Multiobjective Optimization-Aided Decision-Making System for Large-Scale Manufacturing Planning.

This work is geared toward a real-world manufacturing planning (MP) task, whose two objectives are to maximize the order fulfillment rate and minimize the total cost. More important, the requirements and constraints in real manufacturing make the MP task very challenging in several aspects. For example, the MP needs to cover many production components of multiple plants over a 30-day horizon, which means that it involves a large number of decision variables. Furthermore, the MP task's two objectives have extremely different magnitudes, and some constraints are difficult to handle. Facing these uncompromising practical requirements, we introduce an interactive multiobjective optimization-based MP system in this article. It can help the decision maker reach a satisfactory tradeoff between the two objectives without consuming massive calculations. In the MP system, the submitted MP task is modeled as a multiobjective integer programming (MOIP) problem. Then, the MOIP problem is addressed via a two-stage multiobjective optimization algorithm (TSMOA). To alleviate the heavy calculation burden, TSMOA transforms the optimization of the MOIP problem into the optimization of a series of single-objective problems (SOPs). Meanwhile, a new SOP solving strategy is used in the MP system to further reduce the computational cost. It utilizes two sequential easier SOPs as the approximator of the original complex SOP for optimization. As part of the MP system, TSMOA and the SOP solving strategy are demonstrated to be efficient in real-world MP applications. In addition, the effectiveness of TSMOA is also validated on benchmark problems. The results indicate that TSMOA as well as the MP system are promising.

A Preference-Based Multiobjective Evolutionary Approach for Sparse Optimization.

Iterative thresholding is a dominating strategy for sparse optimization problems. The main goal of iterative thresholding methods is to find a so-called -sparse solution. However, the setting of regularization parameters or the estimation of the true sparsity are nontrivial in iterative thresholding methods. To overcome this shortcoming, we propose a preference-based multiobjective evolutionary approach to solve sparse optimization problems in compressive sensing. Our basic strategy is to search the knee part of weakly Pareto front with preference on the true -sparse solution. In the noiseless case, it is easy to locate the exact position of the -sparse solution from the distribution of the solutions found by our proposed method. Therefore, our method has the ability to detect the true sparsity. Moreover, any iterative thresholding methods can be used as a local optimizer in our proposed method, and no prior estimation of sparsity is required. The proposed method can also be extended to solve sparse optimization problems with noise. Extensive experiments have been conducted to study its performance on artificial signals and magnetic resonance imaging signals. Our experimental results have shown that our proposed method is very effective for detecting sparsity and can improve the reconstruction ability of existing iterative thresholding methods.

Biased Multiobjective Optimization and Decomposition Algorithm.

The bias feature is a major factor that makes a multiobjective optimization problem (MOP) difficult for multiobjective evolutionary algorithms (MOEAs). To deal with this problem feature, an algorithm should carefully balance between exploration and exploitation. The decomposition-based MOEA decomposes an MOP into a number of single objective subproblems and solves them in a collaborative manner. Single objective optimizers can be easily used in this algorithm framework. Covariance matrix adaptation evolution strategy (CMA-ES) has proven to be able to strike good balance between the exploration and the exploitation of search space. This paper proposes a scheme to use both differential evolution (DE) and covariance matrix adaptation in the MOEA based on decomposition. In this scheme, single objective optimization problems are clustered into several groups. To reduce the computational overhead, only one subproblem from each group is selected to optimize by CMA-ES while other subproblems are optimized by DE. When an evolution strategy procedure meets some stopping criteria, it will be reinitialized and used for solving another subproblem in the same group. A set of new multiobjective test problems with bias features are constructed in this paper. Extensive experimental studies show that our proposed algorithm is suitable for dealing with problems with biases.