Orthogonal methods based ant colony search for solving continuous optimization problems

Research into ant colony algorithms for solving continuous optimization problems forms one of the most significant and promising areas in swarm computation. Although traditional ant algorithms are designed for combinatorial optimization, they have shown great potential in solving a wide range of optimization problems, including continuous optimization. Aimed at solving continuous problems effectively, this paper develops a novel ant algorithm termed "continuous orthogonal ant colony" (COAC), whose pheromone deposit mechanisms would enable ants to search for solutions collaboratively and effectively. By using the orthogonal design method, ants in the feasible domain can explore their chosen regions rapidly and e±ciently. By implementing an "adaptive regional radius" method, the proposed algorithm can reduce the probability of being trapped in local optima and therefore enhance the global search capability and accuracy. An elitist strategy is also employed to reserve the most valuable points. The performance of the COAC is compared with two other ant algorithms for continuous optimization of API and CACO by testing seventeen functions in the continuous domain. The results demonstrate that the proposed COAC algorithm outperforms the others

An ant colony algorithm for the mixed vehicle routing problem with backhauls

The Vehicle Routing Problem with Pickup and Delivery (VRPPD) is a variant of the Vehicle Routing Problem where the vehicles are not only required to deliver goods but also to pick up some goods from the customers. The Mixed Vehicle Routing Problem with Backhauls (MVRPB) is a special case of VRPPD where each customer has either a delivery or a pickup demand to be satisfied and the customers can be visited in any order along the route. Given a fleet of vehicles and a set of customers with known pickup or delivery demands MVRPB determines a set of vehicle routes originating and ending at a single depot and visiting all customers exactly once. The objective is to minimize the total distance traversed with the least number of vehicles. For this problem, we propose an Ant Colony Optimization algorithm with a new visibility function which attempts to capture the “delivery” and “pickup” nature of the problem. Our numerical tests to compare the performance of the proposed approach with those of the well-known benchmark problems reveal that the proposed approach provides encouraging results

Differential evolution with an evolution path: a DEEP evolutionary algorithm

Utilizing cumulative correlation information already existing in an evolutionary process, this paper proposes a predictive approach to the reproduction mechanism of new individuals for differential evolution (DE) algorithms. DE uses a distributed model (DM) to generate new individuals, which is relatively explorative, whilst evolution strategy (ES) uses a centralized model (CM) to generate offspring, which through adaptation retains a convergence momentum. This paper adopts a key feature in the CM of a covariance matrix adaptation ES, the cumulatively learned evolution path (EP), to formulate a new evolutionary algorithm (EA) framework, termed DEEP, standing for DE with an EP. Without mechanistically combining two CM and DM based algorithms together, the DEEP framework offers advantages of both a DM and a CM and hence substantially enhances performance. Under this architecture, a self-adaptation mechanism can be built inherently in a DEEP algorithm, easing the task of predetermining algorithm control parameters. Two DEEP variants are developed and illustrated in the paper. Experiments on the CEC'13 test suites and two practical problems demonstrate that the DEEP algorithms offer promising results, compared with the original DEs and other relevant state-of-the-art EAs

Hybrid ACO and SVM algorithm for pattern classification

Ant Colony Optimization (ACO) is a metaheuristic algorithm that can be used to solve a variety of combinatorial optimization problems. A new direction for ACO is to optimize continuous and mixed (discrete and continuous) variables. Support Vector Machine (SVM) is a pattern classification approach originated from statistical approaches. However, SVM suffers two main problems which include feature subset selection and parameter tuning. Most approaches related to tuning SVM parameters discretize the continuous value of the parameters which will give a negative effect on the classification performance. This study presents four algorithms for tuning the SVM parameters and selecting feature subset which improved SVM classification accuracy with smaller size of feature subset. This is achieved by performing the SVM parameters’ tuning and feature subset selection processes simultaneously. Hybridization algorithms between ACO and SVM techniques were proposed. The first two algorithms, ACOR-SVM and IACOR-SVM, tune the SVM parameters while the second two algorithms, ACOMV-R-SVM and IACOMV-R-SVM, tune the SVM parameters and select the feature subset simultaneously. Ten benchmark datasets from University of California, Irvine, were used in the experiments to validate the performance of the proposed algorithms. Experimental results obtained from the proposed algorithms are better when compared with other approaches in terms of classification accuracy and size of the feature subset. The average classification accuracies for the ACOR-SVM, IACOR-SVM, ACOMV-R and IACOMV-R algorithms are 94.73%, 95.86%, 97.37% and 98.1% respectively. The average size of feature subset is eight for the ACOR-SVM and IACOR-SVM algorithms and four for the ACOMV-R and IACOMV-R algorithms. This study contributes to a new direction for ACO that can deal with continuous and mixed-variable ACO

Combinatorial optimization and metaheuristics

Today, combinatorial optimization is one of the youngest and most active areas of discrete mathematics. It is a branch of optimization in applied mathematics and computer science, related to operational research, algorithm theory and computational complexity theory. It sits at the intersection of several fields, including artificial intelligence, mathematics and software engineering. Its increasing interest arises for the fact that a large number of scientific and industrial problems can be formulated as abstract combinatorial optimization problems, through graphs and/or (integer) linear programs. Some of these problems have polynomial-time (“efficient”) algorithms, while most of them are NP-hard, i.e. it is not proved that they can be solved in polynomial-time. Mainly, it means that it is not possible to guarantee that an exact solution to the problem can be found and one has to settle for an approximate solution with known performance guarantees. Indeed, the goal of approximate methods is to find “quickly” (reasonable run-times), with “high” probability, provable “good” solutions (low error from the real optimal solution). In the last 20 years, a new kind of algorithm commonly called metaheuristics have emerged in this class, which basically try to combine heuristics in high level frameworks aimed at efficiently and effectively exploring the search space. This report briefly outlines the components, concepts, advantages and disadvantages of different metaheuristic approaches from a conceptual point of view, in order to analyze their similarities and differences. The two very significant forces of intensification and diversification, that mainly determine the behavior of a metaheuristic, will be pointed out. The report concludes by exploring the importance of hybridization and integration methods