nonetheless, it is very often possible to simplify a problem greatly by identifying sub-problems that exhibit some degree of independence. Multi-Objective Optimization, MOO, is similarly familiar and intuitive; there are several features of a system that we wish to optimize simultaneously and we wish to examine the alternatives that optimize each of the features independently, and/or offer a compromise of multiple objectives simultaneously. For example, we wish to minimize both the materials cost and construction time for our vehicle. It is acknowledged that sometimes multiple objectives can be satisfied simultaneously. For example, perhaps there is a simple design that is both cheap and fast to manufacture. This is the basis of Pareto dominance; a solution that is preferred with respect to all objectives. Nonetheless, it is often useful to acknowledge that objectives are constrained and to accept a set of solutions that optimize different objectives, rather than a single compromise.