This paper addresses a non-smooth multi-objective semi-infinite programming problem that involves a feasible set defined by inequality constraints‎. ‎Our focus is on introducing a new weak Slater constraint qualification and deriving the necessary and sufficient conditions for (weakly‎, ‎properly) efficient solutions to the problem using (weak and strong) Karush-Kuhn-Tucker types‎. ‎Additionally‎, ‎we present two duals of the Mond-Weir type for the problem and provide (weak and strong) duality results for them‎. ‎All of the results are given in terms of Clarke subdifferential‎.

A bridge vibration measurement method by Unmanned Aerial Vehicles (UAVs) based on a Convolutional Neural Network (CNN) and Bayesian Optimization (BO) is proposed. In the proposed method, the video of the bridge structure is collected by a UAV, then the reference points in the background of the bridge and the target points on the bridge in the video are tracked by the Kanade-Lucas-Tomasi (KLT) optical flow method, so that their coordinates can be obtained. The BO is used to find the optimal hyper-parameter combination of a CNN, and the CNN based on BO is used to correct the bridge displacement signal collected by the UAV. Finally, the natural frequency of the bridge is extracted by processing the corrected displacement signals with Operational Modal Analysis (OMA). Moreover, a steel truss is used as the experimental model. The number of reference points and the shooting time of the UAV with the optimal correction effect of the BO-based CNN are obtained by two groups of comparative experiments, and the influence of the distance between structure and reference points on the correction effect of the BO-based CNN is determined by another group of comparative experiment. The static reference points are not required for the proposed method, which evidently enhances the applicability of UAVs; the conclusion of this paper has great guiding significance for the actual bridge vibration measurement.

The sewer layout in flat areas significantly influences the construction and operational costs as well as reliability of the network performance. To find an optimum design of sewer networks for flat areas, this study presents a multi-objective optimization problem with the objective functions of 1- the cost and 2- the reliability. The reliability criterion is defined as the effect of a clogging in a sewer on its upstream population. To solve the problem, the NSGA-II Algorithm is coupled to two self-adaptive design algorithms for generating the layout and sizing of sewers. A case study is solved using the proposed model to demonstrate its application and advantages.

A multiobjective security game problem with fuzzy payoffs is studied in this paper. The problem is formulated as a bilevel programming problem with fuzzy coefficients. Using the idea of nearest interval approximation of fuzzy numbers, the problem is transformed into a bilevel programming problem with interval coefficients. The Karush-Kuhn-Tucker conditions is applied then to reduce the problem to an interval multiobjective single-level problem. It is shown that the solutions of this problem are obtained by solving a single-objective programming problem. Validity and applicability of the method are illustrated by a practical example.

Generally, an engineering design problem has multiple objective functions. Some of these problems can be formulated as multiobjective geometric programming models. On the other hand, often in the real world, coefficients of the objective functions are not known precisely. Coefficients may be interpreted as fuzzy numbers, which lead to a multiobjective geometric programming with fuzzy parameters. In this paper, we solve the multiobjective geometric programming problem with fuzzy parameters by applying a linear ranking function. The linear ranking function is used to compare fuzzy numbers. Finally, a numerical example is given.