Sequence-Based Selection Hyper-Heuristic Model via MAP-Elites

Abstract

Combinatorial optimization problems (COPs) are paramount for real-life problems with discrete variables. Even though the number of combinations is finite, some problems exhibit exponential growth, rendering exact approaches unfeasible. So, approximate methods, such as heuristics, are customary for making fast decisions. Despite their small computational cost, each heuristic specializes in specific kinds of problems. Hence, other approaches have appeared for merging their strengths. One of these approaches is commonly known as selection hyper-heuristics. However, a trained hyper-heuristic usually carries the following problem: it provides scarce information about its sensitivity. This makes it more difficult to estimate the effect of changing a parameter. Illumination algorithms seek to improve this issue by focusing on exploration rather than on exploitation while preserving information about the best solutions with different criteria. Still, literature falls short when merging both approaches, representing a knowledge gap. Therefore, in this work, we test the feasibility of using an illumination algorithm, the MAP-Elites (ME), for tuning a sequence-based selection hyper-heuristic model for Balanced Partition problems. We choose ME since it has been successfully applied to a different COP, and by linking it with hyper-heuristics, we may exploit upon its benefits. So, we may achieve a hyper-heuristic that represents the best combination of heuristics. Simultaneously, we can gain information about the expected performance of diverse hyperheuristics, e.g., those that begin with a different heuristic. Our approach operates by creating a multidimensional map, where each design variable represents the application of a given heuristic. Afterward, ME generates mutated sequences and tests them to determine if they represent a better-performing solution. To test our approach, we consider 1500 instances that include easy and hard instances, analyzed under different scenarios. We also include limit instances that are neither easy nor hard. Our resulting data supports the feasibility of the proposed approach. We show that this kind of hyper-heuristic can perform toe-to-toe with a synthetic oracle. Besides, under some conditions, the former may even outperform the latter. This represents an outstanding result, since such an oracle can only be obtained by a brute-force approach, and because it demonstrates that merging both approaches (ME and hyper-heuristics) is a path worth pursuing. We also present how each parameter affects the model performance, concluding that some parameters can be critical while others are virtually irrelevant. This is also a relevant result, since it serves as the groundwork for future works so that they can focus on exploiting the most relevant parameters.

Problem Solving in Crowd Management Using Heuristic Approach

“…Another article [42] proposed using an illumination algorithm called MAP-Elites to train sequence-based hyperheuristics for the balanced partition problem. It is found that training with ME yields better results even in their lousy performance levels than randomly selected heuristics.…”

MatHH: A Matlab-based Hyper-Heuristic framework

“…For example, one may define a set of rules for selecting actions (heuristics) [12]. Conversely, one may just lay out a sequence of such actions and optimize said sequence [13]. Or one could resort to ideas from diverse fields, such as those from reinforcement learning [14,15], or others [16][17][18][19][20][21].…”

“…Specifics aside, HHs (as a whole) have proven to be a path worth pursuing and polishing [1]. For example, Sanchez et al merged HHs with an approach designed for obtaining a variety of quality designs for a single-objective problem [13]. Such an approach is commonly referred to as an illumination algorithm since it seeks to provide insights into good designs for different ranges of the design variables.…”

“…As stated in Fig. 1, one may develop a seqBasedSelectionHH module that uses a HH model based on sequences of heuristics instead of rules [13,36], which was also mentioned in Section 1. We are actually working on such a kind of model, and we plan to provide it in a future release of MatHH.…”

Improving the Size and Quality of MAP-Elites Containers via Multiple Emitters and Decoders for Urban Logistics

“…The use of quality-diversity methods such as the Map of Phenotypic Elites (MAP-Elites) [21,18] that generate multiple high-quality but diverse solutions to an optimisation problem is very well-established in the field of robotics. Increasingly the approach is finding applications in combinatorial optimisation domains such as routing [28], constrained optimisation [25] and instance-generation [2]. Specifically, the MAP-Elites algorithm generates a set of solutions to a singleobjective optimisation problem that are diverse with respect to a set of features defined by a user.…”