Anytime Behavior of Inexact TSP Solvers and Perspectives for Automated Algorithm Selection

The Traveling-Salesperson-Problem (TSP) is arguably one of the best-known NP-hard combinatorial optimization problems. The two sophisticated heuristic solvers LKH and EAX and respective (restart) variants manage to calculate close-to optimal or even optimal solutions, also for large instances with several thousand nodes in reasonable time. In this work we extend existing benchmarking studies by addressing anytime behaviour of inexact TSP solvers based on empirical runtime distributions leading to an increased understanding of solver behaviour and the respective relation to problem hardness. It turns out that performance ranking of solvers is highly dependent on the focused approximation quality. Insights on intersection points of performances offer huge potential for the construction of hybridized solvers depending on instance features. Moreover, instance features tailored to anytime performance and corresponding performance indicators will highly improve automated algorithm selection models by including comprehensive information on solver quality.Comment: This version has been accepted for publication at the IEEE Congress on Evolutionary Computation (IEEE CEC) 2020, which is part of the IEEE World Congress on Computational Intelligence (IEEE WCCI) 202

Experimental Analysis of Design Elements of Scalarizing Functions-based Multiobjective Evolutionary Algorithms

In this paper we systematically study the importance, i.e., the influence on performance, of the main design elements that differentiate scalarizing functions-based multiobjective evolutionary algorithms (MOEAs). This class of MOEAs includes Multiobjecitve Genetic Local Search (MOGLS) and Multiobjective Evolutionary Algorithm Based on Decomposition (MOEA/D) and proved to be very successful in multiple computational experiments and practical applications. The two algorithms share the same common structure and differ only in two main aspects. Using three different multiobjective combinatorial optimization problems, i.e., the multiobjective symmetric traveling salesperson problem, the traveling salesperson problem with profits, and the multiobjective set covering problem, we show that the main differentiating design element is the mechanism for parent selection, while the selection of weight vectors, either random or uniformly distributed, is practically negligible if the number of uniform weight vectors is sufficiently large

Automated Algorithm Selection on Continuous Black-Box Problems By Combining Exploratory Landscape Analysis and Machine Learning

In this paper, we build upon previous work on designing informative and efficient Exploratory Landscape Analysis features for characterizing problems' landscapes and show their effectiveness in automatically constructing algorithm selection models in continuous black-box optimization problems. Focussing on algorithm performance results of the COCO platform of several years, we construct a representative set of high-performing complementary solvers and present an algorithm selection model that - compared to the portfolio's single best solver - on average requires less than half of the resources for solving a given problem. Therefore, there is a huge gain in efficiency compared to classical ensemble methods combined with an increased insight into problem characteristics and algorithm properties by using informative features. Acting on the assumption that the function set of the Black-Box Optimization Benchmark is representative enough for practical applications the model allows for selecting the best suited optimization algorithm within the considered set for unseen problems prior to the optimization itself based on a small sample of function evaluations. Note that such a sample can even be reused for the initial population of an evolutionary (optimization) algorithm so that even the feature costs become negligible.Comment: This is the author's final version, and the article has been accepted for publication in Evolutionary Computatio

PasMoQAP: A Parallel Asynchronous Memetic Algorithm for solving the Multi-Objective Quadratic Assignment Problem

Multi-Objective Optimization Problems (MOPs) have attracted growing attention during the last decades. Multi-Objective Evolutionary Algorithms (MOEAs) have been extensively used to address MOPs because are able to approximate a set of non-dominated high-quality solutions. The Multi-Objective Quadratic Assignment Problem (mQAP) is a MOP. The mQAP is a generalization of the classical QAP which has been extensively studied, and used in several real-life applications. The mQAP is defined as having as input several flows between the facilities which generate multiple cost functions that must be optimized simultaneously. In this study, we propose PasMoQAP, a parallel asynchronous memetic algorithm to solve the Multi-Objective Quadratic Assignment Problem. PasMoQAP is based on an island model that structures the population by creating sub-populations. The memetic algorithm on each island individually evolve a reduced population of solutions, and they asynchronously cooperate by sending selected solutions to the neighboring islands. The experimental results show that our approach significatively outperforms all the island-based variants of the multi-objective evolutionary algorithm NSGA-II. We show that PasMoQAP is a suitable alternative to solve the Multi-Objective Quadratic Assignment Problem.Comment: 8 pages, 3 figures, 2 tables. Accepted at Conference on Evolutionary Computation 2017 (CEC 2017

Algorithms Inspired by Nature: A Survey

Nature is known to be the best optimizer. Natural processes most often than not reach an optimal equilibrium. Scientists have always strived to understand and model such processes.Thus, many algorithms exist today that are inspired by nature. Many of these algorithms and heuristics can be used to solve problems for which no polynomial time algorithms exist,such as Job Shop Scheduling and many other Combinatorial Optimization problems. We will discuss some of these algorithms and heuristics and how they help us solve complex problems of practical importance

On the performance of multi-objective estimation of distribution algorithms for combinatorial problems

Fitness landscape analysis investigates features with a high influence on the performance of optimization algorithms, aiming to take advantage of the addressed problem characteristics. In this work, a fitness landscape analysis using problem features is performed for a Multi-objective Bayesian Optimization Algorithm (mBOA) on instances of MNK-landscape problem for 2, 3, 5 and 8 objectives. We also compare the results of mBOA with those provided by NSGA-III through the analysis of their estimated runtime necessary to identify an approximation of the Pareto front. Moreover, in order to scrutinize the probabilistic graphic model obtained by mBOA, the Pareto front is examined according to a probabilistic view. The fitness landscape study shows that mBOA is moderately or loosely influenced by some problem features, according to a simple and a multiple linear regression model, which is being proposed to predict the algorithms performance in terms of the estimated runtime. Besides, we conclude that the analysis of the probabilistic graphic model produced at the end of evolution can be useful to understand the convergence and diversity performances of the proposed approach.Comment: Accepted in IEEE WCCI/CEC '201

Evolutionary Optimization in an Algorithmic Setting

Evolutionary processes proved very useful for solving optimization problems. In this work, we build a formalization of the notion of cooperation and competition of multiple systems working toward a common optimization goal of the population using evolutionary computation techniques. It is justified that evolutionary algorithms are more expressive than conventional recursive algorithms. Three subclasses of evolutionary algorithms are proposed here: bounded finite, unbounded finite and infinite types. Some results on completeness, optimality and search decidability for the above classes are presented. A natural extension of Evolutionary Turing Machine model developed in this paper allows one to mathematically represent and study properties of cooperation and competition in a population of optimized species

An Experimental Study of Adaptive Control for Evolutionary Algorithms

The balance of exploration versus exploitation (EvE) is a key issue on evolutionary computation. In this paper we will investigate how an adaptive controller aimed to perform Operator Selection can be used to dynamically manage the EvE balance required by the search, showing that the search strategies determined by this control paradigm lead to an improvement of solution quality found by the evolutionary algorithm

A Tribe Competition-Based Genetic Algorithm for Feature Selection in Pattern Classification

Feature selection has always been a critical step in pattern recognition, in which evolutionary algorithms, such as the genetic algorithm (GA), are most commonly used. However, the individual encoding scheme used in various GAs would either pose a bias on the solution or require a pre-specified number of features, and hence may lead to less accurate results. In this paper, a tribe competition-based genetic algorithm (TCbGA) is proposed for feature selection in pattern classification. The population of individuals is divided into multiple tribes, and the initialization and evolutionary operations are modified to ensure that the number of selected features in each tribe follows a Gaussian distribution. Thus each tribe focuses on exploring a specific part of the solution space. Meanwhile, tribe competition is introduced to the evolution process, which allows the winning tribes, which produce better individuals, to enlarge their sizes, i.e. having more individuals to search their parts of the solution space. This algorithm, therefore, avoids the bias on solutions and requirement of a pre-specified number of features. We have evaluated our algorithm against several state-of-the-art feature selection approaches on 20 benchmark datasets. Our results suggest that the proposed TCbGA algorithm can identify the optimal feature subset more effectively and produce more accurate pattern classification

A Novel Genetic Algorithm using Helper Objectives for the 0-1 Knapsack Problem

The 0-1 knapsack problem is a well-known combinatorial optimisation problem. Approximation algorithms have been designed for solving it and they return provably good solutions within polynomial time. On the other hand, genetic algorithms are well suited for solving the knapsack problem and they find reasonably good solutions quickly. A naturally arising question is whether genetic algorithms are able to find solutions as good as approximation algorithms do. This paper presents a novel multi-objective optimisation genetic algorithm for solving the 0-1 knapsack problem. Experiment results show that the new algorithm outperforms its rivals, the greedy algorithm, mixed strategy genetic algorithm, and greedy algorithm + mixed strategy genetic algorithm