Dynamic Uniform Scaling for Multiobjective Genetic Algorithms

Abstract

Abstract. Before Multiobjective Evolutionary Algorithms (MOEAs) can be used as a widespread tool for solving arbitrary real world problems there are some salient issues which require further investigation. One of these issues is how a uniform distribution of solutions along the Pareto non-dominated front can be obtained for badly scaled objective functions. This is especially a problem if the bounds for the objective functions are unknown, which may result in the nondominated solutions found by the MOEA to be biased towards one objective, thus resulting in a less diverse set of tradeoffs. In this paper, the issue of obtaining a diverse set of solutions for badly scaled objective functions will be investigated and the proposed solutions will be implemented using the NSGA-II algorithm.

Multiobjective real-coded bayesian optimization algorithmrevisited: diversity preservation

“…As in [11], ρ adjusts the degree of scaling between objectives, and f2 is much larger scaling than f1 as ρ increases from the value of 1.0. To make matters worse, the function g( y) involves (multivariate) interactions between variables.…”

“…A new test problem can be designed from [11]. It has two important issues that are not encountered in usual benchmark MOPs; scaling (of objectives) and dependency (of variables).…”

“…3, it is necessary to develop a more powerful mechanism for improving diversity performance. In general, most MGEAs employ truncation 11 The composite effect would be significant for highdimensional and badly-scaling problems. No significance by a paired, two-tailed test of α = 0.05. selection due to its ability to naturally incorporate elitism.…”

A diversity preserving selection in multiobjective evolutionary algorithms

“…If the same selection mechanisms are applied to scaling problems, the desired behavior may not be forthcoming. This is because the selection mechanisms that largely exploit Pareto dominance find it hard to break the barrier of badly-scaled objectives (i.e., highly-skewed distribution of solutions) [3,21]. Without a doubt, the selection schemes (i.e., BTS, -DS, and IBS) intensively depend on the Pareto dominance.…”

“…Often, it becomes difficult to obtain a uniform distribution of solutions along the Pareto front when the objective values do not operate over a comparable scale [21]. This is because the scaling evolves individuals in the direction of particular objectives.…”