Multi-Objective Archiving

Most multi-objective optimisation algorithms maintain an archive explicitly or implicitly during their search. Such an archive can be solely used to store high-quality solutions presented to the decision maker, but in many cases may participate in the search process (e.g., as the population in evolutionary computation). Over the last two decades, archiving, the process of comparing new solutions with previous ones and deciding how to update the archive/population, stands as an important issue in evolutionary multi-objective optimisation (EMO). This is evidenced by constant efforts from the community on developing various effective archiving methods, ranging from conventional Pareto-based methods to more recent indicator-based and decomposition-based ones. However, the focus of these efforts is on empirical performance comparison in terms of specific quality indicators; there is lack of systematic study of archiving methods from a general theoretical perspective. In this paper, we attempt to conduct a systematic overview of multi-objective archiving, in the hope of paving the way to understand archiving algorithms from a holistic perspective of theory and practice, and more importantly providing a guidance on how to design theoretically desirable and practically useful archiving algorithms. In doing so, we also present that archiving algorithms based on weakly Pareto compliant indicators (e.g., epsilon-indicator), as long as designed properly, can achieve the same theoretical desirables as archivers based on Pareto compliant indicators (e.g., hypervolume indicator). Such desirables include the property limit-optimal, the limit form of the possible optimal property that a bounded archiving algorithm can have with respect to the most general form of superiority between solution sets.Comment: 21 pages, 4 figures, journa

Elite Accumulative Sampling Strategies for Noisy Multi-Objective Optimisation

The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-15892-1_128th International Conference on Evolutionary Multi-Criterion Optimization 2015, Guimarães, Portugal, 29 March - 1 April 1 2015The codebase for this paper is available at https://github.com/fieldsend/EMO_2015_eliteWhen designing evolutionary algorithms one of the key concerns is the balance between expending function evaluations on exploration versus exploitation. When the optimisation problem experiences observational noise, there is also a trade-off with respect to accuracy refinement – as improving the estimate of a design’s performance typically is at the cost of additional function reevaluations. Empirically the most effective resampling approach developed so far is accumulative resampling of the elite set. In this approach elite members are regularly reevaluated, meaning they progressively accumulate reevaluations over time. This results in their approximated objective values having greater fidelity, meaning non-dominated solutions are more likely to be correctly identified. Here we examine four different approaches to accumulative resampling of elite members, embedded within a differential evolution algorithm. Comparing results on 40 variants of the unconstrained IEEE CEC’09 multi-objective test problems, we find that at low noise levels a low fixed resample rate is usually sufficient, however for larger noise magnitudes progressively raising the number of minimum resamples of elite members based on detecting estimated front oscillation tends to improve performance

Comparing and Combining Lexicase Selection and Novelty Search

Lexicase selection and novelty search, two parent selection methods used in evolutionary computation, emphasize exploring widely in the search space more than traditional methods such as tournament selection. However, lexicase selection is not explicitly driven to select for novelty in the population, and novelty search suffers from lack of direction toward a goal, especially in unconstrained, highly-dimensional spaces. We combine the strengths of lexicase selection and novelty search by creating a novelty score for each test case, and adding those novelty scores to the normal error values used in lexicase selection. We use this new novelty-lexicase selection to solve automatic program synthesis problems, and find it significantly outperforms both novelty search and lexicase selection. Additionally, we find that novelty search has very little success in the problem domain of program synthesis. We explore the effects of each of these methods on population diversity and long-term problem solving performance, and give evidence to support the hypothesis that novelty-lexicase selection resists converging to local optima better than lexicase selection

Natural Selection, Adaptive Evolution and Diversity in Computational Ecosystems

The central goal of this thesis is to provide additional criteria towards implementing open-ended evolution in an artificial system. Methods inspired by biological evolution are frequently applied to generate autonomous agents too complex to design by hand. Despite substantial progress in the area of evolutionary computation, additional efforts are needed to identify a coherent set of requirements for a system capable of exhibiting open-ended evolutionary dynamics. The thesis provides an extensive discussion of existing models and of the major considerations for designing a computational model of evolution by natural selection. Thus, the work in this thesis constitutes a further step towards determining the requirements for such a system and introduces a concrete implementation of an artificial evolution system to evaluate the developed suggestions. The proposed system improves upon existing models with respect to easy interpretability of agent behaviour, high structural freedom, and a low-level sensor and effector model to allow numerous long-term evolutionary gradients. In a series of experiments, the evolutionary dynamics of the system are examined against the set objectives and, where appropriate, compared with existing systems. Typical agent behaviours are introduced to convey a general overview of the system dynamics. These behaviours are related to properties of the respective agent populations and their evolved morphologies. It is shown that an intuitive classification of observed behaviours coincides with a more formal classification based on morphology. The evolutionary dynamics of the system are evaluated and shown to be unbounded according to the classification provided by Bedau and Packard’s measures of evolutionary activity. Further, it is analysed how observed behavioural complexity relates to the complexity of the agent-side mechanisms subserving these behaviours. It is shown that for the concrete definition of complexity applied, the average complexity continually increases for extended periods of evolutionary time. In combination, these two findings show how the observed behaviours are the result of an ongoing and lasting adaptive evolutionary process as opposed to being artifacts of the seeding process. Finally, the effect of variation in the system on the diversity of evolved behaviour is investigated. It is shown that coupling individual survival and reproductive success can restrict the available evolutionary trajectories in more than the trivial sense of removing another dimension, and conversely, decoupling individual survival from reproductive success can increase the number of evolutionary trajectories. The effect of different reproductive mechanisms is contrasted with that of variation in environmental conditions. The diversity of evolved strategies turns out to be sensitive to the reproductive mechanism while being remarkably robust to the variation of environmental conditions. These findings emphasize the importance of being explicit about the abstractions and assumptions underlying an artificial evolution system, particularly if the system is intended to model aspects of biological evolution

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

Developing Parsimonious and Efficient Algorithms for Water Resources Optimization Problems

In the current water resources scientific literature, a wide variety of engineering design problems are solved in a simulation-optimization framework. These problems can have single or multiple objective functions and their decision variables can have discrete or continuous values. The majority of current literature in the field of water resources systems optimization report using heuristic global optimization algorithms, including evolutionary algorithms, with great success. These algorithms have multiple parameters that control their behavior both in terms of computational efficiency and the ability to find near globally optimal solutions. Values of these parameters are generally obtained by trial and error and are case study dependent. On the other hand, water resources simulation-optimization problems often have computationally intensive simulation models that can require seconds to hours for a single simulation. Furthermore, analysts may have limited computational budget to solve these problems, as such, the analyst may not be able to spend some of the computational budget to fine-tune the algorithm settings and parameter values. So, in general, algorithm parsimony in the number of parameters is an important factor in the applicability and performance of optimization algorithms for solving computationally intensive problems. A major contribution of this thesis is the development of a highly efficient, single objective, parsimonious optimization algorithm for solving problems with discrete decision variables. The algorithm is called Hybrid Discrete Dynamically Dimensioned Search, HD-DDS, and is designed based on Dynamically Dimensioned Search (DDS) that was developed by Tolson and Shoemaker (2007) for solving single objective hydrologic model calibration problems with continuous decision variables. The motivation for developing HD-DDS comes from the parsimony and high performance of original version of DDS. Similar to DDS, HD-DDS has a single parameter with a robust default value. HD-DDS is successfully applied to several benchmark water distribution system design problems where decision variables are pipe sizes among the available pipe size options. Results show that HD-DDS exhibits superior performance in specific comparisons to state-of-the-art optimization algorithms. The parsimony and efficiency of the original and discrete versions of DDS and their successful application to single objective water resources optimization problems with discrete and continuous decision variables motivated the development of a multi-objective optimization algorithm based on DDS. This algorithm is called Pareto Archived Dynamically Dimensioned Search (PA-DDS). The algorithm parsimony is a major factor in the design of PA-DDS. PA-DDS has a single parameter from its search engine DDS. In each iteration, PA-DDS selects one archived non-dominated solution and perturbs it to search for new solutions. The solution perturbation scheme of PA-DDS is similar to the original and discrete versions of DDS depending on whether the decision variable is discrete or continuous. So, PA-DDS can handle both types of decision variables. PA-DDS is applied to several benchmark mathematical problems, water distribution system design problems, and water resources model calibration problems with great success. It is shown that hypervolume contribution, HVC1, as defined in Knowles et al. (2003) is the superior selection metric for PA-DDS when solving multi-objective optimization problems with Pareto fronts that have a general (unknown) shape. However, one of the main contributions of this thesis is the development of a selection metric specifically designed for solving multi-objective optimization problems with a known or expected convex Pareto front such as water resources model calibration problems. The selection metric is called convex hull contribution (CHC) and makes the optimization algorithm sample solely from a subset of archived solutions that form the convex approximation of the Pareto front. Although CHC is generally applicable to any stochastic search optimization algorithm, it is applied to PA-DDS for solving six water resources calibration case studies with two or three objective functions. These case studies are solved by PA-DDS with CHC and HVC1 selections using 1,000 solution evaluations and by PA-DDS with CHC selection and two popular multi-objective optimization algorithms, AMALGAM and ε-NSGAII, using 10,000 solution evaluations. Results are compared based on the best case and worst case performances (out of multiple optimization trials) from each algorithm to measure the expected performance range for each algorithm. Comparing the best case performance of these algorithms shows that, PA-DDS with CHC selection using 1,000 solution evaluations perform very well in five out of six case studies. Comparing the worst case performance of the algorithms shows that with 1,000 solution evaluations, PA-DDS with CHC selection perform well in four out of six case studies. Furthermore, PA-DDS with CHC selection using 10,000 solution evaluations perform comparable to AMALGAM and ε-NSGAII. Therefore, it is concluded that PA-DDS with CHC selection is a powerful optimization algorithm for finding high quality solutions of multi-objective water resources model calibration problems with convex Pareto front especially when the computational budget is limited

A Unified Model for Evolutionary Multiobjective Optimization and its Implementation in a General Purpose Software Framework: ParadisEO-MOEO

This paper gives a concise overview of evolutionary algorithms for multiobjective optimization. A substantial number of evolutionary computation methods for multiobjective problem solving has been proposed so far, and an attempt of unifying existing approaches is here presented. Based on a fine-grained decomposition and following the main issues of fitness assignment, diversity preservation and elitism, a conceptual global model is proposed and is validated by regarding a number of state-of-the-art algorithms as simple variants of the same structure. The presented model is then incorporated into a general-purpose software framework dedicated to the design and the implementation of evolutionary multiobjective optimization techniques: ParadisEO-MOEO. This package has proven its validity and flexibility by enabling the resolution of many real-world and hard multiobjective optimization problems

A quantum behaved particle swarm approach to multi-objective optimization

Many real-world optimization problems have multiple objectives that have to be optimized simultaneously. Although a great deal of effort has been devoted to solve multi-objective optimization problems, the problem is still open and the related issues still attract significant research efforts. Quantum-behaved Particle Swarm Optimization (QPSO) is a recently proposed population based metaheuristic that relies on quantum mechanics principles. Since its inception, much effort has been devoted to develop improved versions of QPSO designed for single objective optimization. However, many of its advantages are not yet available for multi-objective optimization. In this thesis, we develop a new framework for multi-objective problems using QPSO. The contribution of the work is threefold. First a hybrid leader selection method has been developed to compute the attractor of a given particle. Second, an archiving strategy has been proposed to control the growth of the archive size. Third, the developed framework has been further extended to handle constrained optimization problems. A comprehensive investigation of the developed framework has been carried out under different selection, archiving and constraint handling strategies. The developed framework is found to be a competitive technique to tackle this type of problems when compared against the state-of-the-art methods in multi-objective optimization

Open-ended Search through Minimal Criterion Coevolution

Search processes guided by objectives are ubiquitous in machine learning. They iteratively reward artifacts based on their proximity to an optimization target, and terminate upon solution space convergence. Some recent studies take a different approach, capitalizing on the disconnect between mainstream methods in artificial intelligence and the field\u27s biological inspirations. Natural evolution has an unparalleled propensity for generating well-adapted artifacts, but these artifacts are decidedly non-convergent. This new class of non-objective algorithms induce a divergent search by rewarding solutions according to their novelty with respect to prior discoveries. While the diversity of resulting innovations exhibit marked parallels to natural evolution, the methods by which search is driven remain unnatural. In particular, nature has no need to characterize and enforce novelty; rather, it is guided by a single, simple constraint: survive long enough to reproduce. The key insight is that such a constraint, called the minimal criterion, can be harnessed in a coevolutionary context where two populations interact, finding novel ways to satisfy their reproductive constraint with respect to each other. Among the contributions of this dissertation, this approach, called minimal criterion coevolution (MCC), is the primary (1). MCC is initially demonstrated in a maze domain (2) where it evolves increasingly complex mazes and solutions. An enhancement to the initial domain (3) is then introduced, allowing mazes to expand unboundedly and validating MCC\u27s propensity for open-ended discovery. A more natural method of diversity preservation through resource limitation (4) is introduced and shown to maintain population diversity without comparing genetic distance. Finally, MCC is demonstrated in an evolutionary robotics domain (5) where it coevolves increasingly complex bodies with brain controllers to achieve principled locomotion. The overall benefit of these contributions is a novel, general, algorithmic framework for the continual production of open-ended dynamics without the need for a characterization of behavioral novelty