Reducing complexity in many objective optimization using community detection

Abstract

Multi-objective optimization problems with many objective functions (≫3) are difficult to solve. This is because the time complexity of optimization algorithms often grows fast with the number of objective functions and the results of many objective optimization algorithms (Pareto front approximation) require large memory and their interpretation can be difficult for the decision maker. It is therefore attractive to reduce complexity of these problems. This can be achieved by decomposing them into a set of independent lower dimensional subproblems, or by aggregating some objective functions into a single objective function. This work introduces a new approach for decomposition and aggregation based on techniques from social network analysis. The key idea is to interpret an objective function as a node (agent) in a social network, and arcs between nodes indicate relationships: Negatively weighted arcs stand for conflicting objectives, zero weighted arcs for independent objectives, and positively weighted arcs for objectives that support each other. Using well-known algorithms BGLL for community detection we show that - given certain preconditions - it is possible to decompose a many objective optimization problem to a set of lower dimensional multi-objective optimization problems. This makes it easier to solve the problem and interpret the resulting trade-off (hyper-)surfaces. In the paper, after introducing the idea of Communtiy Detection for Many-Objective Optimization (CoDeMO), we lay out an interactive workflow and test it on simple, scalable many-objective optimization problems - variants of facility location problems - and thereby provide a prove-of-concept study.