Jean Paulo Martins

On the performance of linkage-tree genetic algorithms for the multidimensional knapsack problem

Model-based Genetic Algorithms (GAs), as the Linkage Tree Genetic Algorithm (LTGA) and most Estimation of Distribution Algorithms (EDAs), assume a reductionist perspective when solving optimization problems. They use machine-learning techniques to discover problem?s substructures that might be useful to generate new solutions. This idea was grounded on Simon?s near-decomposability principle and Holland?s Building Block (BB)-hypothesis, and have enabled the development of effective algorithms in some contexts. Although near-decomposability is commonly seen in nature, we cannot assume the same occurs for optimization problems. Therefore, the existence of problems where these algorithms are not effective is also focus of research. Recent studies have argued that Multidimensional Knapsack Problems (MKPs) are examples of such cases. This paper extends these studies with an extensive comparison of various LTGA variants for the MKP. Using a well-known GA as reference, we analyzed the difficulties faced by the LTGA and explained why its linkage-tree model is not of much help to solve the problem. The results have shown that the LTGA was not able to outperform the GA and performed very similarly to a LTGA using random linkage-models. Further analysis of the linkage-trees, grounded on the knapsack-core concept, enabled interesting conclusions about the reason that linkage-learning did not provide useful information to solve MKPs in the settings used for the experiments.

Multi-Objective Evolutionary Algorithm with Node-Depth Encoding and Strength Pareto for Service Restoration in Large-Scale Distribution Systems

The network reconfiguration for service restoration in distribution systems is a combinatorial complex optimization problem that usually involves multiple non-linear constraints and objectives functions. For large networks, no exact algorithm has found adequate restoration plans in real-time, on the other hand, Multi-objective Evolutionary Algorithms (MOEA) using the Node-depth enconding (MEAN) is able to efficiently generate adequate restorations plans for relatively large distribution systems. An MOEA for the restoration problem should provide restoration plans that satisfy the constraints and reduce the number of switching operations in situations of one fault. For diversity of real-world networks, those goals are met by improving the capacity of the MEAN to explore both the search and objective spaces. This paper proposes a new method called MEA2N with Strength Pareto table (MEA2N-STR) properly designed to restore a feeder fault in networks with significant different bus sizes: 3 860 and 15 440. The metrics R 2, R 3, Hypervolume and e-indicators were used to measure the quality of the obtained fronts.

Multi-objective phylogenetic algorithm: solving multi-objective decomposable deceptive problems

In general, Multi-objective Evolutionary Algorithms do not guarantee find solutions in the Pareto-optimal set. We propose a new approach for solving decomposable deceptive multi-objective problems that can find all solutions of the Pareto-optimal set. Basically, the proposed approach starts by decomposing the problem into subproblems and, then, combining the found solutions. The resultant approach is a Multi-objective Estimation of Distribution Algorithm for solving relatively complex multi-objective decomposable problems, using a probabilistic model based on a phylogenetic tree. The results show that, for the tested problem, the algorithm can efficiently find all the solutions of the Pareto-optimal set, with better scaling than the hierarchical Bayesian Optimization Algorithm and other algorithms of the state of art.

A comparison of Linkage-learning-based Genetic Algorithms in Multidimensional Knapsack Problems

Linkage Learning (LL) was proposed as a methodology to enable Genetic Algorithms (GAs) to solve complex optimization problems more effectively. Its main idea relies on a reductionist assumption, considering optimization problems as being composed of substructures that could be exploited to improve the GAs search mechanism. In general, LL-GAs have been compared in a restricted set of well-known optimization problems, in which the reductionist assumption holds true, and only a few studies have concerned their performances in broader scenarios. To help to fill this gap, we have compared four different LL-GAs in the classic Multidimensional Knapsack Problem (MKP) using all the instances provided by Chu & Beasley (1998). Our objective was to verify if the relative performance of algorithms as: the Extended Compact Genetic Algorithm (eCGA), the Bayesian Optimization Algorithm (BOA) with decision graphs, the BOA with community detection, the Linkage Tree Genetic Algorithm (LTGA) and a simple GA; would remain the same in the MKPs instances, where the existence of substructures is unknown. However, the results have shown the opposite, and algorithms as BOA have only found similar solutions to those found by the eCGA and LTGA when using large population sizes.

A compact transformation of arc routing problems into node routing problems

We describe a compact method to transform arc routing problem instances into node routing problem instances. Any node routing problem instance thus created must be solved by a branch-and-price process, such as the one described in this paper. The purpose is to make the number of nodes in the resulting transformed graphs greater by only one unit than the number

Multimodality and the linkage-learning difficulty of additively separable functions

r

The influence of linkage-learning in the linkage-tree GA when solving multidimensional knapsack problems

r of required arcs (arcs having demand) in the original graph, that is,