Narrow Results

For dynamic multi-objective constrained optimization problem (DMCOP), it is important to find a sufficient number of uniformly distributed and representative dynamic Pareto optimal solutions. In this paper, the time period of the DMCOP is first divided into several random subperiods. In each random subperiod, the DMCOP is approximately regarded as a static optimization problem by taking the time subperiod fixed. Then, in order to decrease the amount of computation and improve the effectiveness of the algorithm, the dynamic multi-objective constrained optimization problem is further transformed into a dynamic bi-objective constrained optimization problem based on the dynamic mean rank variance and dynamic mean density variance of the evolution population. The evolution operators and a self-check operator which can automatically checkout the change of time parameter are introduced to solve the optimization problem efficiently. And finally, a dynamic multi-objective constrained optimization evolutionary algorithm is proposed. Also, the convergence analysis for the proposed algorithm is given. The computer simulations are made on four dynamic multi-objective optimization test functions and the results demonstrate that the proposed algorithm can effectively track and find the varying Pareto optimal solutions or the varying Pareto fronts with the change of time.

Obtaining multi-objective optimization solutions with a small number of points smartly distributed along the Pareto front is a challenge. Optimization methods, such as the normalized normal constraint (NNC), propose the use of a filter to achieve a smart Pareto front distribution. The NCC optimization method presents several disadvantages related with the procedure itself, initial condition dependency, and computational burden. In this article, the epsilon-variable multi-objective genetic algorithm (ev-MOGA) is presented. This algorithm characterizes the Pareto front in a smart way and removes the disadvantages of the NNC method. Finally, examples of a three-bar truss design and controller tuning optimizations are presented for comparison purposes.

For decreasing service centers’ selection risks in emergency facility location selection, it is crucial to have selected candidate service centers within deeply detailed facility location selection model. To achieve this, a new approach developed in this article involves two stages. In the first stage, the fuzzy multi-attribute group decision making (MAGDM) model for evaluation of the selection of candidate service centers is created. For the aggregation of experts’ assessments of candidate service centers (with respect to attributes) aggregation operators’ approach is used. Experts’ assessments are presented in fuzzy terms with semantic form of triangular fuzzy numbers. For the deeply detailed facility location selection modeling and for the intellectual activity of experts in their evaluations, pairwise interactions between attributes of MAGDM model are considered in the construction of the second-order additive triangular fuzzy valued fuzzy measure (TFVFM). The associated triangular fuzzy probability averaging (As-TFPA) aggregation operators’ family is constructed with respect to TFVFM. Analytical properties of the As-TFPA operators are studied. The new operators are certain extensions of the well-known Choquet integral operator. The extensions, in contrast to the Choquet aggregation, consider all possible pair-wise interactions of the attributes by introducing associated fuzzy probabilities of a TFVFM. At the end of the first stage, a candidate service center’s selection index is defined as As-TFPA operator’s aggregation value on experts’ assessments with respect to attributes.

At the second stage, fuzzy multi-objective facility location set covering problem (MOFLSCP) is created for facility location selection optimal planning with new criteria: (1) maximization of candidate service centers selection index and classical two criteria, (2) minimization of the total cost needed to open service centers and (3) minimization of number of agents needed to operate the opened service centers.

For the constructed two-stage methodology a simulation example of emergency service facility location planning for a city is considered. The example gives the Pareto fronts obtained by As-TFPA operators, the Choquet integral-TFCA operator and well-known TOPSIS approach, for optimal selecting candidate sites for the servicing of demand points. The comparative analysis identifies that the differences in the Pareto solutions, obtained by using As-TFPA operators and TFCA operator or TOPSIS aggregation, are also caused by the fact that TFCA operator or TOPSIS approach considers the pair interaction indexes for only one consonant structure of attributes. While new As-TFPA aggregations provide all pairwise interactions for all consonant structures.

In this paper, the concept of adaptive multiobjective genetic algorithm (AMOGA) is applied for the structure optimization of radial basis function network (RBFN). The problem of finding the number of hidden centers remains a critical issue in the design of RBFN. The number of basis function controls the complexity and generalization ability of the network. The most parsimonious network obtained from the pareto front is applied in one of the challenging research area of proteomics and computational biology: Protein superfamily classification. The problem deals with predicting the family membership of a newly discovered amino acid sequence. The modification to the earlier approach of multiobjective genetic algorithm (MOGA) is done based on the two key controlling parameters such as probability of crossover and probability of mutation. These values are adaptively varied based on the performance of the algorithm i.e., based on the percentage of total population present in the best nondomination level. Principal component analysis (PCA) is used for dimension reduction and significant features are extracted from long feature vector of amino acid sequences. Numerical simulation results illustrates the efficiency of our approach in terms of faster convergence, optimal architecture and high level of classification accuracy.

In order to improve the resonant frequency and sensitivity of piezoresistive accelerometer, multi-objective optimization is proposed based on numerical simulation using the finite element software ANSYS. The first natural frequency (representing resonant frequency) and the maximal Mises stress (representing sensitivity) of accelerometer structures are defined as two objective functions, and the geometric parameters as design variables. After that, the metamodels of two objective functions are constructed using radial basis functions (RBF). Finally, multi-objective optimization is carried out with NSGA-II algorithm to generate Pareto front with the best tradeoff between two objective functions. The optimal results demonstrate that some Pareto front results of two objective functions are both improved compared to original design, and multi-objective optimization can elevate the compound performance of accelerometer structures.

We show how an exploratory tool for association rule mining can be used for efficient multi-objective optimization of marketing campaigns for companies within the fashion retail industry. We have earlier designed and implemented a novel digital tool for mining of association rules from given basket data. The tool supports efficient finding of frequent itemsets over multiple hierarchies and interactive visualization of corresponding association rules together with numerical attributes. Normally when optimizing a marketing campaign, factors that cause an increased level of activation among the recipients could in fact reduce the profit, i.e., these factors need to be balanced, rather than optimized individually. Using the tool we can identify important factors that influence the search for an optimal campaign in respect to both activation and profit. We show empirical results from a real-world case-study using campaign data from a well-established company within the fashion retail industry, demonstrating how activation and profit can be simultaneously targeted, using computer-generated algorithms as well as human-controlled visualization.