Finding High-Dimensional D-OptimalDesigns for Logistic Models via Differential Evolution

D-optimal designs are frequently used in controlled experiments to obtain the most accurateestimate of model parameters at minimal cost. Finding them can be a challenging task, especially whenthere are many factors in a nonlinear model. As the number of factors becomes large and interact withone another, there are many more variables to optimize and the D-optimal design problem becomes highdimensionaland non-separable. Consequently, premature convergence issues arise. Candidate solutions gettrapped in local optima and the classical gradient-based optimization approaches to search for the D-optimaldesigns rarely succeed. We propose a specially designed version of differential evolution (DE) which is arepresentative gradient-free optimization approach to solve such high-dimensional optimization problems.The proposed specially designed DE uses a new novelty-based mutation strategy to explore the variousregions in the search space. The exploration of the regions will be carried out differently from the previouslyexplored regions and the diversity of the population can be preserved. The proposed novelty-based mutationstrategy is collaborated with two common DE mutation strategies to balance exploration and exploitationat the early or medium stage of the evolution. Additionally, we adapt the control parameters of DE as theevolution proceeds. Using logistic models with several factors on various design spaces as examples, oursimulation results show our algorithm can find D-optimal designs efficiently and the algorithm outperformsits competitors. As an application, we apply our algorithm and re-design a 10-factor car refueling experimentwith discrete and continuous factors and selected pairwise interactions. Our proposed algorithm was able toconsistently outperform the other algorithms and find a more efficient D-optimal design for the problem

A Novel Memetic Framework for Enhancing Differential Evolution Algorithms via Combination With Alopex Local Search

Differential evolution (DE) represents a class of population-based optimization techniques that uses differences of vectors to search for optimal solutions in the search space. However, promising solutions/regions are not adequately exploited by a traditional DE algorithm. Memetic computing has been popular in recent years to enhance the exploitation of global algorithms via incorporation of local search. This paper proposes a new memetic framework to enhance DE algorithms using Alopex Local Search (MFDEALS). The novelty of the proposed MFDEALS framework lies in that the behavior of exploitation (by Alopex local search) can be controlled based on the DE global exploration status (population diversity and search stage). Additionally, an adaptive parameter inside the Alopex local search enables smooth transition of its behavior from exploratory to exploitative during the search process. A study of the important components of MFDEALS shows that there is a synergy between them. MFDEALS has been integrated with both the canonical DE method and the adaptive DE algorithm L-SHADE, leading to the MDEALS and ML-SHADEALS algorithms, respectively. Both algorithms were tested on the benchmark functions from the IEEE CEC’2014 Conference. The experiment results show that Memetic Differential Evolution with Alopex Local Search (MDEALS) not only improves the original DE algorithm but also outperforms other memetic DE algorithms by obtaining better quality solutions. Further, the comparison between ML-SHADEALS and L-SHADE demonstrates that applying the MFDEALS framework with Alopex local search can significantly enhance the performance of L-SHADEThis research was supported by grants from both Swedish Research Council (project number 2016-05431) and Spanish Ministry of Science TIN2016- 8113-R

Comparing and Combining Lexicase Selection and Novelty Search

Lexicase selection and novelty search, two parent selection methods used in evolutionary computation, emphasize exploring widely in the search space more than traditional methods such as tournament selection. However, lexicase selection is not explicitly driven to select for novelty in the population, and novelty search suffers from lack of direction toward a goal, especially in unconstrained, highly-dimensional spaces. We combine the strengths of lexicase selection and novelty search by creating a novelty score for each test case, and adding those novelty scores to the normal error values used in lexicase selection. We use this new novelty-lexicase selection to solve automatic program synthesis problems, and find it significantly outperforms both novelty search and lexicase selection. Additionally, we find that novelty search has very little success in the problem domain of program synthesis. We explore the effects of each of these methods on population diversity and long-term problem solving performance, and give evidence to support the hypothesis that novelty-lexicase selection resists converging to local optima better than lexicase selection

Neo-Schumpeterian Simulation Models

The use of simulation modelling techniques by neo-Schumpeterian economists dates back to Nelson and Winter’s 1982 book “An Evolutionary Theory of Economic Change”, and has rapidly expanded ever since. This paper considers the way in which successive generations of models have extended the boundaries of research (both with respect to the range of phenomena considered and the different dimensions of innovation that are considered), and while simultaneously introducing novel modelling techniques. At the same time, the paper will highlight the distinct set of features that have emerged in these neo-Schumpeterian models, and which set them apart from the models developed by other schools. In particular, they share a distinct view about the type of world in which real economic agents operate, and a invariably contain a generic set of algorithms. In addition to reviewing past models, the paper considers a number of pressing issues that remain unresolved and which modellers will need to address in future. Notable amongst these are the methodological relationship between empirical studies and simulation (e.g. ‘history friendly modelling’), the development of common standards for sensitivity analysis, and the need to further extend the boundaries of research in order to consider important aspects of innovation and technical change.macroeconomics ;