Jakob Bossek

A novel feature-based approach to characterize algorithm performance for the traveling salesperson problem

Meta-heuristics are frequently used to tackle NP-hard combinatorial optimization problems. With this paper we contribute to the understanding of the success of 2-opt based local search algorithms for solving the traveling salesperson problem (TSP). Although 2-opt is widely used in practice, it is hard to understand its success from a theoretical perspective. We take a statistical approach and examine the features of TSP instances that make the problem either hard or easy to solve. As a measure of problem difficulty for 2-opt we use the approximation ratio that it achieves on a given instance. Our investigations point out important features that make TSP instances hard or easy to be approximated by 2-opt.

Local search and the traveling salesman problem: a feature-based characterization of problem hardness

With this paper we contribute to the understanding of the success of 2-opt based local search algorithms for solving the traveling salesman problem (TSP). Although 2-opt is widely used in practice, it is hard to understand its success from a theoretical perspective. We take a statistical approach and examine the features of TSP instances that make the problem either hard or easy to solve. As a measure of problem difficulty for 2-opt we use the approximation ratio that it achieves on a given instance. Our investigations point out important features that make TSP instances hard or easy to be approximated by 2-opt.

ecr 2.0: a modular framework for evolutionary computation in R

The novel R package ecr (version 2), short for Evolutionary Computation in R, provides a comprehensive collection of building blocks for constructing powerful evolutionary algorithms for single- and multi-objective continuous and combinatorial optimization problems. It allows to solve standard optimization tasks with few lines of code using a black-box approach. Moreover, rapid prototyping of non-standard ideas is possible via an explicit, white-box approach. This paper describes the design principles of the package and gives some introductory examples on how to use the package in practise.

Evaluation of a Multi-Objective EA on Benchmark Instances for Dynamic Routing of a Vehicle

We evaluate the performance of a multi-objective evolutionary algorithm on a class of dynamic routing problems with a single vehicle. In particular we focus on relating algorithmic performance to the most prominent characteristics of problem instances. The routing problem considers two types of customers: mandatory customers must be visited whereas optional customers do not necessarily have to be visited. Moreover, mandatory customers are known prior to the start of the tour whereas optional customers request for service at later points in time with the vehicle already being on its way. The multi-objective optimization problem then results as maximizing the number of visited customers while simultaneously minimizing total travel time. As an a-posteriori evaluation tool, the evolutionary algorithm aims at approximating the related Pareto set for specifically designed benchmarking instances differing in terms of number of customers, geographical layout, fraction of mandatory customers, and request times of optional customers. Conceptional and experimental comparisons to online heuristic procedures are provided.

mcMST: A Toolbox for the Multi-Criteria Minimum Spanning Tree Problem

The single-objective minimum spanning tree (MST) problem is a combinatorial optimization problem known to be polynomial-time solvable, e.g., using the algorithm of Prim (Prim 1957). However, in real-world applications one is frequently confronted with multiple objectives which need to be minimized simultaneously. Since the objectives are usually conflicting, there is no single optimal solution to this problem. Instead the goal is the approximate the so-called Pareto-front, i.e., the set of nondominated solutions (see Deb (2001)).

Understanding Characteristics of Evolved Instances for State-of-the-Art Inexact TSP Solvers with Maximum Performance Difference

State of the Art inexact solvers of the NP-hard Traveling Salesperson Problem TSP are known to mostly yield high-quality solutions in reasonable computation times. With the purpose of understanding different levels of instance difficulties, instances for the current State of the Art heuristic TSP solvers LKH+restart and EAX+restart are presented which are evolved using a sophisticated evolutionary algorithm. More specifically, the performance differences of the respective solvers are maximized resulting in instances which are easier to solve for one solver and much more difficult for the other. Focusing on both optimization directions, instance features are identified which characterize both types of instances and increase the understanding of solver performance differences.

Local search effects in bi-objective orienteering

We analyze the effects of including local search techniques into a multi-objective evolutionary algorithm for solving a bi-objective orienteering problem with a single vehicle while the two conflicting objectives are minimization of travel time and maximization of the number of visited customer locations. Experiments are based on a large set of specifically designed problem instances with different characteristics and it is shown that local search techniques focusing on one of the objectives only improve the performance of the evolutionary algorithm in terms of both objectives. The analysis also shows that local search techniques are capable of sending locally optimal solutions to foremost fronts of the multi-objective optimization process, and that these solutions then become the leading factors of the evolutionary process.

Parameterization of state-of-the-art performance indicators: a robustness study based on inexact TSP solvers

Performance comparisons of optimization algorithms are heavily influenced by the underlying indicator(s). In this paper we investigate commonly used performance indicators for single-objective stochastic solvers, such as the Penalized Average Runtime (e.g., PAR10) or the Expected Running Time (ERT), based on exemplary benchmark performances of state-of-the-art inexact TSP solvers. Thereby, we introduce a methodology for analyzing the effects of (usually heuristically set) indicator parametrizations - such as the penalty factor and the method used for aggregating across multiple runs - w.r.t. the robustness of the considered optimization algorithms.

Performance assessment of multi-objective evolutionary algorithms with the R package ecr

Assessing the performance of stochastic optimization algorithms in the field of multi-objective optimization is of utmost importance. Besides the visual comparison of the obtained approximation sets, more sophisticated methods have been proposed in the last decade, e. g., a variety of quantitative performance indicators or statistical tests. In this paper, we present tools implemented in the R package ecr, which assist in performing comprehensive and sound comparison and evaluation of multi-objective evolutionary algorithms following recommendations from the literature.

Grundbegriffe und Komplexität

Das Kapitel verschafft zuerst einen nicht formalen Einstieg in die Begrifflichkeit der Optimierung und geht dann zur formalen Definition von Optimierungsproblemen uber. Die Abstraktion durch Formalitat verdeutlicht es an einigen beispielhaften Problemstellungen. Dabei spielen insbesondere auch Themen wie Modellbildung/Abstraktion, Losungsmethodik und Losungsverifikation als zentrale Schritte des Optimierungsprozesses eine Rolle. Das Kapitel umfasst zudem eine grundlegende Diskussion des Begriffes der Problemkomplexitat. Dazu wird sowohl in die Laufzeitanalyse wie auch in Aspekte der theoretischen Informatik eingefuhrt (Komplexitatsklassen P und NP).