Large-scale multi-objective problems in industrial and engineering may
involve much higher dimensional problems. They may require decomposing the
numerous operations to be done in the resolution process. In practice, one can be
confronted with the optimization of a large number of objectives as well as with the
great amount of the calculations to be made. This chapter is devoted to possible
approaches to overcome these difficulties namely the so-called ‘many-objective
optimization’ and ‘parallel computation’. Two major inconveniences in handling more
than three (many) objectives are a decrease selection pressure to converge toward the
Pareto front and a decreasing computational efficiency as the number of objectives
increases. Addressing these significant difficulties may consist of adapting or changing
the concept of the Pareto dominance. A stronger dominance relation will allow a better
comparison of the quality of solutions. New concepts are ε-dominance, L-optimality,
fuzzy dominance, preference order ranking. Some essential algorithms for manyoptimization
are proposed, such as the fast hypervolume-based algorithm, the vector
angle-based algorithm, the reference point-based algorithm as with NSGA-III. Test
problem suites for many-objective optimization are proposed. Parallel search
techniques are adapted to new computer architectures with parallel computers and
distributed multiprocessor computers. Two motivations to adopt such configuration are
saving computation time of complex real-world problem and the possibility to solve
large-size problems. The hierarchical master-worker paradigm is a standard way to
implement parallel applications. A master process dispatches specific tasks to multiple
worker processes and receives the computation results back from the worker processes.
Parallel computation of metaheuristic algorithms includes parallelization strategies,
parallel designs, and parallel metaheuristic algorithms. Applications can show how
much computation time can be saved with parallel computation.
Keywords: ε-dominance, Computational efficiency, Hypervolume-based
algorithm, Many-objective optimization, Master-worker paradigm, NSGA-III,
Parallel computation, Parallelization strategies, Pareto dominance, Reference
point-based algorithm, Selection pressure, Vector angle-based algorithm.
