Many-Objective Optimization and Decision-Making Method for Selective Assembly of Complex Mechanical Products Based on Improved NSGA-III and VIKOR

In Industry 4.0, data are sensed and merged to drive intelligent systems. This research focuses on the optimization of selective assembly of complex mechanical products (CMPs) under intelligent system environment conditions. For the batch assembly of CMPs, it is difficult to obtain the best combinations of components from combinations for simultaneous optimization of success rate and multiple assembly quality. Hence, the Taguchi quality loss function was used to quantitatively evaluate each assembly quality and the assembly success rate is combined to establish a many-objective optimization model. The crossover and mutation operators were improved to enhance the ability of NSGA-III to obtain high-quality solution set and jump out of a local optimal solution, and the Pareto optimal solution set was obtained accordingly. Finally, considering the production mode of Human–Machine Intelligent System interaction, the optimal compromise solution is obtained by using fuzzy theory, entropy theory and the VIKOR method. The results show that this work has obvious advantages in improving the quality of batch selective assembly of CMPs and assembly success rate and gives a sorting selection strategy for non-dominated selective assembly schemes while taking into account the group benefit and individual regret.

Sparse Solutions of a Class of Constrained Optimization Problems

In this paper, we consider a well-known sparse optimization problem that aims to find a sparse solution of a possibly noisy underdetermined system of linear equations. Mathematically, it can be modeled in a unified manner by minimizing [Formula: see text] subject to [Formula: see text] for given [Formula: see text] and [Formula: see text]. We then study various properties of the optimal solutions of this problem. Specifically, without any condition on the matrix A, we provide upper bounds in cardinality and infinity norm for the optimal solutions and show that all optimal solutions must be on the boundary of the feasible set when [Formula: see text]. Moreover, for [Formula: see text], we show that the problem with [Formula: see text] has a finite number of optimal solutions and prove that there exists [Formula: see text] such that the solution set of the problem with any [Formula: see text] is contained in the solution set of the problem with p = 0, and there further exists [Formula: see text] such that the solution set of the problem with any [Formula: see text] remains unchanged. An estimation of such [Formula: see text] is also provided. In addition, to solve the constrained nonconvex non-Lipschitz Lp-L1 problem ([Formula: see text] and q = 1), we propose a smoothing penalty method and show that, under some mild conditions, any cluster point of the sequence generated is a stationary point of our problem. Some numerical examples are given to implicitly illustrate the theoretical results and show the efficiency of the proposed algorithm for the constrained Lp-L1 problem under different noises.

On a second-order differential inclusion with certain integral and multi-strip boundary conditions

We study a second-order differential inclusion with integral and multi-strip boundary conditions defined by a set-valued map with nonconvex values. We obtain an existence result and we prove the arcwise connectedness of the solution set of the considered problem.

Compressor Profile Optimization Based on Hybrid Intelligent Algorithm

In order to improve the working characteristics of the scroll compressor, according to the scroll profile of the compressor, the energy efficiency ratio (EER) of the scroll compressor is taken as the objective function, and the number of scroll turns N and knots are determined based on the genetic annealing algorithm. The distance p, the height of the scroll body h, and the thickness of the scroll profile t are optimized. In the optimized solution set, three sets of optimized profile and initial profile are selected for theoretical calculation of thermodynamic characteristics and volume characteristics, and the specific influence of scroll compressor profile parameters on compressor characteristics is explored in detail, and compared with the unoptimized scroll. The initial parameters of the rotary compressor are compared with the theoretical performance. The results show that the pitch p has a significant effect on the energy efficiency ratio and discharge volume of the scroll compressor, and the number of scroll turns N has a significant effect on the characteristic of suction volume. Three kinds of optimized scroll profile parameters S2, S3, S4 are selected in the optimal solution set. Compared with the initial value S1, the working characteristics are improved. The energy efficiency ratio was increased by 38.10%, 42.58%, and 50.26%; the suction volume was increased by 66.1%, 82.3%, and 73.9%; the exhaust volume was increased by 21.1%, 29.6%, and 50%; the internal volume ratio was increased by 36.4%. 40.9%, 27.3%. It is proved that the use of genetic annealing algorithm achieves the purpose of improving the compressor's operating characteristics.

On a structure of the set of positive solutions to second-order equations with a super-linear non-linearity

We study the existence and multiplicity of positive solutions to the periodic problem u ′′ = p ⁢ ( t ) ⁢ u - q ⁢ ( t , u ) ⁢ u + f ⁢ ( t ) ; u ⁢ ( 0 ) = u ⁢ ( ω ) , u ′ ⁢ ( 0 ) = u ′ ⁢ ( ω ) , u^{\prime\prime}=p(t)u-q(t,u)u+f(t);\quad u(0)=u(\omega),\quad u^{\prime}(0)=u^{\prime}(\omega), where p , f ∈ L ⁢ ( [ 0 , ω ] ) p,f\in L([0,\omega]) and q : [ 0 , ω ] × R → R q\colon[0,\omega]\times\mathbb{R}\to\mathbb{R} is a Carathéodory function. By using the method of lower and upper functions, we show some properties of the solution set of the considered problem and, in particular, the existence of a minimal positive solution.

Barrier Solutions of Elliptic Differential Equations in Musielak-Orlicz-Sobolev Spaces

In this paper, we study the solution set of the following Dirichlet boundary equation: − div a 1 x , u , D u + a 0 x , u = f x , u , D u in Musielak-Orlicz-Sobolev spaces, where a 1 : Ω × ℝ × ℝ N ⟶ ℝ N , a 0 : Ω × ℝ ⟶ ℝ , and f : Ω × ℝ × ℝ N ⟶ ℝ are all Carathéodory functions. Both a 1 and f depend on the solution u and its gradient D u . By using a linear functional analysis method, we provide sufficient conditions which ensure that the solution set of the equation is nonempty, and it possesses a greatest element and a smallest element with respect to the ordering “≤,” which are called barrier solutions.

Quantum-inspired firefly algorithm integrated with cuckoo search for optimal path planning

The firefly algorithm and cuckoo search are the meta-heuristic algorithms efficient to determine the solution for the searching and optimization problems. The current work proposes an integrated concept of quantum-inspired firefly algorithm with cuckoo search (IQFACS) that adapts both algorithms’ expedient attributes to optimize the solution set. In the IQFACS algorithm, the quantum-inspired firefly algorithm (QFA) ensures the diversification of fireflies-based generated solution set using the superstitions quantum states of the quantum computing concept. The cuckoo search (CS) algorithm uses the Lévy flight attribute to escape the QFA from the premature convergence and stagnation stage more effectively than the quantum principles. Here, the proposed algorithm is applied for the application of optimal path planning. Before using the proposed algorithm for path planning, the algorithm is tested on different optimization benchmark functions to determine the efficacy of the proposed IQFACS algorithm than the firefly algorithm (FA), CS, and hybrid FA and CS algorithm. Using the proposed IQFACS algorithm, path planning is performed on the satellite images with vegetation as the focused region. These satellite images are captured from Google Earth and belong to the different areas of India. Here, satellite images are converted into morphologically processed binary images and considered as maps for path planning. The path planning process is also executed with the FA, CS, and QFA algorithms. The performance of the proposed algorithm and other algorithms are accessed with the evaluation of simulation time and the number of cycles to attain the shortest path from defined source to destination. The error rate measure is also incorporated to analyze the overall performance of the proposed IQFACS algorithm over the other algorithms.