A topological structural design approach is presented which is based upon the implementation of a two phase evolutionary optimization algorithm in conjunction with a finite element analysis code. The first phase utilizes a conventional genetic approach which performs a global search for the optimal design topology. Dual level material properties are specified within the genetic encoding and are applied to each individual element in the design mesh to represent either design material or a void. The second phase introduces a rule based refinement which allows for user design intent to accelerate the solution process and eliminate obvious design discrepancies resulting from the phase one search. A series of plate design problems are presented where the objective is to minimize the overall volume of the structure under predefined loading and constraint conditions. The constraints include both stress and deflection considerations where stress is calculated through the use of a commercial finite element package. The initial plate example incorporates a coarse mesh, but a gradual decrease in element size was employed for the remaining cases examined. Replacement of the phase one search with a set of randomly generated designs is demonstrated in order to form a greatly reduced design space which drastically increases the efficiency of the solution process. Comparison results are drawn between the conventional genetic algorithm and the two phase procedure.

One of the most interesting applications of genetic algorithms falls into the area of decision support. Decision support problems involve a series of decisions, each of which is influenced by all decisions made prior to that point. This class of problems occurs often in enterprise management, particularly in the area of scheduling or resource allocation. In order to demonstrate the formulation of this class of problems, a series of maze problems will be presented. The complexity of the mazes is intensified as each new maze is introduced. Two solving scenarios are introduced and comparison results are provided. The first scenario incorporated the traditional genetic algorithm procedure for the intended purpose of acquiring a solution based upon a purely evolutionary approach. The second scenario utilized the genetic algorithm in conjunction with embedded domain specific knowledge in the form of decision rules. The implementation of domain specific knowledge is intended to enhance solution convergence time and improve the overall quality of offspring produced which significantly increases the probability of acquiring a more accurate and consistent solution. Results are provided below for all mazes considered. These results include the traditional genetic algorithm final result and the genetic algorithm optimization approach with embedded rules result. Both results were incorporated for comparison purposes. Overall, the incorporation of domain specific knowledge outperformed the traditional genetic algorithm in both performance and computation time. Specifically, the traditional genetic algorithm failed to adequately find an acceptable solution for each example presented and prematurely converged on average within 54% of their specified generations. Additionally, the most complex maze generated an optimal path directional sequence (i.e. N, S, E, W) via a traditional genetic algorithm which possessed only 50% of the required allowable path sequences for maze completion. The incorporation of embedded rules enabled the genetic algorithm to locate the optimum path for all examples considered within 5% of the traditional genetic algorithm computation time.

Short Retraction Notice The paper does not meet the standards of "Open Journal of Optimization". This article has been retracted to straighten the academic record. In making this decision the Editorial Board follows COPE's Retraction Guidelines. The aim is to promote the circulation of scientific research by offering an ideal research publication platform with due consideration of internationally accepted standards on publication ethics. The Editorial Board would like to extend its sincere apologies for any inconvenience this retraction may have caused. Editor guiding this retraction: Prof. Moran Wang (EiC of TEL) The full retraction notice in PDF is preceding the original paper, which is marked "RETRACTED".

Structural designs (i.e. truss structures) are derived by the use of a three phase genetic optimization approach, where the minimization of volume is the objective of each truss structure considered. A genetic algorithm is employed which controls the three phase optimization technique. The first phase utilizes the conventional functionality of the genetic algorithm from an evolutionary perspective, however designer interaction by the use of constant rules is provided to ensure an effective evolutionary search outcome. The second phase enhances the best design constructed from phase one by the use of domain specific knowledge in the form of design rules. Phase three improves the final design assembled within phase two by the reduction of truss element areas. This refinement process ensures that the design constraints provided are active, indicating an optimal search solution. All phases operate from a global perspective; however the phase two optimization methodology operates from a more radical approach which encompasses the concept of designing from a “blank sheet of paper” point of view. Results are provided upon the conclusion of each truss example considered which includes the outcomes of each phase for comparison purposes.

The traveling salesman problem has long been regarded as a challenging application for existing optimization methods as well as a benchmark application for the development of new optimization methods. As with many existing algorithms, a traditional genetic algorithm will have limited success with this problem class, particularly as the problem size increases. A rule based genetic algorithm is proposed and demonstrated on sets of traveling salesman problems of increasing size. The solution character as well as the solution efficiency is compared against a simulated annealing technique as well as a standard genetic algorithm. The rule based genetic algorithm is shown to provide superior performance for all problem sizes considered. Furthermore, a post optimal analysis provides insight into which rules were successfully applied during the solution process which allows for rule modification to further enhance performance.