Convergence results for continuous-time dynamics arising in ant colony optimization

This paper studies the asymptotic behavior of several continuous-time dynamical systems which are analogs of ant colony optimization algorithms that solve shortest path problems. Local asymptotic stability of the equilibrium corresponding to the shortest path is shown under mild assumptions. A complete study is given for a recently proposed model called EigenAnt: global asymptotic stability is shown, and the speed of convergence is calculated explicitly and shown to be proportional to the difference between the reciprocals of the second shortest and the shortest paths.Comment: A short version of this paper was published in the preprints of the 19th World Congress of the International Federation of Automatic Control, Cape Town, South Africa, 24-29 August 201

Ant Colony Optimization approaches for the Sequential Ordering Problem

We present two algorithms within the framework of the Ant Colony Optimization (ACO) metaheuristic. The rst algorithm seeks to increase the exploration bias of Gambardella et al.\u27s (2012) Enhanced Ant Colony System (EACS) model, a model which heavily increases the exploitation bias of the already highly exploitative ACS model in order to gain the bene t of increased speed. Our algorithm aims to strike a balance between these two models. The second is also an extension of EACS, based on Jayadeva et al.\u27s (2013) EigenAnt algorithm. EigenAnt aims to avoid the problem of stagnation found in ACO algorithms by, among other unique properties, utilizing a selective rather than global pheromone evaporation model, and by discarding heuristics in the solution construction phase. A performance comparison between our two models, the legacy ACS model, and the EACS model is presented. The Sequential Ordering Problem (SOP), one of the main problems used to demonstrate EACS, and one still actively studied to this day, was utilized to conduct the comparison

Hybrid tabu search – strawberry algorithm for multidimensional knapsack problem

Multidimensional Knapsack Problem (MKP) has been widely used to model real-life combinatorial problems. It is also used extensively in experiments to test the performances of metaheuristic algorithms and their hybrids. For example, Tabu Search (TS) has been successfully hybridized with other techniques, including particle swarm optimization (PSO) algorithm and the two-stage TS algorithm to solve MKP. In 2011, a new metaheuristic known as Strawberry algorithm (SBA) was initiated. Since then, it has been vastly applied to solve engineering problems. However, SBA has never been deployed to solve MKP. Therefore, a new hybrid of TS-SBA is proposed in this study to solve MKP with the objective of maximizing the total profit. The Greedy heuristics by ratio was employed to construct an initial solution. Next, the solution was enhanced by using the hybrid TS-SBA. The parameters setting to run the hybrid TS-SBA was determined by using a combination of Factorial Design of Experiments and Decision Tree Data Mining methods. Finally, the hybrid TS-SBA was evaluated using an MKP benchmark problem. It consisted of 270 test problems with different sizes of constraints and decision variables. The findings revealed that on average the hybrid TS-SBA was able to increase 1.97% profit of the initial solution. However, the best-known solution from past studies seemed to outperform the hybrid TS-SBA with an average difference of 3.69%. Notably, the novel hybrid TS-SBA proposed in this study may facilitate decisionmakers to solve real applications of MKP. It may also be applied to solve other variants of knapsack problems (KPs) with minor modifications

An improved Ant Colony System for the Sequential Ordering Problem

It is not rare that the performance of one metaheuristic algorithm can be improved by incorporating ideas taken from another. In this article we present how Simulated Annealing (SA) can be used to improve the efficiency of the Ant Colony System (ACS) and Enhanced ACS when solving the Sequential Ordering Problem (SOP). Moreover, we show how the very same ideas can be applied to improve the convergence of a dedicated local search, i.e. the SOP-3-exchange algorithm. A statistical analysis of the proposed algorithms both in terms of finding suitable parameter values and the quality of the generated solutions is presented based on a series of computational experiments conducted on SOP instances from the well-known TSPLIB and SOPLIB2006 repositories. The proposed ACS-SA and EACS-SA algorithms often generate solutions of better quality than the ACS and EACS, respectively. Moreover, the EACS-SA algorithm combined with the proposed SOP-3-exchange-SA local search was able to find 10 new best solutions for the SOP instances from the SOPLIB2006 repository, thus improving the state-of-the-art results as known from the literature. Overall, the best known or improved solutions were found in 41 out of 48 cases.Comment: 30 pages, 8 tables, 11 figure

Uma proposta para uma extensão do algoritmo EigenAnt com avaliação de desempenho em problemas de otimização combinatória

The EigenAnt algorithm has recently been introduced to solve the problem of finding the shortest path between two nodes by using dynamics involving local pheromone evaporation. This algorithm has a mathematical proof of convergence to the shortest path between two nodes. In this thesis, the stability and parameter impact analysis of EigenAnt algorithm applied to N-node Binary Chain Problems is carried out. Motivated by this analysis, an improved EigenAnt algorithm is proposed, in which the exploration of different stable equilibria and speed of convergence to them can be tuned separately. A comparative analysis of Improved EigenAnt algorithm with its predecessor EigenAnt and other Ant Colony Optimization algorithms is performed for combinatorial Routing Network shortest path problems. In addition, the application of the proposed Improved EigenAnt algorithm to Multidimensional Knapsack Problems is investigated, by modeling these problems as an N-node Binary Chain shortest path problems with constraints. Local pheromone evaporation and fast convergence features of the EigenAnt algorithm are advantageous for tracking the optimal solutions of dynamic optimization problems in which the problem instances, objective function and constraint parameters change over time. An experimental investigation of the application of the proposed Improved EigenAnt algorithm to track the optimal Dynamic Routing Networks and Dynamic Multidimensional Knapsack problems is another contribution of this thesis.O algoritmo denominado EigenAnt foi introduzido recentemente para a resolução do problema de encontrar o menor caminho entre dois nós de um grafo, utilizando uma dinâmica com evaporação local de feromônio. O referido algoritmo possui uma prova matemática de convergência ao menor caminho. Nesta tese, realiza-se a análise de estabilidade e sensibilidade paramétrica do algoritmo EigenAnt aplicado a problemas de caminhos mínimos em cadeias binárias entre N nós. Motivado por esta análise, propõe-se uma extensão do algoritmo EigenAnt (denotado Improved EigenAnt), no qual a exploração de distintos equilíbrios estáveis e a velocidade de convergência a estes podem ser ajustada independentemente. Realiza-se também uma análise comparativa entre os algoritmos EigenAnt, Improved EigenAnt e outros algoritmos existentes do tipo Colônia de Formigas, no contexto de problemas de caminho mínimo em redes de roteamento. Adicionalmente, aplica-se o algoritmo novo proposto a problemas multidimensionais de mochileiro, por meio da modelagem destes como problemas de caminhos mínimos em cadeias binárias entre N nós, com restrições. Evaporação local de feromônio e convergência rápida são propriedades de algoritmos da classe EigenAnt que tornam esta classe vantajosa para rastreamento de soluções ótimas de problemas de otimização dinâmica, nos quais as instâncias do problema, a função objetivo e os parâmetros das restrições podem mudar ao longo do tempo. Uma investigação experimental da aplicação do algoritmo proposto (Improved EigenAnt) para rastrear a solução ótima em redes dinâmicas de roteamento e em problemas dinâmicos do mochileiro constituem uma outra contribuição desta tese