Multiobjective Evolutionary Algorithms: Analyzing the State-of-the-Art

Abstract

Solving optimization problems with multiple (often conflicting) objectives is, generally, a very difficult goal. Evolutionary algorithms (EAs) were initially extended and applied during the mid-eighties in an attempt to stochastically solve problems of this generic class. During the past decade, a variety of multiobjective EA (MOEA) techniques have been proposed and applied to many scientific and engineering applications. Our discussion's intent is to rigorously define multiobjective optimization problems and certain related concepts, present an MOEA classification scheme, and evaluate the variety of contemporary MOEAs. Current MOEA theoretical developments are evaluated; specific topics addressed include fitness functions, Pareto ranking, niching, fitness sharing, mating restriction, and secondary populations. Since the development and application of MOEAs is a dynamic and rapidly growing activity, we focus on key analytical insights based upon critical MOEA evaluation of current research and applications. Recommended MOEA designs are presented, along with conclusions and recommendations for future work.

A Similarity-Based Mating Scheme for Evolutionary Multiobjective Optimization

“…While mating restriction has been often discussed in the literature, its effect has not been clearly demonstrated. As a result, it is not used in many EMO algorithms as pointed out in some reviews on EMO algorithms [6,17,21]. The aim of this paper is to clearly demonstrate that the search ability of EMO algorithms can be improved by appropriately choosing parent solutions.…”

Multi-objective Optimisation of Cancer Chemotherapy Using Evolutionary Algorithms

“…, which, if some of the objectives are in conflict, places a partial, rather than normal, ordering on the search space Ω [14]. In order to mathematically define this partial ordering, a notion of Pareto dominance is introduced in the objective space Λ .…”

“…Depending on the order of performing these processes, the preferences of the decision maker (the oncologists in our case) can be made known either before, during or after the search process [14]. In the case of a priori preference articulation, the objectives of the given MOP are aggregated into a single objective that implicitly includes preference information (in the form of objective weights for example).…”

“…This means that after each optimisation step, a number of alternative treatment schedules (temporary Pareto-optimal set) are presented, on the basis of which the oncologist specifies further preference information, thereby guiding the search process. Such an approach is known as progressive preference articulation [14] and is a promising way to combine the advantages of the previous two. One example of how it can be used in the context of cancer chemotherapy is to optimise the modification of an existing treatment schedule rather than a schedule itself [11].…”

“…If all objectives are equally important, the conflict between them requires a compromise to be reached. A good solution to such problems involving conflicting objectives and therefore multiple evaluation criteria, should offer suitable, though possibly suboptimal in the single-objective sense, performance in all objective dimensions [14]. Generally, there exists a multitude of such solutions; hence, the algorithm used to solve a multi-objective optimisation problem should find a wide variety of them, instead of just one.…”