Distributed Pareto Optimization for Subset Selection

Abstract

The subset selection problem that selects a few items from a ground set arises in many applications such as maximum coverage, influence maximization, sparse regression, etc. The recently proposed POSS algorithm is a powerful approximation solver for this problem. However, POSS requires centralized access to the full ground set, and thus is impractical for large-scale real-world applications, where the ground set is too large to be stored on one single machine. In this paper, we propose a distributed version of POSS (DPOSS) with a bounded approximation guarantee. DPOSS can be easily implemented in the MapReduce framework. Our extensive experiments using Spark, on various real-world data sets with size ranging from thousands to millions, show that DPOSS can achieve competitive performance compared with the centralized POSS, and is almost always better than the state-of-the-art distributed greedy algorithm RANDGREEDI.

Quality Evaluation of Solution Sets in Multiobjective Optimisation

“…It is worth mentioning that recently some work Qian et al (2018Qian et al ( , 2016Qian et al ( , 2015) converts a general subset selection problem into a bi-objective problem with an additional objective, the set size, and uses a simple evolutionary algorithm to optimise it. Such a Pareto optimisation subset selection can achieve the same general approximation guarantee as the greedy algorithm, but has better ability to avoid local optima.…”

Maximizing submodular or monotone approximately submodular functions by multi-objective evolutionary algorithms

“…For concise illustration, we will mainly show the difference in the proof of Theorem 3. [34] Assume that a set function f is monotone and non-submodular. Then, for any x ∈ {0, 1} n , there…”

A Parallel Divide-and-Conquer-Based Evolutionary Algorithm for Large-Scale Optimization

“…One is to enhance the search ability of existing EAs by re-scheduling the local search operators [20], [21]; while the other is to simplify the problem via Divide-and-Conquer (DC) [22], [23], [24] or Dimension Reduction [25], [26]. For saving the computational time in each iteration, parallel computing or distributed computing techniques are frequently employed to optimize individual solutions or decision variables on different threads [12], [13], [27], [28], [29]. Among them, the DC methodology has been frequently introduced into EAs for large-scale optimization problems, since it can be regarded as an integrated solution to improve the above two factors for EAs.…”