Multi-objective Evolutionary Algorithms: Introducing Bias Among Pareto-optimal Solutions

Abstract

Summary. Sin ce the beginning of the 1990s, research and applicat ion of multiobjective evoluti ona ry algorithms (MOEAs) have a tt rac te d increasing at te nt ion. This is mainly du e to t he abilit y of evolut iona ry algorit hms to find multiple P ar etooptimal solutions in one single simulation run. In thi s chapte r, we present a n overview of MO EAs and then discuss a particular algorit hm in detail. Although MOEAs ca n find multiple Par et o-optimal solutions, oft en, users need to impose a pa rti cular order of priorit y to obj ectiv es. In this chapte r, we pr esent a few classical t echniques to identify a pr eferred or a compromise solution , and finally sugg est a biased sharing technique whi ch ca n be used during the optimization phase to find a biased distribution of Pareto-optimal solutions in the region of inte rest. The results are encouraging and suggest further application of the proposed strategy to more complex multi-objective optimization problems.

Integrating user preferences and decomposition methods for many-objective optimization

“…Although G-MOEA is more flexible and intuitive than other approaches, it is not always an easy task for the decision maker to specify the trade-off between objectives, especially for many-objective problems. Deb [22] applied bias sharing technique on NSGA [23] where the biased Pareto-optimal solutions are generated on a desired region by changing the weights. An objective with a higher priority takes a higher weight value.…”

Many-Objective Portfolio Optimization of Interdependent Projects with ‘a priori’ Incorporation of Decision-Maker Preferences

“…[38,39,40]). 2.Those in which the DM makes pair-wise comparisons on a subset of the current population, in order to rank the sample's solutions (e.g.…”

Multicriteria optimization of interdependent project portfolios with a priori incorporation of decision maker preferences

“…According to Bechikh ([35]), the most commonly used ways are the following:  those in which importance factors (weights) are assigned by the DM to each objective function (e.g. [36,37]),  those in which the DM makes pair-wise comparisons on a subset of the current population in order to rank the sample's solutions (e.g. [38,39]),  when pair-wise comparisons between pairs of objective functions are performed in order to rank the set of objective functions (e.g.…”