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

Supply chain management: An opportunity for metaheuristics

In today’s highly competitive and global marketplace the pressure on organizations to find new ways to create and deliver value to customers grows ever stronger. In the last two decades, logistics and supply chain has moved to the center stage. There has been a growing recognition that it is through an effective management of the logistics function and the supply chain that the goal of cost reduction and service enhancement can be achieved. The key to success in Supply Chain Management (SCM) require heavy emphasis on integration of activities, cooperation, coordination and information sharing throughout the entire supply chain, from suppliers to customers. To be able to respond to the challenge of integration there is the need of sophisticated decision support systems based on powerful mathematical models and solution techniques, together with the advances in information and communication technologies. The industry and the academia have become increasingly interested in SCM to be able to respond to the problems and issues posed by the changes in the logistics and supply chain. We present a brief discussion on the important issues in SCM. We then argue that metaheuristics can play an important role in solving complex supply chain related problems derived by the importance of designing and managing the entire supply chain as a single entity. We will focus specially on the Iterated Local Search, Tabu Search and Scatter Search as the ones, but not limited to, with great potential to be used on solving the SCM related problems. We will present briefly some successful applications.Supply chain management, metaheuristics, iterated local search, tabu search and scatter search

Improving the Generalisability of Brain Computer Interface Applications via Machine Learning and Search-Based Heuristics

Brain Computer Interfaces (BCI) are a domain of hardware/software in which a user can interact with a machine without the need for motor activity, communicating instead via signals generated by the nervous system. These interfaces provide life-altering benefits to users, and refinement will both allow their application to a much wider variety of disabilities, and increase their practicality. The primary method of acquiring these signals is Electroencephalography (EEG). This technique is susceptible to a variety of different sources of noise, which compounds the inherent problems in BCI training data: large dimensionality, low numbers of samples, and non-stationarity between users and recording sessions. Feature Selection and Transfer Learning have been used to overcome these problems, but they fail to account for several characteristics of BCI. This thesis extends both of these approaches by the use of Search-based algorithms. Feature Selection techniques, known as Wrappers use ‘black box’ evaluation of feature subsets, leading to higher classification accuracies than ranking methods known as Filters. However, Wrappers are more computationally expensive, and are prone to over-fitting to training data. In this thesis, we applied Iterated Local Search (ILS) to the BCI field for the first time in literature, and demonstrated competitive results with state-of-the-art methods such as Least Absolute Shrinkage and Selection Operator and Genetic Algorithms. We then developed ILS variants with guided perturbation operators. Linkage was used to develop a multivariate metric, Intrasolution Linkage. This takes into account pair-wise dependencies of features with the label, in the context of the solution. Intrasolution Linkage was then integrated into two ILS variants. The Intrasolution Linkage Score was discovered to have a stronger correlation with the solutions predictive accuracy on unseen data than Cross Validation Error (CVE) on the training set, the typical approach to feature subset evaluation. Mutual Information was used to create Minimum Redundancy Maximum Relevance Iterated Local Search (MRMR-ILS). In this algorithm, the perturbation operator was guided using an existing Mutual Information measure, and compared with current Filter and Wrapper methods. It was found to achieve generally lower CVE rates and higher predictive accuracy on unseen data than existing algorithms. It was also noted that solutions found by the MRMR-ILS provided CVE rates that had a stronger correlation with the accuracy on unseen data than solutions found by other algorithms. We suggest that this may be due to the guided perturbation leading to solutions that are richer in Mutual Information. Feature Selection reduces computational demands and can increase the accuracy of our desired models, as evidenced in this thesis. However, limited quantities of training samples restricts these models, and greatly reduces their generalisability. For this reason, utilisation of data from a wide range of users is an ideal solution. Due to the differences in neural structures between users, creating adequate models is difficult. We adopted an existing state-of-the-art ensemble technique Ensemble Learning Generic Information (ELGI), and developed an initial optimisation phase. This involved using search to transplant instances between user subsets to increase the generalisability of each subset, before combination in the ELGI. We termed this Evolved Ensemble Learning Generic Information (eELGI). The eELGI achieved higher accuracy than user-specific BCI models, across all eight users. Optimisation of the training dataset allowed smaller training sets to be used, offered protection against neural drift, and created models that performed similarly across participants, regardless of neural impairment. Through the introduction and hybridisation of search based algorithms to several problems in BCI we have been able to show improvements in modelling accuracy and efficiency. Ultimately, this represents a step towards more practical BCI systems that will provide life altering benefits to users

Evolutionary-inspired probabilistic search for enhancing sampling of local minima in the protein energy surface

<p>Abstract</p> <p>Background</p> <p>Despite computational challenges, elucidating conformations that a protein system assumes under physiologic conditions for the purpose of biological activity is a central problem in computational structural biology. While these conformations are associated with low energies in the energy surface that underlies the protein conformational space, few existing conformational search algorithms focus on explicitly sampling low-energy local minima in the protein energy surface.</p> <p>Methods</p> <p>This work proposes a novel probabilistic search framework, PLOW, that explicitly samples low-energy local minima in the protein energy surface. The framework combines algorithmic ingredients from evolutionary computation and computational structural biology to effectively explore the subspace of local minima. A greedy local search maps a conformation sampled in conformational space to a nearby local minimum. A perturbation move jumps out of a local minimum to obtain a new starting conformation for the greedy local search. The process repeats in an iterative fashion, resulting in a trajectory-based exploration of the subspace of local minima.</p> <p>Results and conclusions</p> <p>The analysis of PLOW's performance shows that, by navigating only the subspace of local minima, PLOW is able to sample conformations near a protein's native structure, either more effectively or as well as state-of-the-art methods that focus on reproducing the native structure for a protein system. Analysis of the actual subspace of local minima shows that PLOW samples this subspace more effectively that a naive sampling approach. Additional theoretical analysis reveals that the perturbation function employed by PLOW is key to its ability to sample a diverse set of low-energy conformations. This analysis also suggests directions for further research and novel applications for the proposed framework.</p

A cycle-based evolutionary algorithm for the fixed-charge capacitated multi-commodity network design problem

This paper presents an evolutionary algorithm for the fixed-charge multicommodity network design problem (MCNDP), which concerns routing multiple commodities from origins to destinations by designing a network through selecting arcs, with an objective of minimizing the fixed costs of the selected arcs plus the variable costs of the flows on each arc. The proposed algorithm evolves a pool of solutions using principles of scatter search, interlinked with an iterated local search as an improvement method. New cycle-based neighborhood operators are presented which enable complete or partial re-routing of multiple commodities. An efficient perturbation strategy, inspired by ejection chains, is introduced to perform local compound cycle-based moves to explore different parts of the solution space. The algorithm also allows infeasible solutions violating arc capacities while performing the "ejection cycles", and subsequently restores feasibility by systematically applying correction moves. Computational experiments on benchmark MCNDP instances show that the proposed solution method consistently produces high-quality solutions in reasonable computational times

Pigmentation pattern formation in butterflies: experiments and models

Butterfly pigmentation patterns are one of the most spectacular and vivid examples of pattern formation in biology. They have attracted much attention from experimentalists and theoreticians, who have tried to understand the underlying genetic, chemical and physical processes that lead to patterning. In this paper, we present a brief review of this field by first considering the generation of the localised, eyespot, patterns and then the formation of more globally controlled patterns. We present some new results applied to pattern formation on the wing of the mimetic butterfly Papilio dardanus. To cite this article: H.F. Nijhout et al., C. R. Biologies 326 (2003)