Abstract-Evolutionary algorithms use crossover to combine information from pairs of solutions and use selection to retain the best solutions. Ideally, crossover takes distinct good features from each of the two structures involved. This process creates a conflict: progress results from crossing over structures with different features, but crossover produces new structures that are like their parents and so reduces the diversity on which it depends. As evolution continues, the algorithm searches a smaller and smaller portion of the search space. Mutation can help maintain diversity but is not a panacea for diversity loss. This paper explores evolutionary algorithms that use combinatorial graphs to limit possible crossover partners. These graphs limit the speed and manner in which information can spread giving competing solutions time to mature. This use of graphs is a computationally inexpensive method of picking a global level of tradeoff between exploration and exploitation. The results of using 26 graphs with a diverse collection of graphical properties are presented. The test problems used are: one-max, the De Jong functions, the Griewangk function in three to seven dimensions, the self-avoiding random walk problem in 9, 12, 16, 20, 25, 30, and 36 dimensions, the plus-one-recall-store (PORS) problem with = 15 16 and 17, location of length-six one-error-correcting DNA barcodes, and solving a simple differential equation semi-symbolically.The choice of combinatorial graph has a significant effect on the time-to-solution. In the cases studied, the optimal choice of graph improved solution time as much as 63-fold with typical impact being in the range of 15% to 100% variation. The graph yielding superior performance is found to be problem dependent. In general, the optimal graph diameter increases and the optimal average degree decreases with the complexity and difficulty of the fitness landscape. The use of diverse graphs as population structures for a collection of problems also permits a classification of the problems. A phylogenetic analysis of the problems using normalized time to solution on each graph groups the numerical problems as a clade together with one-max; self-avoiding walks form a clade with the semisymbolic differential equation solution; and the PORS and DNA barcode problems form a superclade with the numerical problems but are substantially distinct from them. This novel form of analysis has the potential to aid researchers choosing problems for a test suite.Index Terms-Evolutionary algorithm, graph-based algorithms, population structure, test suite.

Purpose – The aim of this research is to determine the importance and impact of project-based learning (PBL) on students' knowledge in Lean and Six Sigma courses where practical application of theoretical knowledge is necessary. Design/methodology/approach – Students teams were given hands-on collaborative projects conducted with local companies. After the completion of the project, a student evaluation survey was conducted and the responses were analysed in two different phases. The first phase consisted of collecting responses from the Lean and Six Sigma courses; observing the impact of the semester project on students' knowledge based on the response percentages. The second phase analyses the responses from both the Lean and Six Sigma courses, by performing a Fisher's exact test to examine how similar the students received knowledge from the use of the semester project. Findings – Results showed that the inclusion of the semester project in the courses had a positive impact on the students' knowledge in learning course concepts and the students were able to apply theoretical knowledge in solving real-world problems. It is also observed that the response patterns are different in most of the aspects between both the courses. Research limitations/implications – This research evaluates student learning with statistical tests and is limited only for classroom teaching techniques. Further, this research states that application-oriented courses should be accompanied by projects as it helps in better understanding the course deliverables for the students. Originality/value – Research evaluating the impact of PBL on students' knowledge in Lean and Six Sigma courses does not currently exist. Statistical analysis of survey responses from both the Lean and Six Sigma courses was performed using a χ2 test of independence to examine how similar the students received knowledge from the use of the semester project.

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Graph based evolutionary algorithms use combinatorial graphs to impose a topology or "geographic structure" on an evolving population. It has been demonstrated that, for a fixed problem, time to solution varies substantially with the choice of graph. This variation is not simple with very different graphs yielding faster solution times for different problems. Normalized time to solution for many graphs thus forms an objective character that can be used for classifying the type of a problem, separate from its hardness measured with average time to solution. This study uses fifteen combinatorial graphs to classify 40 evolutionary computation problems. The resulting classification is done using neighbor joining, and the results are also displayed using non-linear projection. The different methods of grouping evolutionary computation problems into similar types exhibit substantial agreement. Numerical optimization problems form a close grouping while some other groups of problems scatter across the taxonomy. This paper updates an earlier taxonomy of 23 problems and introduces new classification techniques.

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