Ordered Structures The data structures we have evolved thus far have all been arrays or vectors of similar Summary: Chapter 7 Ordered Structures The data structures we have evolved thus far have all been arrays or vectors of similar elements, be they characters, real numbers, the ships's systems from Sunburn, or states of a finite state automaton. The value at one state in a gene has no effect on what values may be present at another location, except for non-explicit constraints implied by the fitness function. In this chapter, we will work with lists of items called permutations in which the list contains a specified collection of items once each. We will store the permutations as lists of integers 1, 2, ..., n varying only the order in which the integers appear. Just as we used the simple string evolver in Chapter 2 to learn how evolutionary algorithms worked, we will start with easy problems to learn how systems for evolving ordered genes work. The first section of this chapter is devoted to implementing two different representations for permutations, a direct representation storing permutations in an array and the random key representation which stores a permutation as an array of real numbers. These representation will be tested on minimizing the number of reversals in a permutation, in effect sorting it, and on maximizing the order of the permutation as a member of a group of permutations. The second section of the chapter will introduce the Traveling Salesman problem. This problem takes an existing set of cities and attempts to find the order of the cities that form a minimum length circular tour of those cities. The third section combines permutations Collections: Mathematics