Abstract
Today, many complex multiobjective problems are dealt with using genetic algorithms (GAs). They apply the evolution mechanism of a natural population to a “numerical” population of solutions to optimize a fitness function. GA implementations must find a compromise between the breath of the search (to avoid being trapped into local minima) and its depth (to prevent a rough approximation of the optimal solution). Most algorithms use “elitism”, which allows preserving some of the current best solutions in the successive generations. If the initial population is randomly selected, as in many GA packages, the elite may concentrate in a limited part of the Pareto frontier preventing its complete spanning. A full view of the frontier is possible if one, first, solves the single-objective problems that correspond to the extremes of the Pareto boundary, and then uses such solutions as elite members of the initial population. The paper compares this approach with more conventional initializations by using some classical tests with a variable number of objectives and known analytical solutions. Then we show the results of the proposed algorithm in the optimization of a real-world system, contrasting its performances with those of standard packages.
Highlights
Multiobjective (MO) optimization is one of the most common tools developed in recent decades to support decision-making
A further well-known property of the Pareto frontier is that it allows determining the trade-offs of each individual choice, namely the decrease of performance of the other objectives when one is improved along the frontier
Even assuming that the real Pareto frontier is farther apart from that determined by the single-objective plus multiobjective (SO+MO) approach, the solution obtained by the random initialization has a hypervolume that is just a fraction of that obtained with the proposed approach
Summary
Multiobjective (MO) optimization is one of the most common tools developed in recent decades to support decision-making. A further well-known property of the Pareto frontier is that it allows determining the trade-offs of each individual choice, namely the decrease of performance of the other objectives when one is improved along the frontier These important positive characteristics are usually counterbalanced by the high computational burden that is needed for the determination of the solutions of a multiobjective problem. Modern solution tools for these problems are based on evolutionary heuristics often mimicking some natural process [19,20,21] Algorithms of this type comprise simulated annealing [22], ant colony optimization [23], and cuckoo search [24], but the most common is by far the class of genetic algorithms (GAs) [25].
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