Inherent in model selection is the problem of simultaneously optimizing multiple performance metrics. Some of these metrics express potentially conflicting criteria, like accuracy and simplicity. Pareto optimization is a branch of mathematical optimization that deals precisely with problems involving conflicting objective functions. In this article, an algorithm was developed that searches automatically for Pareto optimal linear regression models given a dataset and a set of performance metrics. The optimization task was framed as one of sequential variable selection on a graph. A search strategy was proposed that draws on ant colony optimization, a probabilistic technique well suited for graph-based problems. Experiments were run in which the metrics to be minimized were the root-mean-square error, expressing accuracy, and the number of coefficients, expressing simplicity. To substantiate the usefulness of our algorithm, cases were presented in which it outperformed AIC-based stepwise regression. Results suggested that our algorithm copes well with small datasets and correlated predictors, that it is efficient and that it informs model selection. Key properties of our algorithm were discussed and areas of improvement highlighted.
A combination of the two most important problems in logistics called the capacitated vehicle routing problem with two-dimensional loading constraint is studied in this article. It aims in designing the most appropriate pathways, starting and terminating at a central depot, minimising the total transportation cost with a homogenous fleet of vehicles. Items loaded in each vehicle's trip must satisfy the two-dimensional of orthogonal packing constraint. Since the problem is an NP-hard optimisation problem, a large number of approaches have been proposed. Whereas, finding the exact solution via optimisation is still a challenging problem due to their complexity. In order to increase the exploration in the solution space, we propose the parallel variable neighbourhood search algorithm. It is tested with 180 benchmark instances and compared with state-of-the-art approaches. The results showed that our approach is competitive in terms of the quality of solutions found.
General solvers exist for several types of optimisation problems, with the commercially available solvers for mixed integer programming (MIP) being a prime example. Although binary integer programming (BIP) can be used to model a wide variety of important combinatorial optimisation problems, relatively few contributions have been made to develop heuristic algorithms for BIP. This paper examines whether variable neighbourhood search can be successfully used to tackle BIP instances, when avoiding very large neighbourhoods explored by the means of external MIP solvers. The results indicate that methods based on variable neighbourhood search are more successful than exact and heuristic commercial solvers on certain types of instances, while the opposite holds true on others. A general variable neighbourhood search proves very effective on instances with up to 200 variables, in particular some instances that are tightly constrained.
K nearest neighbours algorithm is a classic, well studied yet a promising classification technique with high accuracy and best learning time compared to other classification algorithms. The goal is to overcome its slow classification time using instance selection by eliminating redundant and erroneous data. The instance selection problem has been classified as a non-deterministic polynomial time hard problem. In this article, the aim is to keep up with real time applications such as robotics with limited memory, while maintaining the fast-learning speed and high classification accuracy. We introduce a new multistage genetic algorithm for instance selection consisting of successive genetic instance selection stages with iterative search space reduction. The results witnessed an extreme reduction in classification time, reaching 99% without any significant penalty in the accuracy. It has been tested successfully using real traces of robot wall following navigation datasets and favourably compared to other approaches using various datasets.
