Samadhi Nallaperuma

A feature-based comparison of local search and the christofides algorithm for the travelling salesperson problem

Understanding the behaviour of well-known algorithms for classical NP-hard optimisation problems is still a difficult task. With this paper, we contribute to this research direction and carry out a feature based comparison of local search and the well-known Christofides approximation algorithm for the Traveling Salesperson Problem. We use an evolutionary algorithm approach to construct easy and hard instances for the Christofides algorithm, where we measure hardness in terms of approximation ratio. Our results point out important features and lead to hard and easy instances for this famous algorithm. Furthermore, our cross-comparison gives new insights on the complementary benefits of the different approaches.

A case study of algorithm selection for the traveling thief problem

Many real-world problems are composed of several interacting components. In order to facilitate research on such interactions, the Traveling Thief Problem (TTP) was created in 2013 as the combination of two well-understood combinatorial optimization problems. With this article, we contribute in four ways. First, we create a comprehensive dataset that comprises the performance data of 21 TTP algorithms on the full original set of 9720 TTP instances. Second, we define 55 characteristics for all TPP instances that can be used to select the best algorithm on a per-instance basis. Third, we use these algorithms and features to construct the first algorithm portfolios for TTP, clearly outperforming the single best algorithm. Finally, we study which algorithms contribute most to this portfolio.

Parameterized runtime analyses of evolutionary algorithms for the planar euclidean traveling salesperson problem

Parameterized runtime analysis seeks to understand the influence of problem structure on algorithmic runtime. In this paper, we contribute to the theoretical understanding of evolutionary algorithms and carry out a parameterized analysis of evolutionary algorithms for the Euclidean traveling salesperson problem (Euclidean TSP). We investigate the structural properties in TSP instances that influence the optimization process of evolutionary algorithms and use this information to bound their runtime. We analyze the runtime in dependence of the number of inner points k. In the first part of the paper, we study a EA in a strictly black box setting and show that it can solve the Euclidean TSP in expected time where A is a function of the minimum angle between any three points. Based on insights provided by the analysis, we improve this upper bound by introducing a mixed mutation strategy that incorporates both 2-opt moves and permutation jumps. This strategy improves the upper bound to . In the second part of the paper, we use the information gained in the analysis to incorporate domain knowledge to design two fixed-parameter tractable (FPT) evolutionary algorithms for the planar Euclidean TSP. We first develop a EA based on an analysis by M. Theile, 2009, ”Exact solutions to the traveling salesperson problem by a population-based evolutionary algorithm,” Lecture notes in computer science, Vol. 5482 (pp. 145–155), that solves the TSP with k inner points in generations with probability . We then design a EA that incorporates a dynamic programming step into the fitness evaluation. We prove that a variant of this evolutionary algorithm using 2-opt mutation solves the problem after steps in expectation with a cost of for each fitness evaluation.

Analyzing the Effects of Instance Features and Algorithm Parameters for Max–Min Ant System and the Traveling Salesperson Problem

Ant colony optimization (ACO) performs very well on many hard optimization problems, even though no good worst case guarantee can be given. Understanding the effects of different ACO parameters and the structural features of the considered problem on algorithm performance has become an interesting problem. In this paper, we study structural features of easy and hard instances of the Traveling Salesperson problem for a well-known ACO variant called Max Min Ant System MMAS) for several parameter settings. The four considered parameters are the importance of pheromone values, the heuristic information, the pheromone update strength and the number of ants. We further use this knowledge to predict the best parameter setting for a wide range of instances taken from TSPLIB.

Parameter Prediction Based on Features of Evolved Instances for Ant Colony Optimization and the Traveling Salesperson Problem

Ant colony optimization performs very well on many hard optimization problems, even though no good worst case guarantee can be given. Understanding the reasons for the performance and the influence of its different parameter settings has become an interesting problem. In this paper, we build a parameter prediction model for the Traveling Salesperson problem based on features of evolved instances. The two considered parameters are the importance of the pheromone values and of the heuristic information. Based on the features of the evolved instances, we successfully predict the best parameter setting for a wide range of instances taken from TSPLIB.

A fixed budget analysis of randomized search heuristics for the traveling salesperson problem

Randomized Search heuristics are frequently applied to NP-hard combinatorial optimization problems. The runtime analysis of randomized search heuristics has contributed tremendously to their theoretical understanding. Recently, randomized search heuristics have been examined regarding their achievable progress within a fixed time budget. We follow this approach and present a first fixed budget runtime analysis for a NP-hard combinatorial optimization problem. We consider the well-known Traveling Salesperson problem (TSP) and analyze the fitness increase that randomized search heuristics are able to achieve within a given fixed budget.

Fixed-parameter evolutionary algorithms for the Euclidean Traveling Salesperson problem

Recently, Sutton and Neumann [1] have studied evolutionary algorithms for the Euclidean traveling salesman problem by parameterized runtime analyses taking into account the number of inner points k and the number of cities n. They have shown that simple evolutionary algorithms are XP-algorithms for the problem, i.e., they obtain an optimal solution in expected time O(ng(k)) where g(k) is a function only depending on k. We extend these investigations and design two evolutionary algorithms for the Euclidean Traveling Salesperson problem that run in expected time g(k) · poly(n) where k is a parameter denoting the number inner points for the given TSP instance, i.e., they are fixed-parameter tractable evolutionary algorithms for the Euclidean TSP parameterized by the number of inner points. While our first approach is mainly of theoretical interest, our second approach leverages problem structure by directly searching for good orderings of the inner points and provides a novel and highly effective way of tackling this important problem. Our experimental results show that searching for a permutation on the inner points is a significantly powerful practical strategy.

EVOR: an online evolutionary algorithm for car racing games

In this paper, we present evolutionary racer (EVOR) a simulated car dynamically controlled by an online evolutionary algorithm (EA). The key distinction between EVOR and earlier car racing methods is that it considers car racing as a dynamic optimization problem and is addressed by an evolutionary algorithm. Our approach calculates a car trajectory based on a controller decision and adjusts this decision according to the suitability of its resultant trajectory with the current track status. Furthermore, it allows to integrate features such as opponent handling implicitly. Our experimental results show that EVOR outperforms current best AI controllers on a wide range of tracks.

Ant colony optimisation and the traveling salesperson problem: hardness, features and parameter settings

Our study on ant colony optimization (ACO) and the Travelling Salesperson Problem (TSP) attempts to understand the effect of parameters and instance features on performance using statistical analysis of the hard, easy and average problem instances for an algorithm instance.

Feature-Based Diversity Optimization for Problem Instance Classification

Understanding the behaviour of heuristic search methods is a challenge. This even holds for simple local search methods such as 2-OPT for the Traveling Salesperson problem. In this paper, we present a general framework that is able to construct a diverse set of instances that are hard or easy for a given search heuristic. Such a diverse set is obtained by using an evolutionary algorithm for constructing hard or easy instances that are diverse with respect to different features of the underlying problem. Examining the constructed instance sets, we show that many combinations of two or three features give a good classification of the TSP instances in terms of whether they are hard to be solved by 2-OPT.