Pawel Zabielski

Genetic Algorithm Solving the Orienteering Problem with Time Windows

The Orienteering Problem with Time Windows (OPTW) is a well-known routing problem in which a given positive profit and time interval are associated with each location. The solution to the OPTW finds a route comprising a subset of the locations, with a fixed limit on length or travel time, that maximises the cumulative score of the locations visited in the predefined time intervals. This paper proposes a new genetic algorithm (GA) for solving the OPTW. We use specific mutation based on the idea of insertion and shake steps taken from the well-known iterated local search method (ILS). Computational experiments are conducted on popular benchmark instances. The tests show that repetition of the mutation step for the same route during one iteration of GA can improve the solution so that it outperforms the ILS result.

Genetic Algorithm with Path Relinking for the Orienteering Problem with Time Windows

The Orienteering Problem with Time Windows (OPTW) is an optimisation NP-hard problem. This paper proposes a hybrid genetic algorithm (GAPR) for approximating a solution to the OPTW. Instead of a crossover we use a path relinking (PR) strategy as a form of intensification solution. PR generates a new solution by exploring trajectories between two random solutions: genes not present in one solution are included in the other one. Experiments performed on popular benchmark instances show that the proposed GAPR gives good quality solutions using short computing times. Moreover, GAPR gives new best solutions for some test instances.

A Genetic Algorithm with Grouping Selection and Searching Operators for the Orienteering Problem

In the Orienteering Problem (OP), a set of linked vertices, each with a score, is given. The objective is to find a route, limited in length, over a subset of vertices that maximises the collective score of the visited vertices. In this paper, we present a new, efficient genetic algorithm (nGA) that solves the OP. We use a special grouping during selection, which results in better-adapted routes in the population. Furthermore, we apply a searching crossover to each generation, which uses the common vertices between distinct routes in the population; we also apply a searching mutation. Computer experiments on the nGA are conducted on popular data sets. In some cases, the nGA yields better results than well-known heuristics.

A genetic algorithm vs. local search methods for solving the orienteering problem in large networks

The Orienteering problem (OP) can be modelled as a weighted graph with set of vertices where each has a score. The main OP goal is to find a route that maximises the sum of scores, in addition the length of the route not exceeded the given limit. In this paper we present our genetic algorithm (GA) with inserting as well as removing mutation solving the OP. We compare our results with other local search methods such as: the greedy randomised adaptive search procedure (GRASP) (in addition with path relinking (PR)) and the guided local search method (GLS). The computer experiments have been conducted on the large transport network (908 cities in Poland). They indicate that our algorithm gives better results and is significantly faster than the mentioned local search methods.

Maximization of Attractiveness EV Tourist Routes.

This paper presents model and an algorithmic approach for the problem of generation optimal tourist route for electric vehicles (EVs). In the discussed problem a starting and a final point of a route are EV charging stations where tourist could charge the battery and then continue a journey. The main objective is to select to the route points of interests (POIs) which maximizing tourist attractiveness. Furthermore maximum length of the route is limited by the number of kilometers that the car can travel on a single battery charge. The model applied by us is the graph routing problem named as the Orienteering Problem with Time Windows (OPTW). In OPTW each location has positive score and a specific time interval in which a location can be visited. The solution of OPTW is a route (from the given starting to the ending point) with a fixed limit of length including a subset of locations. Moreover the route maximizes the total score of the locations visited in the predefined time intervals. As a solution we present the evolutionary algorithm with combines path relinking method instead crossover. Computational experiments are conducted on realistic database POIs and EV charging stations of Podlasie region in Poland. Tests results and execution time of the algorithm shows that the described solution could be a part of EV software module with generates the most interesting route.

Learning Algorithms Aimed at Collinear Patterns

Collinear (flat) pattern appears in a given set of multidimensional feature vectors when many of these vectors are located on (or near) some plane in the feature space. Flat pattern discovered in a given data set can give indications for creating a model of interaction between selected features. Patterns located on planes can be discovered even in large and multidimensional data sets through minimization of the convex and piecewise linear (CPL) criterion functions. Discovering flat patterns can be based on the search for degenerated vertices in the parameter space. The possibility of using learning algorithms for this purpose is examined in this paper.

Models of Multiple Interactions from Collinear Patterns.

Each collinear pattern should be made up of a large number of feature vectors which are located on a plane in a multidimensional feature space. Data subset located on a plane can represent linear interactions between multiple variables (features, genes). Collinear (flat) patterns can be efficiently extracted from large, multidimensional data sets through minimization of the collinearity criterion function which is convex and piecewise linear (CPL). Flat patterns extracted from representative data sets could provide an opportunity to discover new, important interaction models. As an example, exploration of data sets representing clinical practice and genetic testing could result in multiple interaction models of phenotype and genotype features.

Basis exchange and learning algorithms for extracting collinear patterns

ABSTRACT Understanding large data sets is one of the most important and challenging problem in modern days. Exploration of genetic data sets composed of high-dimensional feature vectors can be treated as a leading example in this context. A better understanding of large, multivariate data sets can be achieved through exploration and extraction of their structure. Collinear patterns can be an important part of a given data set structure. Collinear (flat) patterns exist in a given set of feature vectors when many of these vectors are located on (or near) some planes in the feature space. Discovered flat patterns can reflect various types of interaction in an explored data set. The presented paper compares basis exchange algorithms with learning algorithms in the task of flat patterns extraction.