Vincent A. Cicirello

Non-wrapping order crossover: an order preserving crossover operator that respects absolute position

In this paper, we introduce a new crossover operator for the permutation representation of a GA. This new operator---Non-Wrapping Order Crossover (NWOX)---is a variation of the well-known Order Crossover (OX) operator. It strongly preserves relative order, as does the original OX, but also respects the absolute positions within the parent permutations. This crossover operator is experimentally compared to several other permutation crossover operators on an NP-Hard problem known as weighted tardiness scheduling with sequence-dependent setups. A GA using this NWOX operator finds new best known solutions for several benchmark problem instances and proves to be superior to the previous best performing metaheuristic for the problem.

The Permutation in a Haystack Problem and the Calculus of Search Landscapes

The natural encoding for many search and optimization problems is the permutation, such as the traveling salesperson, vehicle routing, scheduling, assignment and mapping problems, among others. The effectiveness of a given mutation or crossover operator depends upon the nature of what the permutation represents. For some problems, it is the absolute locations of the elements that most directly influences solution fitness; while for others, element adjacencies or even element precedences are most important. Different permutation operators respect different properties. We aim to provide the genetic algorithm or metaheuristic practitioner with a framework enabling effective permutation search landscape analysis. To this end, we contribute a new family of optimization problems, the permutation in a haystack, that can be parameterized to the various types of permutation problem (e.g., absolute versus relative positioning). Additionally, we propose a calculus of search landscapes, enabling analysis of search landscapes through examination of local fitness rates of change. We use our approach to analyze the behavior of common permutation mutation operators on a variety of permutation in a haystack landscapes; and empirically validate the prescriptive power of the search landscape calculus via experiments with simulated annealing.

Weighted Tardiness Scheduling with Sequence-Dependent Setups: A Benchmark Problem for Soft Computing

In this paper we present a set of benchmark instances and a benchmark instance generator for a single-machine scheduling problem known as the weighted tardiness scheduling problem with sequence-dependent setups. Furthermore, we argue that it is an ideal benchmark problem for soft computing in that it is computationally hard and does not lend itself well to exact solution procedures. Additionally, it has a number of important real world applications.

Genetic Algorithm Parameter Control: Application to Scheduling with Sequence-Dependent Setups

Genetic algorithms, and other forms of evolutionary computation, are controlled by numerous parameters, such as crossover and mutation rates, population size, among others depending upon the specific form of evolutionary computation as well as which operators are employed. Setting the values for these parameters is no simple task. In this paper, we develop a genetic algorithm with adaptive control parameters for an NP-Hard scheduling problem known as weighted tardiness scheduling with sequence-dependent setups. Our genetic algorithm uses the permutation representation along with the non-wrapping order crossover and insertion mutation operators. We encode the control parameters within the members of the population and evolve these during search using Gaussian mutation. We demonstrate this approach out-performs a manually tuned genetic algorithm for the problem, and that it converges upon effective parameter values very early in the run.