A Survey of Multiobjective Evolutionary Algorithms Based on Decomposition: Variants, Challenges and Future Directions <s> B. COMBINATION <s> The use of Pareto dominance for fitness evaluation has been the mainstream in evolutionary multiobjective optimization for the last two decades. Recently, it has been pointed out in some studies that Pareto dominance-based algorithms do not always work well on multiobjective problems with many objectives. Scalarizing function-based fitness evaluation is a promising alternative to Pareto dominance especially for the case of many objectives. A representative scalarizing function-based algorithm is MOEA/D (multiobjective evolutionary algorithm based on decomposition) of Zhang & Li (2007). Its high search ability has already been shown for various problems. One important implementation issue of MOEA/D is a choice of a scalarizing function because its search ability strongly depends on this choice. It is, however, not easy to choose an appropriate scalarizing function for each multiobjective problem. In this paper, we propose an idea of using different types of scalarizing functions simultaneously. For example, both the weighted Tchebycheff (Chebyshev) and the weighted sum are used for fitness evaluation. We examine two methods for implementing our idea. One is to use multiple grids of weight vectors and the other is to assign a different scalarizing function alternately to each weight vector in a single grid. <s> BIB001 </s> A Survey of Multiobjective Evolutionary Algorithms Based on Decomposition: Variants, Challenges and Future Directions <s> B. COMBINATION <s> MOEA/D is a generic multiobjective evolutionary optimization algorithm. MOEA/D needs a approach to decompose a multiobjective optimization problem into a number of single objective optimization problems. The commonly-used weighted sum approach and the Tchebycheff approach may not be able to handle disparately scaled objectives. This paper suggests a new decomposition approach, called NBI-style Tchebycheff approach, for MOEA/D to deal with such objectives. A portfolio management MOP has been used as an example to test the effectiveness of MOEA/D with NBI-style Tchebycheff approach. <s> BIB002 </s> A Survey of Multiobjective Evolutionary Algorithms Based on Decomposition: Variants, Challenges and Future Directions <s> B. COMBINATION <s> Combining ant colony optimization (ACO) and the multiobjective evolutionary algorithm (EA) based on decomposition (MOEA/D), this paper proposes a multiobjective EA, i.e., MOEA/D-ACO. Following other MOEA/D-like algorithms, MOEA/D-ACO decomposes a multiobjective optimization problem into a number of single-objective optimization problems. Each ant (i.e., agent) is responsible for solving one subproblem. All the ants are divided into a few groups, and each ant has several neighboring ants. An ant group maintains a pheromone matrix, and an individual ant has a heuristic information matrix. During the search, each ant also records the best solution found so far for its subproblem. To construct a new solution, an ant combines information from its group's pheromone matrix, its own heuristic information matrix, and its current solution. An ant checks the new solutions constructed by itself and its neighbors, and updates its current solution if it has found a better one in terms of its own objective. Extensive experiments have been conducted in this paper to study and compare MOEA/D-ACO with other algorithms on two sets of test problems. On the multiobjective 0-1 knapsack problem, MOEA/D-ACO outperforms the MOEA/D with conventional genetic operators and local search on all the nine test instances. We also demonstrate that the heuristic information matrices in MOEA/D-ACO are crucial to the good performance of MOEA/D-ACO for the knapsack problem. On the biobjective traveling salesman problem, MOEA/D-ACO performs much better than the BicriterionAnt on all the 12 test instances. We also evaluate the effects of grouping, neighborhood, and the location information of current solutions on the performance of MOEA/D-ACO. The work in this paper shows that reactive search optimization scheme, i.e., the “learning while optimizing” principle, is effective in improving multiobjective optimization algorithms. <s> BIB003 </s> A Survey of Multiobjective Evolutionary Algorithms Based on Decomposition: Variants, Challenges and Future Directions <s> B. COMBINATION <s> This paper studies how to use two reproduction operators with different characteristics for balancing the convergence and the diversity in MOEA/D. We consider two operators. One is a differential evolution and polynomial mutation, and the other is a neighbor learning and inversion mutation. We show that these two operators have different search abilities. Then we propose a scheme to use these two operators in our recently proposed MOEA/D-GR framework. We test the proposed algorithm on some benchmark problems to demonstrate its effectiveness. <s> BIB004 </s> A Survey of Multiobjective Evolutionary Algorithms Based on Decomposition: Variants, Challenges and Future Directions <s> B. COMBINATION <s> A Multi-Skilled Project Scheduling Problem (MSPSP) that is an extension of a Multi-Mode Resource-Constrained Project Scheduling Problem (MM-RCPSP) has been generally presented to schedule a project with staff members as resources. In MSPSP, each activity requires different skills and staff members have various skill levels too. This causes to encounter a huge number of modes while performing activities of a project. This research is focused on a special type of MSPSP known as Multi-Objective Multi-Skilled Project Scheduling Problem (MOMSPSP) which incorporates some new objectives in the MSPSP and develops a multi-objective mixed-integer non-linear programming model for it. The problem is exactly solved for small-sized instances using CPLEX solver. the results are obtained by the CPLEX solver for small size is identified as the super solver for solving the propounded MOMSPSP. <s> BIB005
The combination of different methods BIB001 , BIB002 or diverse operators BIB004 can fully utilize their complementary advantages to maintain the balance between diversity and convergence. Other heuristic algorithms (e.g., ACO BIB003 ) or mathematical optimization tools (e.g., Cplex BIB005 ) can be combined with MOEA/D to conduct both global and local searches in the objective space, and to ensure the quality and diversity of the solution set.