# Permutation Based Encoding

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This chapter focuses on the evolutionary approaches to optimization problems based on permutation encoded individuals. A new proposed recombination operator for permutation based encoding is described \cite{Chira-2012}. The proposed operator is using not only genetic information from the two parents, but from the best individual obtained up to the current generation too. Some of the most widely studied NP-hard optimization problems with many applications in domains such as logistics, planning, routing, and scheduling are considered to test the efficiency of the proposed operator. A comparative analysis of several recombination operators is presented based on computational experiments for Traveling Salesman Problem, Vehicle Routing Problem, Resource-Constrained Project Scheduling Problem and some generalized versions of these problems. Numerical results emphasize a good performance of the proposed crossover scheme. \section{Combinatorial Optimization Problems} \label{sec:combopt} A combinatorial optimization problem $(S,C,f)$ is defined by a finite or possibly countable infinite search space $S$, a set of constraints $C=\{c_1,c_2,...\}$ and an objective function $f:S->\mathbb{R}$. A feasible solution for the problem is one that satisfies all the constraints from the set $C$. Let $F$ be the set of all feasible solutions from the search space. To solve a combinatorial optimization problem one has to find an optimal solution $s^* \in S$, according to the objective function