Preliminary Investigation of the `Learnable Evolution Model' for Faster/Better Multiobjective Water Systems Design

The design of large scale water distribution systems is a very difficult optimisation problem which invariably requires the use of time-expensive simulations within the fitness function. The need to accelerate optimisation for such problems has not so far been seriously tackled. However, this is a very important issue, since as MOEAs become more and more recognised as the lsquoindustry standardrsquo technique for water system design, the demands placed on such systems (larger and larger water networks) will quickly meet with problems of scaleup. Meanwhile, LEM (Learnable Evolution Modelrsquo) has appeared in the Machine Learning literature, and provides a general approach to integrating machine learning into evolutionary search. Published results using LEM show very great promise in terms of finding near-optimal solutions with significantly reduced numbers of evaluations. Here we introduce LEMMO (Learnable Evolution Model for Multi-Objective optimization), which is a multi-objective adaptation of LEM, and we apply it to certain problems commonly used as benchmarks in the water systems community. Compared with NSGA-II, we find that LEMMO both significantly improves performance, and significantly reduces the number of evaluations needed to reach a given target. We conclude that the general approach used in LEMMO is a promising direction for meeting the scale-up challenges in multiobjective water system design

Hybridizing Non-dominated Sorting Algorithms: Divide-and-Conquer Meets Best Order Sort

Many production-grade algorithms benefit from combining an asymptotically efficient algorithm for solving big problem instances, by splitting them into smaller ones, and an asymptotically inefficient algorithm with a very small implementation constant for solving small subproblems. A well-known example is stable sorting, where mergesort is often combined with insertion sort to achieve a constant but noticeable speed-up. We apply this idea to non-dominated sorting. Namely, we combine the divide-and-conquer algorithm, which has the currently best known asymptotic runtime of $O(N (\log N)^{M - 1})$, with the Best Order Sort algorithm, which has the runtime of $O(N^2 M)$ but demonstrates the best practical performance out of quadratic algorithms. Empirical evaluation shows that the hybrid's running time is typically not worse than of both original algorithms, while for large numbers of points it outperforms them by at least 20%. For smaller numbers of objectives, the speedup can be as large as four times.Comment: A two-page abstract of this paper will appear in the proceedings companion of the 2017 Genetic and Evolutionary Computation Conference (GECCO 2017

Introducing Complexity Curtailing Techniques for the Tour Construction Heuristics for the Travelling Salesperson Problem

In this paper, complexity curtailing techniques are introduced to create faster version of insertion heuristics, that is, cheapest insertion heuristic (CIH) and largest insertion heuristic (LIH), effectively reducing their complexities from O(n3) to O(n2) with no significant effect on quality of solution. This paper also examines relatively not very known heuristic concept of max difference and shows that it can be culminated into a full-fledged max difference insertion heuristic (MDIH) by defining its missing steps. Further to this the paper extends the complexity curtailing techniques to MDIH to create its faster version. The resultant heuristic, that is, fast max difference insertion heuristic (FMDIH), outperforms the “farthest insertion” heuristic (FIH) across a wide spectrum of popular datasets with statistical significance, even though both the heuristics have the same worst case complexity of O(n2). It should be noted that FIH is considered best among lowest order complexity heuristics. The complexity curtailing techniques presented here open up the new area of research for their possible extension to other heuristics

Evolutionary Algorithms

Evolutionary algorithms (EAs) are population-based metaheuristics, originally inspired by aspects of natural evolution. Modern varieties incorporate a broad mixture of search mechanisms, and tend to blend inspiration from nature with pragmatic engineering concerns; however, all EAs essentially operate by maintaining a population of potential solutions and in some way artificially 'evolving' that population over time. Particularly well-known categories of EAs include genetic algorithms (GAs), Genetic Programming (GP), and Evolution Strategies (ES). EAs have proven very successful in practical applications, particularly those requiring solutions to combinatorial problems. EAs are highly flexible and can be configured to address any optimization task, without the requirements for reformulation and/or simplification that would be needed for other techniques. However, this flexibility goes hand in hand with a cost: the tailoring of an EA's configuration and parameters, so as to provide robust performance for a given class of tasks, is often a complex and time-consuming process. This tailoring process is one of the many ongoing research areas associated with EAs.Comment: To appear in R. Marti, P. Pardalos, and M. Resende, eds., Handbook of Heuristics, Springe

Sensitivity of marine protected area network connectivity to atmospheric variability

International efforts are underway to establish well-connected systems of marine protected areas (MPAs) covering at least 10% of the ocean by 2020. But the nature and dynamics of ocean ecosystem connectivity are poorly understood, with unresolved effects of climate variability. We used 40-year runs of a particle tracking model to examine the sensitivity of an MPA network for habitat-forming cold-water corals in the northeast Atlantic to changes in larval dispersal driven by atmospheric cycles and larval behaviour. Trajectories of Lophelia pertusa larvae were strongly correlated to the North Atlantic Oscillation (NAO), the dominant pattern of interannual atmospheric circulation variability over the northeast Atlantic. Variability in trajectories significantly altered network connectivity and source–sink dynamics, with positive phase NAO conditions producing a well-connected but asymmetrical network connected from west to east. Negative phase NAO produced reduced connectivity, but notably some larvae tracked westward-flowing currents towards coral populations on the mid-Atlantic ridge. Graph theoretical metrics demonstrate critical roles played by seamounts and offshore banks in larval supply and maintaining connectivity across the network. Larval longevity and behaviour mediated dispersal and connectivity, with shorter lived and passive larvae associated with reduced connectivity. We conclude that the existing MPA network is vulnerable to atmospheric-driven changes in ocean circulation

An efficient multi-objective optimisation method for use in the design of marine protected area networks

An efficient connectivity-based method for multi-objective optimization applicable to the design of marine protected area networks is described. Multi-objective network optimization highlighted previously unreported step changes in the structure of optimal subnetworks for protection associated with minimal changes in cost or benefit functions. This emphasizes the desirability of performing a full, unconstrained, multi-objective optimization for marine spatial planning. Brute force methods, examining all possible combinations of protected and unprotected sites for a network of sites, are impractical for all but the smallest networks as the number of possible networks grows as 2m, where m is the number of sites within the network. A metaheuristic method based around Markov Chain Monte Carlo methods is described which searches for the set of Pareto optimal networks (or a good approximation thereto) given two separate objective functions, for example for network quality or effectiveness, population persistence, or cost of protection. The optimization and search methods are independent of the choice of objective functions and can be easily extended to more than two functions. The speed, accuracy and convergence of the method under a range of network configurations are tested with model networks based on an extension of random geometric graphs. Examination of two real-world marine networks, one designated for the protection of the stony coral Lophelia pertusa, the other a hypothetical man-made network of oil and gas installations to protect hard substrate ecosystems, demonstrates the power of the method in finding multi-objective optimal solutions for networks of up to 100 sites. Results using network average shortest path as a proxy for population resilience and gene flow within the network supports the use of a conservation strategy based around highly connected clusters of sites

Structural bias in population-based algorithms

Challenging optimisation problems are abundant in all areas of science and industry. Since the 1950s, scientists have responded to this by developing ever-diversifying families of 'black box' optimisation algorithms. The latter are designed to be able to address any optimisation problem, requiring only that the quality of any candidate solution can be calculated via a 'fitness function' specific to the problem. For such algorithms to be successful, at least three properties are required: (i) an effective informed sampling strategy, that guides the generation of new candidates on the basis of the fitnesses and locations of previously visited candidates; (ii) mechanisms to ensure efficiency, so that (for example) the same candidates are not repeatedly visited; and (iii) the absence of structural bias, which, if present, would predispose the algorithm towards limiting its search to specific regions of the solution space. The first two of these properties have been extensively investigated, however the third is little understood and rarely explored. In this article we provide theoretical and empirical analyses that contribute to the understanding of structural bias. In particular, we state and prove a theorem concerning the dynamics of population variance in the case of real-valued search spaces and a 'flat' fitness landscape. This reveals how structural bias can arise and manifest as non-uniform clustering of the population over time. Critically, theory predicts that structural bias is exacerbated with (independently) increasing population size, and increasing problem difficulty. These predictions, supported by our empirical analyses, reveal two previously unrecognised aspects of structural bias that would seem vital for algorithm designers and practitioners. Respectively, (i) increasing the population size, though ostensibly promoting diversity, will magnify any inherent structural bias, and (ii) the effects of structural bias are more apparent when faced with (many classes of) 'difficult' problems. Our theoretical result also contributes to the 'exploitation/exploration' conundrum in optimisation algorithm design, by suggesting that two commonly used approaches to enhancing exploration - increasing the population size, and increasing the disruptiveness of search operators - have quite distinct implications in terms of structural bias