Improved binary artificial fish swarm algorithm for the 0–1 multidimensional knapsack problems

The 0–1 multidimensional knapsack problem (MKP) arises in many fields of optimization and is NP-hard. Several exact as well as heuristic methods exist. Recently, an artificial fish swarm algorithm has been developed in continuous global optimization. The algorithm uses a population of points in space to represent the position of fish in the school. In this paper, a binary version of the artificial fish swarm algorithm is proposed for solving the 0–1 MKP. In the proposed method, a point is represented by a binary string of 0/1 bits. Each bit of a trial point is generated by copying the corresponding bit from the current point or from some other specified point, with equal probability. Occasionally, some randomly chosen bits of a selected point are changed from 0 to 1, or 1 to 0, with an user defined probability. The infeasible solutions are made feasible by a decoding algorithm. A simple heuristic add_item is implemented to each feasible point aiming to improve the quality of that solution. A periodic reinitialization of the population greatly improves the quality of the solutions obtained by the algorithm. The proposed method is tested on a set of benchmark instances and a comparison with other methods available in literature is shown. The comparison shows that the proposed method gives a competitive performance when solving this kind of problems.Fundação para a Ciência e a Tecnologia (FCT

Structural optimization using evolutionary multimodal and bilevel optimization techniques

This research aims to investigate the multimodal properties of structural optimization using techniques from the field of evolutionary computation, specifically niching and bilevel techniques. Truss design is a well-known structural optimization problem which has important practical applications in many fields. Truss design problems are typically multimodal by nature, meaning that it offers multiple equally good design solutions with respect to the topology and/or sizes of the members, but they are evaluated to have similar or equally good objective function values. From a practical standpoint, it is desirable to find as many alternative designs as possible, rather than finding a single design, as often practiced. Niching is an intuitive way of finding multiple optimal solutions in a single optimization run. Literature shows that existing niching methods are largely designed for handling continuous optimization problems. There does not exist a well-studied niching method for constrained discrete optimization problems like truss design problems. In addition, there are no well-defined multimodal discrete benchmark problems that can be used to evaluate the reliability and robustness of such a niching method. This thesis fills the identified research gaps by means of five major contributions. In the first contribution, we design a test suite for producing a diverse set of challenging multimodal discrete benchmark problems, which can be used for evaluating the discrete niching methods. In the second contribution, we develop a binary speciation-based PSO (B-SPSO) niching method using the concept of speciation in nature along with the binary PSO (BPSO). The results show that the proposed multimodal discrete benchmark problems are useful for the evaluation of the discrete niching methods like B-SPSO. In light of this study, a time-varying transfer function based binary PSO (TVT-BPSO) is developed for the B-SPSO which is the third contribution of this thesis. We propose this TVT-BPSO for maintaining a better balance between exploration/exploitation during the search process of the BPSO. The results show that the TVT-BPSO outperforms the state-of-the-art discrete optimization methods on the large-scale 0-1 knapsack problems. The fourth contribution is to consider and formulate the truss design problem as a bilevel optimization problem. With this new formulation, truss topology can be optimized in the upper level, at the same time the size of that truss topology can be optimized in the lower level. The proposed bilevel formulation is a precursor to the development of a bilevel niching method (Bi-NM) which constitutes the fifth contribution of this thesis. The proposed Bi-NM method performs niching at the upper level and a local search at the lower level to further refine the solutions. Extensive empirical studies are carried out to examine the accuracy, robustness, and efficiency of the proposed bilevel niching method in finding multiple topologies and their size solutions. Our results confirm that the proposed bilevel niching method is superior in all these three aspects over the state-of-the-art methods on several low to high-dimensional truss design problems

A NOVEL APPROACH TO ORBITAL DEBRIS MITIGATION

Since mankind launched the first satellite into orbit in 1957, we have been inadvertently, yet deliberately, creating an environment in space that may ultimately lead to the end of our space exploration. Space debris, more specifically, orbital debris is a growing problem that must be dealt with sooner, rather than later. Several ideas have been developed to address the complex problem of orbital debris mitigation. This research will investigate the possibility of removing orbital debris from the Low Earth Orbit (LEO) regime by using a metaheuristic algorithm to maximize collection of debris resulting from the February 2009 on-orbit collision of Iridium 33 and Cosmos 2251. This treatment will concentrate on the Iridium debris field for analysis. This research is necessary today, more than ever, as we embark on the launch of thousands of LEO spacecraft, which could result in the realization of the Kessler Syndrome, “The certain risk of failure on launch or during operations due to an on-orbit collision with debris” (Kessler & Cour-Palais, 1978)

Uma Abordagem com Multi-Mochilas Multidimensionais para o Problema de Alocação de Ações de Redução de Perdas na Distribuição de Energia

Em países em desenvolvimento, perdas não-técnicas são consideradas pelas companhias de distribuição de energia como algumas das maiores causas de prejuízos. No Brasil, parte dessas perdas pode ser repassada ao consumidor nas tarifas, entretanto o valor máximo deste repasse é limitado pela agência reguladora, como forma de incentivar melhorias por parte das distribuidoras. Este limite é definido na forma de metas de redução de perdas. O problema de otimização abordado neste trabalho trata da redução de perdas do ponto de vista da distribuidora. Para atingir as metas estabelecidas pela agência reguladora, as distribuidoras possuem várias ações de redução de perdas, que devem ser alocadas em planos multianuais. Estes planos tentam atingir a meta estabelecida, respeitando alguns orçamentos disponíveis, e objetivando sempre obter o maior lucro possível com a alocação das ações. Este trabalho aborda o problema como uma generalização do Problema da Mochila. Uma modelagem formal é definida e a dificuldade da mesma é analisada através de testes computacionais, utilizando um resolvedor genérico aplicado a uma variedade de instâncias para obter a solução exata. Duas heurísticas são então propostas, a primeira baseada em uma abordagem gulosa e a segunda na metaheurística Busca Tabu, e aplicadas ao problema. Finalmente, as técnicas são comparadas considerando a qualidade das soluções encontradas

Binary accelerated particle swarm algorithm (BAPSA) for discrete optimization problems

The majority of Combinatorial Optimization Problems (COPs) are defined in the discrete space. Hence, proposing an efficient algorithm to solve the problems has become an attractive subject in recent years. In this paper, a meta-heuristic algorithm based on Binary Particle Swarm Algorithm (BPSO) and the governing Newtonian motion laws, so-called Binary Accelerated Particle Swarm Algorithm (BAPSA) is offered for discrete search spaces. The method is presented in two global and local topologies and evaluated on the 0–1 Multidimensional Knapsack Problem (MKP) as a famous problem in the class of COPs and NP-hard problems. Besides, the results are compared with BPSO for both global and local topologies as well as Genetic Algorithm (GA). We applied three methods of Penalty Function (PF) technique, Check-and-Drop (CD) and Improved Check-and-Repair Operator (ICRO) algorithms to solve the problem of infeasible solutions in the 0–1 MKP. Experimental results show that the proposed methods have better performance than BPSO and GA especially when ICRO algorithm is applied to convert infeasible solutions to feasible ones