Scheduling in parallel machines with two objectives: analysis of factors that influence the Pareto frontier

This paper explores the characteristics of solutions when scheduling jobs in a shop with parallel machines. Three classical objective functions were considered: makespan, total completion time, and total tardiness. These three criteria were combined in pairs, resulting in three bi-objective formulations. These formulations were solved using the ε-constraint method to obtain a Pareto frontier for each pair. The objective of the research is to evaluate the Pareto set of efficient schedules to characterize the solution sets. The characterization of the solutions sets is based on two performance metrics: the span of the objective functions' values for the points in the frontier and their closeness to the ideal point. Results that consider four experimental factors indicate that when the makespan is one of the objective functions, the range of the processing times among jobs has a significant influence on the characteristics of the Pareto frontier. Simultaneously, the slack of due dates is the most relevant factor when total tardiness is considered.

On Multi-Objective Minimum Spanning Tree Problem under Uncertain Paradigm

Minimum spanning tree problem (MSTP) has allured many researchers and practitioners due to its varied range of applications in real world scenarios. Modelling these applications involves the incorporation of indeterminate phenomena based on their subjective estimations. Such phenomena can be represented rationally using uncertainty theory. Being a more realistic variant of MSTP, in this article, based on the principles of the uncertainty theory, we have studied a multi-objective minimum spanning tree problem (MMSTP) with indeterminate problem parameters. Subsequently, two uncertain programming models of the proposed uncertain multi-objective minimum spanning tree problem (UMMSTP) are developed and their corresponding crisp equivalence models are investigated, and eventually solved using a classical multi-objective solution technique, the epsilon-constraint method. Additionally, two multi-objective evolutionary algorithms (MOEAs), non-dominated sorting genetic algorithm II (NSGAII) and duplicate elimination non-dominated sorting evolutionary algorithm (DENSEA) are also employed as solution methodologies. With the help of the proposed UMMSTP models, the practical problem of optimizing the distribution of petroleum products was solved, consisting in the search for symmetry (balance) between the transportation cost and the transportation time. Thereafter, the performance of the MOEAs is analyzed on five randomly developed instances of the proposed problem.

A single foot-mounted pedestrian navigation algorithm based on maximum gait displacement constraint in three-dimensional space

Inertial navigation technology composed of inertial sensors is widely used in foot-mounted pedestrian positioning. However, inertial sensors are susceptible to noise, which affects the performance of the system. The zero-velocity update (ZUPT) as a traditional method is utilized to suppress the cumulative error. Unfortunately, the walking distance calculated by a Kalman filter still has position error. To improve the positioning accuracy, a nonlinear Kalman filter with spatial distance inequality constraint for single foot is proposed in this work. Since the stride distance between adjacent stance phases has an upper bound in plane and height, an inertial navigation system (INS) established by one inertial measurement unit (IMU) is adopted to constrain the stride process. Eventually, the performance of the proposed method is verified by experiments. Compared to the single foot-mounted ZUPT method, the proposed method suppresses the plane error and the height error by 46.04% and 65.48%, respectively. For the dual foot constraint method, the proposed constraint method can reduce the number of sensors while ensuring the positioning accuracy. Moreover, the height error is reduced by 59.98% on average by optimizing the constraint algorithm. The experimental results show that the trajectory estimated by the proposed method is closer to the actual path.

Existence of multiple nontrivial solutions of the nonlinear Schrödinger-Korteweg-de Vries type system

In this paper we are concerned with the existence, nonexistence and bifurcation of nontrivial solution of the nonlinear Schrödinger-Korteweg-de Vries type system(NLS-NLS-KdV). First, we find some conditions to guarantee the existence and nonexistence of positive solution of the system. Second, we study the asymptotic behavior of the positive ground state solution. Finally, we use the classical Crandall-Rabinowitz local bifurcation theory to get the nontrivial positive solution. To get these results we encounter some new challenges. By combining the Nehari manifolds constraint method and the delicate energy estimates, we overcome the difficulties and find the two bifurcation branches from one semitrivial solution. This is an new interesting phenomenon but which have not previously been found.

Exact Zoning Optimization Model for Marine Spatial Planning (MSP)

Marine spatial planning (MSP) has recently attracted more attention as an efficient decision support tool. MSP is a strategic and long-term process gathering multiple competing users of the ocean with the objective to simplify decisions regarding the sustainable use of marine resources. One of the challenges in MSP is to determine an optimal zone to locate a new activity while taking into account the locations of the other existing activities. Most approaches to spatial zoning are formulated as non-linear optimization models involving multiple objectives, which are usually solved using stochastic search algorithms, leading to sub-optimal solutions. In this paper, we propose to model the problem as a Multi-Objective Integer Linear Program. The model is developed for raster data and it aims at maximizing the interest of the area of the zone dedicated to the new activity while maximizing its spatial compactness. We study two resolution methods: first, a weighted-sum of the two objectives, and second, an interactive approach based on an improved augmented version of the ϵ-constraint method, AUGMECON2. To validate and study the model, we perform experiments on artificially generated data. Our experimental study shows that AUGMECON2 represents the most promising approach in terms of relevance and diversity of the solutions, compactness, and computation time.

Multiple positive solutions for a class of Kirchhoff type equations with indefinite nonlinearities

We study the following Kirchhoff type equation: − a + b ∫ R N | ∇ u | 2 d x Δ u + u = k ( x ) | u | p − 2 u + m ( x ) | u | q − 2 u in R N , $$\begin{equation*}\begin{array}{ll} -\left(a+b\int\limits_{\mathbb{R}^{N}}|\nabla u|^{2}\mathrm{d}x\right)\Delta u+u =k(x)|u|^{p-2}u+m(x)|u|^{q-2}u~~\text{in}~~\mathbb{R}^{N}, \end{array} \end{equation*}$$ where N=3, a , b > 0 $ a,b \gt 0 $ , 1 < q < 2 < p < min { 4 , 2 ∗ } $ 1 \lt q \lt 2 \lt p \lt \min\{4, 2^{*}\} $ , 2≤=2N/(N − 2), k ∈ C (ℝ N ) is bounded and m ∈ L p/(p−q)(ℝ N ). By imposing some suitable conditions on functions k(x) and m(x), we firstly introduce some novel techniques to recover the compactness of the Sobolev embedding H 1 ( R N ) ↪ L r ( R N ) ( 2 ≤ r < 2 ∗ ) $ H^{1}(\mathbb{R}^{N})\hookrightarrow L^{r}(\mathbb{R}^{N}) (2\leq r \lt 2^{*}) $ ; then the Ekeland variational principle and an innovative constraint method of the Nehari manifold are adopted to get three positive solutions for the above problem.

Research on Building DSM Fusion Method Based on Adaptive Spline and Target Characteristic Guidance

In order to adapt to the actual scene of a stereo satellite observing the same area sequentially and improve the accuracy of the target-oriented 3D reconstruction, this paper proposed a building DSM fusion update method based on adaptive splines and target characteristic guidance. This method analyzed the target characteristics of surface building targets to explore their intrinsic geometric structure information, established a nonlinear fusion method guided by the target characteristics to achieve the effective fusion of multiple DSMs on the basis of maintaining the target structural characteristics, and supported the online updating of DSM to ensure the needs of practical engineering applications. This paper presented a DSM fusion method for surface building targets and finally conducted DSM fusion experiments using typical urban area images of different scenes. The experimental results showed that the proposed method can effectively constrain and improve the DSM of buildings, and the integrity of the overall construction of the target 3D model structure was significantly improved, indicating that this paper provides an effective and efficient DSM constraint method for buildings.