The optimization of functions to find the best solution according to one or several objectives has a central role in many engineering and research fields. Recently, a new family of optimization algorithms, named Quality-Diversity optimization, has been introduced, and contrasts with classic algorithms. Instead of searching for a single solution, Quality-Diversity algorithms are searching for a large collection of both diverse and high-performing solutions. The role of this collection is to cover the range of possible solution types as much as possible, and to contain the best solution for each type. The contribution of this paper is threefold. Firstly, we present a unifying framework of Quality-Diversity optimization algorithms that covers the two main algorithms of this family (Multi-dimensional Archive of Phenotypic Elites and the Novelty Search with Local Competition), and that highlights the large variety of variants that can be investigated within this family. Secondly, we propose algorithms with a new selection mechanism for Quality-Diversity algorithms that outperforms all the algorithms tested in this paper. Lastly, we present a new collection management that overcomes the erosion issues observed when using unstructured collections. These three contributions are supported by extensive experimental comparisons of Quality-Diversity algorithms on three different experimental scenarios.
The first applications of NSLC consisted of evolving both the morphology and the behavior of virtual creatures in order to generate a population containing diverse species, ranging from slow and massive quadrupeds to fast and lightweight unipedal hoppers by comparing velocity only between similar species @cite_42 . In this experiment, the solution descriptor was defined as the height, the mass and the number of active joints, while the quality of the solutions was governed by their walking speed. At the end of the evolutionary process, the population contained 1,000 different species. These results represent the very first step in the direction of generating a collection of diverse and high-performing solutions covering a significant part of the spectrum of possibilities.
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Experimental determinations of Drosophila population dynamics cannot be explained by the Lotka-Volterra model of interspecific competition. This paper presents other possible mathematical models of competition between species, and gives the results of experiments designed to test the validity of such models. Eight of the ten new models presented contain the Lotka-Volterra model as a special case. The experiments made to test the models are of two kinds. Type 1 experiments are continuous one- or two-species populations, which permit the estimation of the carrying capacity of each species and the numbers of the two species at the point of stable equilibrium. Type 2 experiments measure the change in numbers over a short time interval in populations started with many different initial densities of the two species. Type 2 experiments give information on the dynamics of the two-species system in the phase plane whose coordinates are the number of individuals of each species. The models accounting best for the results are models five and seven (Table II). Each of these two models contains one parameter more than the Lotka-Volterra model. Model five adds a nonlinear term of self-interaction (iN2i). Model seven has the form, dNi dt = riN Kii(Kii  Ni i  ijNj1i i). The exponential parameter  removes the restriction of the logistic theory of population growth, that each individual added to the population decrease the rate of growth of the population by a constant amount. With model seven the rate of growth of a population of a single species need not have its maximum at K2, that is when the number of individuals is half the carrying capacity of the environment.