ND-Tree-based update: a Fast Algorithm for the Dynamic Non-Dominance Problem

In this paper we propose a new method called ND-Tree-based update (or shortly ND-Tree) for the dynamic non-dominance problem, i.e. the problem of online update of a Pareto archive composed of mutually non-dominated points. It uses a new ND-Tree data structure in which each node represents a subset of points contained in a hyperrectangle defined by its local approximate ideal and nadir points. By building subsets containing points located close in the objective space and using basic properties of the local ideal and nadir points we can efficiently avoid searching many branches in the tree. ND-Tree may be used in multiobjective evolutionary algorithms and other multiobjective metaheuristics to update an archive of potentially non-dominated points. We prove that the proposed algorithm has sub-linear time complexity under mild assumptions. We experimentally compare ND-Tree to the simple list, Quad-tree, and M-Front methods using artificial and realistic benchmarks with up to 10 objectives and show that with this new method substantial reduction of the number of point comparisons and computational time can be obtained. Furthermore, we apply the method to the non-dominated sorting problem showing that it is highly competitive to some recently proposed algorithms dedicated to this problem.Comment: 15 pages, 21 figures, 3 table

Efficiently identifying pareto solutions when objective values change

Copyright © 2014 ACMThe example code for this paper is available at https://github.com/fieldsend/gecco_2014_changing_objectivesIn many multi-objective problems the objective values assigned to a particular design can change during the course of an optimisation. This may be due to dynamic changes in the problem itself, or updates to estimated objectives in noisy problems. In these situations, designs which are non-dominated at one time step may become dominated later not just because a new and better solution has been found, but because the existing solution's performance has degraded. Likewise, a dominated solution may later be identified as non-dominated because its objectives have comparatively improved. We propose management algorithms based on recording single “guardian dominators" for each solution which allow rapid discovery and updating of the non-dominated subset of solutions evaluated by an optimiser. We examine the computational complexity of our proposed approach, and compare the performance of different ways of selecting the guardian dominators

Strength through diversity: Disaggregation and multi-objectivisation approaches for genetic programming

The codebase for this paper is available at https://github.com/fieldsend/gecco_2015_mogpAn underlying problem in genetic programming (GP) is how to ensure sufficient useful diversity in the population during search. Having a wide range of diverse (sub)component structures available for recombination and/or mutation is important in preventing premature converge. We propose two new fitness disaggregation approaches that make explicit use of the information in the test cases (i.e., program semantics) to preserve diversity in the population. The first method preserves the best programs which pass each individual test case, the second preserves those which are non-dominated across test cases (multi-objectivisation). We use these in standard GP, and compare them to using standard fitness sharing, and using standard (aggregate) fitness in tournament selection. We also examine the effect of including a simple anti-bloat criterion in the selection mechanism.We find that the non-domination approach, employing anti-bloat, significantly speeds up convergence to the optimum on a range of standard Boolean test problems. Furthermore, its best performance occurs with a considerably smaller population size than typically employed in GP

Data structures for non-dominated sets: implementations and empirical assessment of two decades of advances

This is the author accepted manuscript. The final version is available from ACM via the DOI in this recordGenetic and Evolutionary Computation Conference (GECCO ’20), 8-12 July 2020, Cancún, MexicoMany data structures have been developed over the last two decades for the storage and efficient update of unconstrained sets of mutually non-dominating solutions. Typically, analysis has been provided in the original works for these data structures in terms of worst/average case complexity performance. Often, however, other aspects such as rebalancing costs of underlying data structures, cache sizes, etc., can also significantly affect behaviour. Empirical performance comparison has often (but not always) been limited to run-time comparison with a basic linear list. No comprehensive comparison between the different specialised data structures proposed in the last two decades has thus far been undertaken. We take significant strides in addressing this here. Eight data structures from the literature are implemented within the same overarching open source Java framework. We additionally highlight and rectify some errors in published work --- and offer additional efficiency gains. Run-time performances are compared and contrasted, using data sequences embodying a number of different characteristics. We show that in different scenarios different data structures are preferable, and that those with the lowest big O complexity are not always the best performing. We also find that performance profiles can vary drastically with computational architecture, in a non-linear fashion.Engineering and Physical Sciences Research Council (EPSRC)Innovate U

Graph-based solution batch management for Multi-Objective Evolutionary Algorithms

In Alberto and Mateo [2], 2004, a graph-based structure used for manipulating populations of Multi-Objective Evolutionary Algorithms in a more efficient way than the structures existing at that point was defined. In this paper, an improvement of such tool is presented. It consists of the simultaneous insertion of a set of solutions (solution batch), instead of a single one, into the created graph structure. Furthermore, two experiments devoted to comparing the behavior of the new algorithms with the original version from Alberto and Mateo [2] and with a well-known non-dominated sorting algorithm are carried out. The first shows how the new version outperforms the original one in time and number of Pareto comparisons. The second experiment shows a reduction in the time needed in all the cases and an important reduction in the number of Pareto comparisons when inserting chains of dominated solutions. From these experiments it is verified that, in general, the new proposals save computational time and, in the majority of the cases, the number of Pareto comparisons carried out for the insertion. In addition, when the new proposals outperform the others, they increase their gain over them as the size of the population and/or the size of the batch increases. The new tool can also be used, for example, in parallel genetic algorithms such as the ones based on islands, to carry out the migrations of the solutions