The Vehicle Routing Problem with Time windows (VRPTW) is an extension of the capacity constrained Vehicle Routing Problem (VRP). The VRPTW is NP-Complete and instances with 100 customers or more are very hard to solve optimally. We represent the VRPTW as a multi-objective problem and present a genetic algorithm solution using the Pareto ranking technique. We use a direct interpretation of the VRPTW as a multi-objective problem, in which the two objective dimensions are number of vehicles and total cost (distance). An advantage of this approach is that it is unnecessary to derive weights for a weighted sum scoring formula. This prevents the introduction of solution bias towards either of the problem dimensions. We argue that the VRPTW is most naturally viewed as a multi-objective problem, in which both vehicles and cost are of equal value, depending on the needs of the user. A result of our research is that the multi-objective optimization genetic algorithm returns a set of solutions that fairly consider both of these dimensions. Our approach is quite effective, as it provides solutions competitive with the best known in the literature, as well as new solutions that are not biased toward the number of vehicles. A set of well-known benchmark data are used to compare the effectiveness of the proposed method for solving the VRPTW.

Abstract-The automatic synthesis of aesthetically pleasing images is investigated. Genetic programming with multiobjective fitness evaluation is used to evolve procedural texture formulae. With multi-objective fitness testing, candidate textures are evaluated according to multiple criteria. Each criteria designates a dimension of a multi-dimensional fitness space. The main feature test uses Ralph's model of aesthetics. This aesthetic model is based on empirical analyses of fine art, in which analyzed art work exhibits bell curve distributions of color gradients. Subjectively speaking, this bell-curve gradient measurement tends to favor images that have harmonious and balanced visual characteristics. Another feature test is color histogram scoring. This test permits some control of the color composition, by matching a candidate texture's color composition with the color histogram of a target image. This target image may be a digital image of another artwork. We found that the use of the bell curve model often resulted in images that were harmonious and easy-on-the-eyes. Without the use of the model, generated images were often too chaotic or boring. Although our approach does not guarantee aesthetically pleasing results, it does increase the likelihood that generated textures are visually interesting.

A dynamic Bayesian network (DBN) is a probabilistic network that models interdependent entities that change over time. Given example sequences of multivariate data, we use a genetic algorithm to synthesize a network structure that models the causal relationships that explain the sequence. We use a multi-objective evaluation strategy with a genetic algorithm. The multi-objective criteria are a network's probabilistic score and structural complexity score. Our use of Pareto ranking is ideal for this application, because it naturally balances the effect of the likelihood and structural simplicity terms used in the BIC network evaluation heuristic. We use a basic structural scoring formula, which tries to keep the number of links in the network approximately equivalent to the number of variables. We also use a simple representation that favors sparsely connected networks similar in structure to those modeling biological phenomenon. Our experiments show promising results when evolving networks ranging from 10 to 30 variables, using a maximal connectivity of between 3 and 4 parents per node. The results from the multi-objective GA were superior to those obtained with a single objective GA.

Genetic programming is used to evolve mineral identification functions for hyperspectral images. The input image set comprises 168 images from different wavelengths ranging from 428 nm (visible blue) to 2507 nm (invisible shortwave in the infrared), taken over Cuprite, Nevada, with the AVIRIS hyperspectral sensor. A composite mineral image indicating the overall reflectance percentage of three minerals (alunite, kaolnite, buddingtonite) is used as a reference or "solution" image. The training set is manually selected from this composite image. The task of the GP system is to evolve mineral identifiers, where each identifier is trained to identify one of the three mineral specimens. A number of different GP experiments were undertaken, which parameterized features such as thresholded mineral reflectance intensity and target GP language. The results are promising, especially for minerals with higher reflectance thresholds (more intense concentrations).

Gentropy is a genetic programming system that evolves two-dimensional procedural textures. It synthesizes textures by combining mathematical and image manipulation functions into formulas. A formula can be reevaluated with arbitrary texture-space coordinates, to generate a new portion of the texture in texture space. Most evolutionary art programs are interactive, and require the user to repeatedly choose the best images from a displayed generation. Gentropy uses an unsupervised approach, where one or more target texture image is supplied to the system, and represent the desired texture features, such as colour, shape and smoothness (contrast). Then, Gentropy evolves textures independent of any further user involvement. The evolved texture will not be identical to the target texture, but rather, will exhibit characteristics similar to it. When more than one texture is supplied as a target, multi-objective feature analysis is performed. These feature tests may be combined and given different priorities during evaluation. It is therefore possible to use several target images, each with its own fitness function measuring particular visual characteristics. Gentropy also permits the use of multiple subpopulations, each of which may use its own texture evaluation criteria and target texture. r