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.Comment: 20 pages, 18 figure

Evolutionary diversity optimization using multi-objective indicators

Evolutionary diversity optimization aims to compute a set of solutions that are diverse in the search space or instance feature space, and where all solutions meet a given quality criterion. With this paper, we bridge the areas of evolutionary diversity optimization and evolutionary multi-objective optimization. We show how popular indicators frequently used in the area of multi-objective optimization can be used for evolutionary diversity optimization. Our experimental investigations for evolving diverse sets of TSP instances and images according to various features show that two of the most prominent multi-objective indicators, namely the hypervolume indicator and the inverted generational distance, provide excellent results in terms of visualization and various diversity indicators.Aneta Neumann, Wanru Gao, Markus Wagner, Frank Neuman

On the Analysis of Trajectory-Based Search Algorithms: When is it Beneficial to Reject Improvements?

We investigate popular trajectory-based algorithms inspired by biology and physics to answer a question of general significance: when is it beneficial to reject improvements? A distinguishing factor of SSWM (strong selection weak mutation), a popular model from population genetics, compared to the Metropolis algorithm (MA), is that the former can reject improvements, while the latter always accepts them. We investigate when one strategy outperforms the other. Since we prove that both algorithms converge to the same stationary distribution, we concentrate on identifying a class of functions inducing large mixing times, where the algorithms will outperform each other over a long period of time. The outcome of the analysis is the definition of a function where SSWM is efficient, while Metropolis requires at least exponential time. The identified function favours algorithms that prefer high quality improvements over smaller ones, revealing similarities in the optimisation strategies of SSWM and Metropolis respectively with best-improvement (BILS) and first-improvement (FILS) local search. We conclude the paper with a comparison of the performance of these algorithms and a (1, λ ) RLS on the identified function. The algorithm favours the steepest gradient with a probability that increases with the size of its offspring population. The results confirm that BILS excels and that the (1, λ ) RLS is efficient only for large enough population sizes

Parameterized analysis of bio-inspired computation and the traveling salesperson problem.

Bio-inspired algorithms such as evolutionary algorithms (EA) and ant colony optimization (ACO) have become very popular in recent years to solve a wide range of complex real world problems. However, the understanding about the conditions under which these algorithms perform well is still limited. Classical computational complexity analysis often taking a worst case perspective, hardly captures what is happening during the actual algorithm run and, lacks implications for guiding algorithm design. This issue is more significant on the problems such as the traveling salesperson problem (TSP) where the problem is hard in a theoretical sense and has a lot of real world applications. Thus, more practical perspectives of algorithm analysis and design are essential to bridge the gap between the theory and the practice in bio-inspired computation specially with respect to the hard problems such as the TSP. We introduce “parameterized analysis” of bio-inspired computation by linking together several emerging methods of algorithm analysis and design with the aim of explaining the relationship between various problem and algorithm parameters and their effects on the algorithm performance. Moreover, we gain novel insights into bio-inspired computation and the TSP through parameterized analysis.Thesis (Ph.D.) -- University of Adelaide, School of Computer Science, 201

Interpreting Multi-Objective Reinforcement Learning for Routing and Wavelength Assignment in Optical Networks

Performance optimization literature in optical networks predominantly consists of single objective optimization studies while often in practice multiple performance goals are to be met. This study addresses this issue with a generalized reinforcement learning (RL) model for parameter optimization in optical networks in the presence of multiple performance goals. Using this generic model, two multi-objective variants of a classical optimization problem in optical network operation, routing and wavelength assignment (RWA) are derived and solved to near optimality. The allocated route and wavelength for each demand are optimized with respect to the number of accepted services, the number of transmitters and network availability. The resultant approximated Pareto front provides a set of solutions from which network operators can make decisions based on their preferences for particular objectives. These results contribute to the understanding into the relationships between different network parameters and performance metrics which would be beneficial in future network design and growth. Moreover, benchmarking results against the state-of-the-art RWA heuristics suggest the applicability of RL in dynamic settings under changing traffic and generalizability for unseen traffic

Training and evaluation data for routing and wavelength assignment using multi objective reinforcement learning

This dataset contains training and evaluation data generated from multi objective RL models for bi objective and 3 objective cases and the trained models. The training_monitor.csv provides the details for the training data in terms of the rewards and accepted and processed services where each row corresponds to an episode. The evaluation_monitor.csv contains the respective evaluation data including the rewards, processed and accepted numbr of services for each episode represented by a row. The trained models are saved as best_model.zip which can be used to reproduce evaluation results.EPSRC TRANSNET project (EP/R035342/1

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 [Formula: see text] EA in a strictly black box setting and show that it can solve the Euclidean TSP in expected time [Formula: see text] where A is a function of the minimum angle [Formula: see text] 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 [Formula: see text]. 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 [Formula: see text] 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 [Formula: see text] generations with probability [Formula: see text]. We then design a [Formula: see text] 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 [Formula: see text] steps in expectation with a cost of [Formula: see text] for each fitness evaluation.Andrew M. Sutton, Frank Neumann, Samadhi Nallaperumahttp://www.aaai.org/Conferences/AAAI/aaai12.ph