Multi-objective optimization (MOO) problems belong to programming
approaches in which the decision-maker is faced with a multiplicity of conflicting
objectives. This situation occurs with real-world problems involving engineering
design, chemical processes, financial management, etc. In such problems, we will
obtain rather a set of equally good solutions and not just one best solution. Classical
methods for solving problems have shown their limits to find Pareto-optimality
fronts. The difficulties were the necessity of repetitive applications, the requirement of
some knowledge about the problem, the insufficient spread of non-dominated
solutions, and the sensitivity of results to the shape of the Pareto-optimal front.
accelerated development in the decades 1980s and 1990s. A variety of nature-inspired
algorithms have been proposed in the recent years with extensive applications. The
concept of dominance is the basis of the Pareto optimality. The dominance binary
relation is a strict partial order relation. This approach allows a comparison between
feasible solutions in the fitness space and decision space. The non-dominated solution
sets yield Pareto fronts. Different techniques were proposed to find good
approximations of the Pareto sets when a Pareto front cannot be determined
analytically. Our method uses graph theory analysis. This approach provides a nondominated
set by using the Hasse diagram of an acyclic graph. Numerous examples
from the literature show connected and disconnected Pareto-optimal fronts. In
particular, Pareto-optimal fronts change if we decide to maximize instead to minimize
the objectives. Algorithms use different selection procedures. The selection criteria can
be an elitist Pareto ordering, non-Pareto criteria like indicators, a bi-criteria evolution,
and the extended concepts of dominance like ε-dominance and grid dominance.
Keywords: Attraction-based algorithm, Conflicting/nonconflicting objectives,
Darwinian evolution, Engineering design problem, Globally/locally Paretooptimality,
Hasse diagram, Master strategy, Metaheuristics, Multi-objective
optimization, Nature-inspired algorithm, Near/exact Pareto-optimal front, Nondominated
solution, Pareto-optimal solution, Pareto ranking, Population-based
algorithm, Strongly/weakly Pareto-optimality, Subordinate heuristics, Swarm
intelligence, Trajectory-based algorithm.
