Comparing Multi-Objective Local Search Algorithms for the Beam Angle Selection Problem

In intensity-modulated radiation therapy, treatment planners aim to irradiate the tumour according to a medical prescription while sparing surrounding organs at risk as much as possible. Although this problem is inherently a multi-objective optimisation (MO) problem, most of the models in the literature are single-objective ones. For this reason, a large number of single-objective algorithms have been proposed in the literature to solve such single-objective models rather than multi-objective ones. Further, a difficulty that one has to face when solving the MO version of the problem is that the algorithms take too long before converging to a set of (approximately) non-dominated points. In this paper, we propose and compare three different strategies, namely random PLS (rPLS), judgement-function-guided PLS (jPLS) and neighbour-first PLS (nPLS), to accelerate a previously proposed Pareto local search (PLS) algorithm to solve the beam angle selection problem in IMRT. A distinctive feature of these strategies when compared to the PLS algorithms in the literature is that they do not evaluate their entire neighbourhood before performing the dominance analysis. The rPLS algorithm randomly chooses the next non-dominated solution in the archive and it is used as a baseline for the other implemented algorithms. The jPLS algorithm first chooses the non-dominated solution in the archive that has the best objective function value. Finally, the nPLS algorithm first chooses the solutions that are within the neighbourhood of the current solution. All these strategies prevent us from evaluating a large set of BACs, without any major impairment in the obtained solutions’ quality. We apply our algorithms to a prostate case and compare the obtained results to those obtained by the PLS from the literature. The results show that algorithms proposed in this paper reach a similar performance than PLS and require fewer function evaluations.

Self-Configuring (1 + 1)-Evolutionary Algorithm for the Continuous p-Median Problem with Agglomerative Mutation

The continuous p-median problem (CPMP) is one of the most popular and widely used models in location theory that minimizes the sum of distances from known demand points to the sought points called centers or medians. This NP-hard location problem is also useful for clustering (automatic grouping). In this case, sought points are considered as cluster centers. Unlike similar k-means model, p-median clustering is less sensitive to noisy data and appearance of the outliers (separately located demand points that do not belong to any cluster). Local search algorithms including Variable Neighborhood Search as well as evolutionary algorithms demonstrate rather precise results. Various algorithms based on the use of greedy agglomerative procedures are capable of obtaining very accurate results that are difficult to improve on with other methods. The computational complexity of such procedures limits their use for large problems, although computations on massively parallel systems significantly expand their capabilities. In addition, the efficiency of agglomerative procedures is highly dependent on the setting of their parameters. For the majority of practically important p-median problems, one can choose a very efficient algorithm based on the agglomerative procedures. However, the parameters of such algorithms, which ensure their high efficiency, are difficult to predict. We introduce the concept of the AGGLr neighborhood based on the application of the agglomerative procedure, and investigate the search efficiency in such a neighborhood depending on its parameter r. Using the similarities between local search algorithms and (1 + 1)-evolutionary algorithms, as well as the ability of the latter to adapt their search parameters, we propose a new algorithm based on a greedy agglomerative procedure with the automatically tuned parameter r. Our new algorithm does not require preliminary tuning of the parameter r of the agglomerative procedure, adjusting this parameter online, thus representing a more versatile computational tool. The advantages of the new algorithm are shown experimentally on problems with a data volume of up to 2,000,000 demand points.

Solving the Traveling Salesman Problem: A Modified Metaheuristic Algorithm

The traveling salesman problem (TSP) is one of the most important issues in combinatorial optimization problems that are used in many engineering sciences and has attracted the attention of many scientists and researchers. In this issue, a salesman starts to move from a desired node called warehouse and returns to the starting place after meeting n customers provided that each customer is only met once. The aim of this issue is to determine a cycle with a minimum cost for this salesman. One of the major weaknesses of the PSO algorithm in the classical version is that it gets stuck in local optimizations. Therefore, in the proposed algorithm, called MPSO, the best solution in the current iteration is also used in the movement step. In addition, a variety of local search algorithms are provided that are used when better answers are generated than before. Also, a new method for moving the particle towards the best particle is presented, which, in addition to probably increasing the quality of the new answer, prevents the premature convergence of the algorithm due to consideration of the concept of random. The results evaluated with the results of several metaheuristic algorithms in the literature show the efficiency of the MPSO algorithm because it has been able to achieve excellent solutions in most of these instances.

Stochastic Local Search Algorithms for Feature Selection: A Review

In today’s world, the data generated by many applications are increasing drastically, and finding an optimal subset of features from the data has become a crucial task. The main objective of this review is to analyze and comprehend different stochastic local search algorithms to find an optimal feature subset. Simulated annealing, tabu search, genetic programming, genetic algorithm, particle swarm optimization, artificial bee colony, grey wolf optimization, and bat algorithm, which have been used in feature selection, are discussed. This review also highlights the filter and wrapper approaches for feature selection. Furthermore, this review highlights the main components of stochastic local search algorithms, categorizes these algorithms in accordance with the type, and discusses the promising research directions for such algorithms in future research of feature selection.

Stochastic local search: a state-of-the-art review

The main objective of this paper is to provide a state-of-the-art review, analyze and discuss stochastic local search techniques used for solving hard combinatorial problems. It begins with a short introduction, motivation and some basic notation on combinatorial problems, search paradigms and other relevant features of searching techniques as needed for background. In the following a brief overview of the stochastic local search methods along with an analysis of the state-of-the-art stochastic local search algorithms is given. Finally, the last part of the paper present and discuss some of the most latest trends in application of stochastic local search algorithms in machine learning, data mining and some other areas of science and engineering. We conclude with a discussion on capabilities and limitations of stochastic local search algorithms.