Virtual Reality High Dimensional Objective Spaces for Multi-objective Optimization: An Improved Representation

Abstract

Abstract-This paper presents an approach for constructing improved visual representations of high dimensional objective spaces using virtual reality. These spaces arise from the solution of multi-objective optimization problems with more than 3 objective functions which lead to high dimensional Pareto fronts. The 3-D representations of m-dimensional Pareto fronts, or their approximations, are constructed via similarity structure mappings between the original objective spaces and the 3-D space. Alpha shapes are introduced for the representation and compared with previous approaches based on convex hulls. In addition, the mappings minimizing a measure of the amount of dissimilarity loss are obtained via genetic programming. This approach is preliminarily investigated using both theoretically derived high dimensional Pareto fronts for a test problem (DTLZ2) and practically obtained objective spaces for the 4 dimensional knapsack problem via multi-objective evolutionary algorithms like HLGA, NSGA, and VEGA. The improved representation captures more accurately the real nature of the m-dimensional objective spaces and the quality of the mappings obtained with genetic programming is equivalent to those computed with classical optimization algorithms.

Multi‐objective optimization for channel allocation in mobile computing using NSGA‐II

“…Several algorithms inspired by this principle have been proposed. Among these are VEGA [28], HLGA [29], NSGA, NSGA-II [30][31][32], SPEA [33], SPEA-II [11,34], PESA-II [35] and many others [26].…”

“…Therefore the goal is to find a set of optimal solutions representing the best trade-offs, as diverse as possible, from which the user with further higher-level information about the problem can make a decision. Most MOO algorithms use the concept of dominance in their formulation [26].…”

Identity verification based on haptic handwritten Signature: Novel fitness functions for GP framework

“…The parameter values used in the experiments are shown in Table I which have proved to be reasonable general choices for a broad variety of problems [23].…”