Conclusion
Correct determination of design variable, functional, and criteria constraints is a major challenge in real-life optimization problems. The most promising solution approach involves two stages. In the first stage, the feasible solution and Pareto optimal sets are constructed and analyzed. These sets are constructed on the basis of the PSI method. Analysis of the feasible solution set shows the work of all constraints; the cost of making concessions in various constraints, i.e. what are the losses and the gains; expediency of modification of constraints; and resources for improvement of the object by all criteria. Only after the first stage one can make a decision as to whether it is necessary to improve the obtained results by means of various optimization methods, including stochastic, genetic.
Let see another example with not that much mathematical base.
Combinatorial optimization problems occur in a variety of fields including scheduling, routing, design layout, engineering disciplines, management and econometrics. Solutions to these problems are characterized by identifying an optimum combination of individual choice selections from among a multitude of possibilities. Examples of such enumerative search, graph search, or combinatorial optimization problems include moves in board games such as chess or go, determining how articles of different sizes can be packed in containers of limited capacity, determining optimum scheduling of operations in a manufacturing process, and capacitated vehicle routing with time windows.
Enumerative search, or combinatorial optimization problems is a Ill established field, for example, see Aho et al. in "Data Structures & Algorithms,"
In the prior art, the time required to solve combinatorial optimization problems has been reduced by using efficient heuristic methods that are not guaranteed to find an optimal solution, but one that is near optimal.
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