An implementation of 
        representation-dependent gene level operations for
        genetic algorithms with genes representing permutations: 
        Initialization of genes, mutation, and crossover.
        The crossover operation provided is position-based crossover 
        (Syswerda, G., Chap. 21 in Davis, L. (1991, ISBN:0-442-00173-8). 
        For mutation, several variants are included: Order-based mutation
        (Syswerda, G., Chap. 21 in Davis, L. (1991, ISBN:0-442-00173-8), 
        randomized Lin-Kernighan heuristics
        (Croes, G. A. (1958) <doi:10.1287/opre.6.6.791> and
         Lin, S. and Kernighan. B. W. (1973) 
        <doi:10.1287/opre.21.2.498>), 
        and randomized greedy operators.
        A random mix operator for mutation selects a mutation variant 
        randomly.

This collection of gene representation-independent functions 
   implements the population layer of extended evolutionary and genetic 
   algorithms and its support. The population layer consists of functions 
   for initializing, logging, observing, evaluating a population of genes, 
   as well as of computing the next population. For parallel evaluation of a 
   population of genes 4 execution models - named Sequential, MultiCore, 
   FutureApply, and Cluster - are provided. They are implemented by 
   configuring the lapply() function. The execution model FutureApply can be 
   externally configured as recommended by Bengtsson (2021) 
   <doi:10.32614/RJ-2021-048>. Configurable acceptance rules and cooling 
   schedules (see Kirkpatrick, S., Gelatt, C. D. J, and Vecchi, M. P. (1983) 
   <doi:10.1126/science.220.4598.671>, and Aarts, E., and Korst, J. 
   (1989, ISBN:0-471-92146-7) offer simulated annealing or greedy randomized 
   approximate search procedure elements. Adaptive crossover and mutation 
   rates depending on population statistics generalize the approach of 
   Stanhope, S. A. and Daida, J. M. (1996, ISBN:0-18-201-031-7). 
   For xega's architecture, 
   see Geyer-Schulz, A. (2025) <doi:10.5445/IR/1000187255>.