Enhanced Optimization with Composite Objectives and Novelty Selection

Abstract

An important benefit of multi-objective search is that it maintains a diverse population of candidates, which helps in deceptive problems in particular. Not all diversity is useful, however: candidates that optimize only one objective while ignoring others are rarely helpful. This paper proposes a solution: The original objectives are replaced by their linear combinations, thus focusing the search on the most useful tradeoffs between objectives. To compensate for the loss of diversity, this transformation is accompanied by a selection mechanism that favors novelty. In the highly deceptive problem of discovering minimal sorting networks, this approach finds better solutions, and finds them faster and more consistently than standard methods. It is therefore a promising approach to solving deceptive problems through multi-objective optimization.

Enhanced optimization with composite objectives and novelty pulsation

“…Previous work in the sorting networks domain demonstrated that composite novelty can match the minimal known networks up to 18 input line with reasonable computational resources [39,40]. The goal of the sorting network experiments was to achieve the same result faster, i.e.…”

“…An alternative method is to use composite multi-objective axes to focus the search on the area with most useful tradeoffs [39]. Since the axes are not orthogonal, solutions that optimize only one objective will not be on the Pareto front.…”

“…Since the same layout can sort any input, it represents an oblivious or data-independent sorting algorithm, that is, the layout of comparisons does not depend on the input data. The resulting fixed communication pattern makes sorting networks desirable in parallel implementations of sorting, such as those in graphics processing units, multi-processor computers, and switching networks [2,24,39]. Beyond validity, the main goal in designing sorting networks is to minimize the number of layers, because it determines how many steps are required in a parallel implementation.…”

“…In particular, candidates that optimize one objective only and ignore the others are less likely to lead to useful tradeoffs, and they are less likely to escape deception. Prior research demonstrated that it is beneficial to replace the objectives with their linear combinations, thus focusing the search in more useful areas of the search space, and make up for the lost diversity by including a novelty metric in parent selection [39]. This paper improves upon this approach by introducing the concept of novelty pulsation: the novelty selection is turned on and off periodically, thereby allowing exploration and exploitation to leverage each other repeatedly.…”

“…This idea is tested in two domains. The first one is the highly deceptive domain of sorting networks [25] used in the original work on composite novelty selection [39]. Such networks consist of comparators that map any set of numbers represented in their input lines to a sorted order in their output lines.…”