A Provably Asymptotically Fast Version of the Generalized Jensen Algorithm for Non-dominated Sorting

Proceedings of the 2016 on Genetic and Evolutionary Computation Conference Companion

Stankevich

2016

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Many evolutionary multi-objective algorithms rely heavily on non-dominated sorting, the procedure of assigning ranks to individuals according to Pareto domination relation. The steady-state versions of these algorithms need efficient implementations of incremental non-dominated sorting, an algorithm or data structure which supports efficient addition of a new individual and deletion of the worst individual. Recent research brought new advanced algorithms, but none of them can be cheaply adapted to sublinear location of the point having the smallest crowding distance, a measure used in the NSGA-II algorithm. In this paper we address this issue by reducing it to a series of extreme point queries to certain convex polygons. We present theoretical estimation of the worst-case running time, as well as experimental results which show that the proposed modifications reduce the running time significantly on benchmark problems for large population sizes.

Section: Gecco'16 Companionmentioning

confidence: 99%

Efficient Removal of Points with Smallest Crowding Distance in Two-dimensional Incremental Non-dominated Sorting

Nigmatullin

Proceedings of the 2016 on Genetic and Evolutionary Computation Conference Companion

Stankevich

2016

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“…The existence of only two ranks, 0 or 1, may improve the performance of non-dominated sorting: for instance, the algorithm from [2,9], which normally runs in O(n · (log n) k−1 ), speeds up to O(n · (log n) k−2 ), because the O(n log n) algorithms that form its baseline for the divide-and-conquer degenerate to O(n) in the presence of two ranks. Together with the fact that points from L +1 can never dominate points from M , this also enables calling directly the internal procedure of this algorithm, which assigns ranks to inferior points given that superior points are fully evaluated (this procedure is often called HelperB following the notation of the paper which introduced the methodology [9]).…”

Section: Incremental Non-dominated Sortingmentioning

confidence: 99%

On asynchronous non-dominated sorting for steady-state multiobjective evolutionary algorithms

Yakupov

Proceedings of the Genetic and Evolutionary Computation Conference Companion

2018

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In parallel and distributed environments, generational evolutionary algorithms often do not exploit the full potential of the computation system since they have to wait until the entire population is evaluated before starting selection procedures. Steady-state algorithms are often seen as a solution to this problem, since fitness evaluation can be done by multiple threads in an asynchronous way. However, if the algorithm updates its state in a complicated way, the threads will eventually have to wait until this update finishes. State update procedures that are computationally expensive are common in multiobjective evolutionary algorithms.We have implemented an asynchronous steady-state version of the NSGA-II algorithm. Its most expensive part, non-dominated sorting, determines the time needed to update the state. We turned the existing incremental non-dominated sorting algorithm into an asynchronous one using several concurrency techniques: a single entry-level lock, finer-grained locks working with non-domination levels, and a non-blocking approach using compare-and-set operations. Our experimental results reveal the trade-off between the work-efficiency of the algorithm and the achieved amount of parallelism.

“…The corrected (or, as in [7], "generalized") algorithm works in all cases, and for the general case the performance is still O(N log K−1 N ), but the only upper bound that was proven for the worst case is O(N 2 K). Finally, Buzdalov et al in [2] proposed several modifications to the algorithm of Fortin et al to make the O(N log K−1 N ) bound provable as well.…”

Section: Introductionmentioning

confidence: 97%

“…However, running times become very high: O(KN 2 ) for a single insertion when the fast non-dominated sorting [5] is used, or O(N log K−1 N ) when the sorting from [2] is used. Thus, it is needed to develop new algorithms and data structures to handle incremental non-dominated sorting efficiently.…”

Section: Introductionmentioning

confidence: 98%

Fast Implementation of the Steady-State NSGA-II Algorithm for Two Dimensions Based on Incremental Non-Dominated Sorting

Proceedings of the 2015 Annual Conference on Genetic and Evolutionary Computation

Yakupov

Stankevich

2015

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Genetic algorithms (GAs) are widely used in multi-objective optimization for solving complex problems. There are two distinct approaches for GA design: generational and steadystate algorithms. Most of the current state-of-the-art GAs are generational, although there is an increasing interest to steady-state algorithms as well. However, for algorithms based on non-dominated sorting, most of steady-state implementations have higher computation complexity than their generational counterparts, which limits their applicability.We present a fast implementation of a steady-state version of the NSGA-II algorithm for two dimensions. This implementation is based on a data structure which has O(N ) complexity for single solution insertion and deletion in the worst case. The experimental results show that our implementation works noticeably faster than steady-state NSGA-II implementations which use fast non-dominated sorting.