A Survey of Multiobjective Evolutionary Algorithms Based on Decomposition: Variants, Challenges and Future Directions <s> E. CONSTRAINED MULTIOBJECTIVE OPTIMIZATION <s> Due to the development of the green economy, green manufacturing has been a hot topic. This paper proposes a new problem, i.e., the resource constrained unrelated parallel machine green manufacturing scheduling problem (RCUPMGSP) with the criteria of minimizing the makespan and the total carbon emission. To solve the problem, a collaborative multiobjective fruit fly optimization algorithm (CMFOA) is proposed. First, a job-speed pair-based solution representation is presented, and an effective decoding method is designed. Second, a heuristic for initialization of the population is proposed. Third, three collaborative search operators are designed to handle three subproblems in the smell-based search phase, i.e., job-to-machine assignment, job sequence, and processing speed selection. The technique for order preference by similarity to an ideal solution and the fast nondominated sorting methods are both employed for multiobjective evaluation in the vision-based search phase. Moreover, a critical-path-based carbon saving technique is designed according to the problem analysis to further improve the nondominated solutions explored in the fruit fly optimization algorithm-based evolution. In addition, the effect of parameter setting is investigated and the suitable parameter values are recommended. Finally, numerical tests and comparisons are carried out using the randomly generated instances, which show that the CMFOA is able to obtain more and better nondominated solutions than other algorithms. The comparisons also demonstrate the effectiveness of the collaborative scheme and the carbon saving technique as well as the CMFOA in solving the RCUPMGSP. <s> BIB001 </s> A Survey of Multiobjective Evolutionary Algorithms Based on Decomposition: Variants, Challenges and Future Directions <s> E. CONSTRAINED MULTIOBJECTIVE OPTIMIZATION <s> The large-scale integration of wind generation in power systems increases the need for reserve procurement in order to accommodate its highly uncertain nature, a fact that may overshadow its environmental and economic benefits. For this reason, the design of reserve procurement mechanisms should be reconsidered in order to embed resources that are capable of providing reserve services in an economically optimal way. In this study, a joint energy and reserve day-ahead market structure based on two-stage stochastic programming is presented. The developed model incorporates explicitly the participation of demand side resources in the provision of load following reserves. Since a load that incurs a demand reduction may need to recover this energy in other periods, different types of load recovery requirements are modeled. Furthermore, in order to evaluate the risk associated with the decisions of the system operator and to assess the effect of procuring and compensating load reductions, the Conditional Value-at-Risk metric is employed. In order to solve the resulting multi-objective optimization problem, a new approach based on an improved variant of the epsilon-constraint method is adopted. This study demonstrates that the proposed approach to risk management presents conceptual advantages over the commonly used weighted sum method. <s> BIB002 </s> A Survey of Multiobjective Evolutionary Algorithms Based on Decomposition: Variants, Challenges and Future Directions <s> E. CONSTRAINED MULTIOBJECTIVE OPTIMIZATION <s> Portfolio optimization is an important financial problem, which involves an optimal allocation of finite capital to a series of assets to achieve an acceptable trade-off between profit and risk in a given investment period. In this paper, an extended Markowitz’s mean-variance portfolio optimization model, which is converted as a constrained multi-objective problem, is studied. Since this model involves both discrete and continuous variables, a multi-dimensional mapping coding scheme (MDM) has been adopted to convert discrete variables to continuous ones. Although the basic MDM is effective for dealing with the constrained multi-objective portfolio optimization problems, it sometimes prefers to choose some balanced investments, in which the allocation of funds for each selected asset is very similar. This may result in a focus on the low-risk and low-yield solutions. To solve this problem, an improved multi-dimensional mapping coding scheme is proposed in this paper. This new coding scheme is integrated into the decomposition based multi-objective evolutionary algorithm (MOEA/D). The algorithm is then applied to some test data, with the asset size ranging from 31 to 255, and the experimental results have indicated that the improved MDM coding scheme can significantly improve the performance comparing to the basic MDM coding scheme. <s> BIB003
Many real-world optimization problems belong to CMOPs, such as constrained multiobjective portfolio optimization BIB003 , resource-constrained unrelated parallel machine green scheduling problem BIB001 , and risk-constrained energy and reserve procurement BIB002 . A CMOP usually includes multiple diversionary or conflicting objectives and different types of constraints that need to be satisfied simultaneously. These constraints lead to a number of infeasible solutions violating such constraints. Therefore, how to deal with the infeasible solutions generated during the search process and to realize the effective utilization of computational resources are the challenges when solving CMOPs. In recent years, many constraint handling techniques have been organically integrated into the MOEA/D framework to solve various CMOPs successfully. The following briefly introduces these techniques and their algorithms combined with MOEA/D.