A critical analysis of parameter adaptation in ant colony optimization

Applying parameter adaptation means operating on parameters of an algorithm while it is tackling an instance. For ant colony optimization, several parameter adaptation methods have been proposed. In the literature, these methods have been shown to improve the quality of the results achieved in some particular contexts. In particular, they proved to be successful when applied to novel ant colony optimization algorithms for tackling problems that are not a classical testbed for optimization algorithms. In this paper, we show that the adaptation methods proposed so far do not improve, and often even worsen the performance when applied to high performing ant colony optimization algorithms for some classical combinatorial optimization problems.     

Estimation-based ant colony optimization and local search for the probabilistic traveling salesman problem

The use of ant colony optimization for solving stochastic optimization problems has received a significant amount of attention in recent years. In this paper, we present a study of enhanced ant colony optimization algorithms for tackling a stochastic optimization problem, the probabilistic traveling salesman problem. In particular, we propose an empirical estimation approach to evaluate the cost of the solutions constructed by the ants. Moreover, we use a recent estimation-based iterative improvement algorithm as a local search. Experimental results on a large number of problem instances show that the proposed ant colony optimization algorithms outperform the current best algorithm tailored to solve the given problem, which also happened to be an ant colony optimization algorithm. As a consequence, we have obtained a new state-of-the-art ant colony optimization algorithm for the probabilistic traveling salesman problem.     

An experimental analysis of design choices of multi-objective ant colony optimization algorithms

There have been several proposals on how to apply the ant colony optimization (ACO) metaheuristic to multi-objective combinatorial optimization problems (MOCOPs). This paper proposes a new formulation of these multi-objective ant colony optimization (MOACO) algorithms. This formulation is based on adding specific algorithm components for tackling multiple objectives to the basic ACO metaheuristic. Examples of these components are how to represent multiple objectives using pheromone and heuristic information, how to select the best solutions for updating the pheromone information, and how to define and use weights to aggregate the different objectives. This formulation reveals more similarities than previously thought in the design choices made in existing MOACO algorithms. The main contribution of this paper is an experimental analysis of how particular design choices affect the quality and the shape of the Pareto front approximations generated by each MOACO algorithm. This study provides general guidelines to understand how MOACO algorithms work, and how to improve their design.     

An Ant Colony Optimization Based Dimension Reduction Method for High-Dimensional Datasets

In this paper, a bionic optimization algorithm based dimension reduction method named Ant Colony Optimization -Selection (ACO-S) is proposed for high-dimensional datasets. Because microarray datasets comprise tens of thousands of features (genes), they are usually used to test the dimension reduction techniques. ACO-S consists of two stages in which two well-known ACO algorithms, namely ant system and ant colony system, are utilized to seek for genes, respectively. In the first stage, a modified ant system is used to filter the nonsignificant genes from high-dimensional space, and a number of promising genes are reserved in the next step. In the second stage, an improved ant colony system is applied to gene selection. In order to enhance the search ability of ACOs, we propose a method for calculating priori available heuristic information and design a fuzzy logic controller to dynamically adjust the number of ants in ant colony system. Furthermore, we devise another fuzzy logic controller to tune the parameter (q₀) in ant colony system. We evaluate the performance of ACO-S on five microarray datasets, which have dimensions varying from 7129 to 12000. We also compare the performance of ACO-S with the results obtained from four existing well-known bionic optimization algorithms. The comparison results show that ACO-S has a notable ability to generate a gene subset with the smallest size and salient features while yielding high classification accuracy. The comparative results generated by ACO-S adopting different classifiers are also given. The proposed method is shown to be a promising and effective tool for mining high-dimension data and mobile robot navigation.     

Branch-and-terminate: a combinatorial optimization algorithm for protein design.

BACKGROUND: Several deterministic and stochastic combinatorial optimization algorithms have been applied to computational protein design and homology modeling. As structural targets increase in size, however, it has become necessary to find more powerful methods to address the increased combinatorial complexity. RESULTS: We present a new deterministic combinatorial search algorithm called 'Branch-and-Terminate' (B&T), which is derived from the Branch-and-Bound search method. The B&T approach is based on the construction of an efficient but very restrictive bounding expression, which is used for the search of a combinatorial tree representing the protein system. The bounding expression is used both to determine the optimal organization of the tree and to perform a highly effective pruning procedure named 'termination'. For some calculations, the B&T method rivals the current deterministic standard, dead-end elimination (DEE), sometimes finding the solution up to 21 times faster. A more significant feature of the B&T algorithm is that it can provide an efficient way to complete the optimization of problems that have been partially reduced by a DEE algorithm. CONCLUSIONS: The B&T algorithm is an effective optimization algorithm when used alone. Moreover, it can increase the problem size limit of amino acid sidechain placement calculations, such as protein design, by completing DEE optimizations that reach a point at which the DEE criteria become inefficient. Together the two algorithms make it possible to find solutions to problems that are intractable by either algorithm alone.     

Ant colony optimization for real-world vehicle routing problems

Ant colony optimization (ACO) is a metaheuristic for combinatorial optimization problems. In this paper we report on its successful application to the vehicle routing problem (VRP). First, we introduce the VRP and some of its variants, such as the VRP with time windows, the time dependent VRP, the VRP with pickup and delivery, and the dynamic VRP. These variants have been formulated in order to bring the VRP closer to the kind of situations encountered in the real-world. Then, we introduce the basic principles of ant colony optimization, and we briefly present its application to the solution of the VRP and of its variants.     

Stability analysis of higher-order neural networks for combinatorial optimization

Recurrent neural networks with higher order connections, from here on referred to as higher-order neural networks (HONNs), may be used for the solution of combinatorial optimization problems. In Ref. 5 a mapping of the traveling salesman problem (TSP) onto a HONN of arbitrary order was developed, thereby creating a family of related networks that can be used to solve the TSP. In this paper, we explore the trade-off between network complexity and quality of solution that is made available by the HONN mapping of the TSP. The trade-off is investigated by undertaking an analysis of the stability of valid solutions to the TSP in a HONN of arbitrary order. The techniques used to perform the stability analysis are not new, but have been widely used elsewhere in the literature. The original contribution in this paper is the application of these techniques to a HONN of arbitrary order used to solve the TSP. The results of the stability analysis show that the quality of solution is improved by increasing the network complexity, as measured by the order of the network. Furthermore, it is shown that the Hopfield network, as the simplest network in the family of higher-order networks, is expected to produce the poorest quality of solution.     

Mathematical runtime analysis of ACO algorithms: survey on an emerging issue

The paper gives an overview on the status of the theoretical analysis of Ant Colony Optimization (ACO) algorithms, with a special focus on the analytical investigation of the runtime required to find an optimal solution to a given combinatorial optimization problem. First, a general framework for studying questions of this type is presented, and three important ACO variants are recalled within this framework. Secondly, two classes of formal techniques for runtime investigations of the considered type are outlined. Finally, some available runtime complexity results for ACO variants, referring to elementary test problems that have been introduced in the theoretical literature on evolutionary algorithms, are cited and discussed.     

Metaheuristics for the bi-objective orienteering problem

In this paper, heuristic solution techniques for the multi-objective orienteering problem are developed. The motivation stems from the problem of planning individual tourist routes in a city. Each point of interest in a city provides different benefits for different categories (e.g., culture, shopping). Each tourist has different preferences for the different categories when selecting and visiting the points of interests (e.g., museums, churches). Hence, a multi-objective decision situation arises. To determine all the Pareto optimal solutions, two metaheuristic search techniques are developed and applied. We use the Pareto ant colony optimization algorithm and extend the design of the variable neighborhood search method to the multi-objective case. Both methods are hybridized with path relinking procedures. The performances of the two algorithms are tested on several benchmark instances as well as on real world instances from different Austrian regions and the cities of Vienna and Padua. The computational results show that both implemented methods are well performing algorithms to solve the multi-objective orienteering problem.     

Artificial bee colonies for continuous optimization: Experimental analysis and improvements

The artificial bee colony (ABC) algorithm is a recent class of swarm intelligence algorithms that is loosely inspired by the foraging behavior of honeybee swarms. It was introduced in 2005 using continuous optimization problems as an example application. Similar to what has happened with other swarm intelligence techniques, after the initial proposal, several researchers have studied variants of the original algorithm. Unfortunately, often these variants have been tested under different experimental conditions and different fine-tuning efforts for the algorithm parameters. In this article, we review various variants of the original ABC algorithm and experimentally study nine ABC algorithms under two settings: either using the original parameter settings as proposed by the authors, or using an automatic algorithm configuration tool using a same tuning effort for each algorithm. We also study the effect of adding local search to the ABC algorithms. Our experimental results show that local search can improve considerably the performance of several ABC variants and that it reduces strongly the performance differences between the studied ABC variants. We also show that the best ABC variants are competitive with recent state-of-the-art algorithms on the benchmark set we used, which establishes ABC algorithms as serious competitors in continuous optimization.     

A Discrete Fruit Fly Optimization Algorithm for the Traveling Salesman Problem

The fruit fly optimization algorithm (FOA) is a newly developed bio-inspired algorithm. The continuous variant version of FOA has been proven to be a powerful evolutionary approach to determining the optima of a numerical function on a continuous definition domain. In this study, a discrete FOA (DFOA) is developed and applied to the traveling salesman problem (TSP), a common combinatorial problem. In the DFOA, the TSP tour is represented by an ordering of city indices, and the bio-inspired meta-heuristic search processes are executed with two elaborately designed main procedures: the smelling and tasting processes. In the smelling process, an effective crossover operator is used by the fruit fly group to search for the neighbors of the best-known swarm location. During the tasting process, an edge intersection elimination (EXE) operator is designed to improve the neighbors of the non-optimum food location in order to enhance the exploration performance of the DFOA. In addition, benchmark instances from the TSPLIB are classified in order to test the searching ability of the proposed algorithm. Furthermore, the effectiveness of the proposed DFOA is compared to that of other meta-heuristic algorithms. The results indicate that the proposed DFOA can be effectively used to solve TSPs, especially large-scale problems.     

An optimization-based sampling scheme for phylogenetic trees

Much modern work in phylogenetics depends on statistical sampling approaches to phylogeny construction to estimate probability distributions of possible trees for any given input data set. Our theoretical understanding of sampling approaches to phylogenetics remains far less developed than that for optimization approaches, however, particularly with regard to the number of sampling steps needed to produce accurate samples of tree partition functions. Despite the many advantages in principle of being able to sample trees from sophisticated probabilistic models, we have little theoretical basis for concluding that the prevailing sampling approaches do in fact yield accurate samples from those models within realistic numbers of steps. We propose a novel approach to phylogenetic sampling intended to be both efficient in practice and more amenable to theoretical analysis than the prevailing methods. The method depends on replacing the standard tree rearrangement moves with an alternative Markov model in which one solves a theoretically hard but practically tractable optimization problem on each step of sampling. The resulting method can be applied to a broad range of standard probability models, yielding practical algorithms for efficient sampling and rigorous proofs of accurate sampling for heated versions of some important special cases. We demonstrate the efficiency and versatility of the method by an analysis of uncertainty in tree inference over varying input sizes. In addition to providing a new practical method for phylogenetic sampling, the technique is likely to prove applicable to many similar problems involving sampling over combinatorial objects weighted by a likelihood model.     

The combinatorial distance geometry method for the calculation of molecular conformation. I. A new approach to an old problem

A new approach to the long-standing local minimum problem of molecular energy minimization is proposed. The approach relies upon a field of computer mathematics known as combinatorial optimization, together with methods of conformational analysis derived from distance geometry. The advantages over the usual numerical techniques of optimization are, first, that the algorithms derived are globally convergent, and second, that the mathematical problems involved are well-posed and suitable for study within the modern theory of computational complexity. In this paper we introduce the approach, and describe a computer program based on it.     

蚂蚁群落优化算法在蛋白质折叠二维亲-疏水格点模型中的应用

氨基酸的亲疏水格点模型是研究蛋白质折叠的一种重要的简化模型,其优化问题是一个非确定型的多项式问题。采用蚂蚁群落优化算法对这一问题进行了研究,对测试数据的计算结果表明,在一定规模下,此算法能够有效地获得亲-疏水格点模型的最优解,其效率优于传统的Monte Carlo仿真等方法。     

Development and validation of evolutionary algorithm software as an optimization tool for biological and environmental applications

A flexible, extendable tool for the optimization of (micro)biological processes and protocols using evolutionary algorithms was developed. It has been tested using three different theoretical optimization problems: 2 two-dimensional problems, one with three maxima and one with five maxima and a river autopurification optimization problem with boundary conditions. For each problem, different evolutionary parameter settings were used for the optimization. For each combination of evolutionary parameters, 15 generations were run 20 times. It has been shown that in all cases, the evolutionary algorithm gave rise to valuable results. Generally, the algorithms were able to detect the more stable sub-maximum even if there existed less stable maxima. The latter is, from a practical point of view, generally more desired. The most important factors influencing the convergence process were the parameter value randomization rate and distribution. The developed software, described in this work, is available for free.     

An efficient approach to the travelling salesman problem using self-organizing maps

This paper presents an approach to the well-known Travelling Salesman Problem (TSP) using Self-Organizing Maps (SOM). The SOM algorithm has interesting topological information about its neurons configuration on cartesian space, which can be used to solve optimization problems. Aspects of initialization, parameters adaptation, and complexity analysis of the proposed SOM based algorithm are discussed. The results show an average deviation of 3.7% from the optimal tour length for a set of 12 TSP instances.     

Computational Modeling of Proteins based on Cellular Automata: A Method of HP Folding Approximation

The design of a protein folding approximation algorithm is not straightforward even when a simplified model is used. The folding problem is a combinatorial problem, where approximation and heuristic algorithms are usually used to find near optimal folds of proteins primary structures. Approximation algorithms provide guarantees on the distance to the optimal solution. The folding approximation approach proposed here depends on two-dimensional cellular automata to fold proteins presented in a well-studied simplified model called the hydrophobic–hydrophilic model. Cellular automata are discrete computational models that rely on local rules to produce some overall global behavior. One-third and one-fourth approximation algorithms choose a subset of the hydrophobic amino acids to form H–H contacts. Those algorithms start with finding a point to fold the protein sequence into two sides where one side ignores H’s at even positions and the other side ignores H’s at odd positions. In addition, blocks or groups of amino acids fold the same way according to a predefined normal form. We intend to improve approximation algorithms by considering all hydrophobic amino acids and folding based on the local neighborhood instead of using normal forms. The CA does not assume a fixed folding point. The proposed approach guarantees one half approximation minus the H–H endpoints. This lower bound guaranteed applies to short sequences only. This is proved as the core and the folds of the protein will have two identical sides for all short sequences.     

Ant colony optimization for multicasting in static wireless ad-hoc networks

Nodes of wireless ad-hoc networks are generally equipped with batteries. This makes energy a scarce resource. Therefore, power consumption of network operations is critical and subject to optimization. One of the fundamental problems in ad-hoc networks is multicasting. In this work, we consider the so-called minimum energy multicast (MEM) problem in static ad-hoc networks. This problem can be stated as a combinatorial optimization problem. We develop an ant colony optimization algorithm for networks with omni-directional as well as directional antennas. The results show that our algorithm consistently outperforms existing techniques. This work was supported by grant TIN2007-66523 (FORMALISM) of the Spanish Government, and by the EU project FRONTS (FP7-ICT-2007-1) funded by the European Commission under the FET Proactive Initiative Pervasive Adaptation. In addition, Christian Blum acknowledges support from the Ramón y Cajal program of the Spanish Ministry of Science and Innovation, and Hugo Hernández acknowledges support from the Catalan Government through an FI grant.     

Learning Bayesian network classifiers using ant colony optimization

Bayesian networks are knowledge representation tools that model the (in)dependency relationships among variables for probabilistic reasoning. Classification with Bayesian networks aims to compute the class with the highest probability given a case. This special kind is referred to as Bayesian network classifiers. Since learning the Bayesian network structure from a dataset can be viewed as an optimization problem, heuristic search algorithms may be applied to build high-quality networks in medium- or large-scale problems, as exhaustive search is often feasible only for small problems. In this paper, we present our new algorithm, ABC-Miner, and propose several extensions to it. ABC-Miner uses ant colony optimization for learning the structure of Bayesian network classifiers. We report extended computational results comparing the performance of our algorithm with eight other classification algorithms, namely six variations of well-known Bayesian network classifiers, cAnt-Miner for discovering classification rules and a support vector machine algorithm.     

Learning cluster-based classification systems with ant colony optimization algorithms

Classification is a data mining task the goal of which is to learn a model, from a training dataset, that can predict the class of a new data instance, while clustering aims to discover natural instance-groupings within a given dataset. Learning cluster-based classification systems involves partitioning a training set into data subsets (clusters) and building a local classification model for each data cluster. The class of a new instance is predicted by first assigning the instance to its nearest cluster and then using that cluster’s local classification model to predict the instance’s class. In this paper, we present an ant colony optimization (ACO) approach to building cluster-based classification systems. Our ACO approach optimizes the number of clusters, the positioning of the clusters, and the choice of classification algorithm to use as the local classifier for each cluster. We also present an ensemble approach that allows the system to decide on the class of a given instance by considering the predictions of all local classifiers, employing a weighted voting mechanism based on the fuzzy degree of membership in each cluster. Our experimental evaluation employs five widely used classification algorithms: naïve Bayes, nearest neighbour, Ripper, C4.5, and support vector machines, and results are reported on a suite of 54 popular UCI benchmark datasets.