Decomposition evolutionary algorithms for noisy multiobjective optimization

Multi-objective problems are a category of optimization problem that contains more than one objective function and these objective functions must be optimized simultaneously. Should the objective functions be conflicting, then a set of solutions instead of a single solution is required. This set is known as Pareto optimal. Multi-objective optimization problems arise in many real world applications where several competing objectives must be evaluated and optimal solutions found for them, in the presence of trade offs among conflicting objectives. Maximizing returns while minimizing the risk of stock market investments, or maximizing performance whilst minimizing fuel consumption and hazardous gas emission when buying a car are typical examples of real world multi-objective optimization problems. In this case a number of optimal solutions can be found, known as non-dominated or Pareto optimal solutions. Pareto optimal solutions are reached when it is impossible to improve one objective without making the others worse. Classical ways to address this problem used direct or gradient based methods that rendered them insufficient or computationally expensive for large scale or combinatorial problems. Other difficulties attended the classical methods, such as problem knowledge, which may not be available, or sensitivity to some problem features. For example, finding solutions on the entire Pareto optimal set can only be guaranteed for convex problems. Classical methods for generating the Pareto front set aggregate the objectives into a single or parametrized function before search. Thus, several run and parameter setting are performed to achieve a set of solutions that approximate the Pareto optimals. Consequently new methods have been developed, based on computer experiments with meta-heuristic algorithms. Most of these meta-heuristics implement some sort of stochastic search method, amongst which ‘Evolutionary Algorithm’ is garnering much attention. It possesses several characteristics that make it a desirable method for confronting multi-objective problems. As a result, a number of studies in recent decades have developed or modified the Multi-objective Optimization Evolutionary Algorithm (MOEA) for different purposes. This algorithm works with a population of iv