In this paper, we propose a new method for solving multiobjective optimization problems with a large number of decision variables. The proposed method called weighted optimization framework is intended to serve as a generic method that can be used with any population-based metaheuristic algorithm. After explaining some general issues of large-scale optimization, we introduce a problem transformation scheme that is used to reduce the dimensionality of the search space and search for improved solutions in the reduced subspace. This involves so-called weights that are applied to alter the decision variables and are also subject to optimization. Our method relies on grouping mechanisms and employs a population-based algorithm as an optimizer for both original variables and weight variables. Different grouping mechanisms and transformation functions within the framework are explained and their advantages and disadvantages are examined. Our experiments use test problems with 2-3 objectives 40-5000 variables. Using our approach on three well-known algorithms and comparing its performance with other large-scale optimizers, we show that our method can significantly outperform most existing methods in terms of solution quality as well as convergence rate on almost all tested problems for many-variable instances.

In multi-objective particle swarm optimization (MOPSO) methods, selecting the best local guide (the global best particle) for each particle of the population from a set of Pareto-optimal solutions has a great impact on the convergence and diversity of solutions, especially when optimizing problems with high number of objectives. This paper introduces the Sigma method as a new method for finding best local guides for each particle of the population. The Sigma method is implemented and is compared with another method, which uses the strategy of an existing MOPSO method for finding the local guides. These methods are examined for different test functions and the results are compared with the results of a multi-objective evolutionary algorithm (MOEA).

Many practical optimization problems are constrained and have a bounded search space. In this paper, we propose and compare a wide variety of bound handling techniques for particle swarm optimization. By examining their performance on flat landscapes, we show that many bound handling techniques introduce significant search bias. Furthermore, we compare the performance of many bound handling techniques on a variety of test problems, demonstrating that the bound handling technique can have a major impact on the algorithm performance, and that the method recently proposed as the standard does not, in general, perform well.

For real-world problems, the task of decision-makers is to identify a solution that can satisfy a set of performance criteria, which are often in conflict with each other. Multi-objective evolutionary algorithms tend to focus on obtaining a family of solutions that represent the trade-offs between the criteria; however ultimately a single solution must be selected. This need has driven a requirement to incorporate decision-maker preference models into such algorithms - a technique that is very common in the wider field of multiple criteria decision making. This paper reviews techniques which have combined evolutionary multi-objective optimization and multiple criteria decision making. Three classes of hybrid techniques are presented: a posteriori, a priori, and interactive, including methods used to model the decision-makers preferences and example algorithms for each category. To encourage future research directions, a commentary on the remaining issues within this research area is also provided.