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# Chapter 7 - Programming Combinatorial Problems with the DLL Details

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# Chapter 7 - Programming Combinatorial Problems with the DLL Details

 In the previous chapter, we discussed the problem of searching for the optimal values of continuous parameters.  In real life, however, we often have optimization problems of a different nature.   Imagine that, on Saturday, you have to visit a number of shops.  You will probably plan your trip to minimize the length of your route.  This means that you will order the list of shops.  In other words, you will solve an optimization problem of a combinatorial nature.  There are a lot of practical examples of combinatorial problems in real life.  They include the routing of VLSI chips and printed circuit boards, scheduling school classes, bin packing, etc.  It is difficult to solve combinatorial problems because the number of possible solutions is usually very large.  For example, if you have 10 points on your shopping route and will visit every point only once, there are (10-1)!/2 = 181,440 possible ways to visit all of the places, provided there are direct paths between all of them.   It is very time-consuming if not impossible to examine all alternatives.  We would like to have a method that will find the best solution by looking at a minimum number of combinations.  GeneHunter can help you solve your optimization problems effectively.   Enumerated Chromosomes Length of Continuous Chromosomes Length of Enumerated Chromosomes Programming the DLL for Combinatorial Problems Traveling Salesman Problem