Establishing a Lymphatic Venous Anastomotic Training Model in Pig Trotters

Background Lymphatic venous anastomosis (LVA) is a widely accepted surgical procedure for lymphedema. To obtain the best outcomes, surgeons should be well trained. A recent study introduced an LVA training model using pig trotters for their utility and structural similarity to human tissues. However, details regarding the utilization of anastomosis models, such as feasible points for training based on vessel anatomy, have not been clarified. Therefore, we assessed the anatomical details of lymphatic vessels and veins of trotters to establish a practical training model of LVA. Methods Ten frozen trotters were used. After thawing at room temperature, indocyanine green fluorescent lymphography was used to visualize the lymphatic course. To dissect the lymphatic vessels and veins from the distal to the proximal end, whole skins were detached thoroughly from the plantar side. Data from the lymphatic vessels and veins were collected based on their courses, diameters, and layouts to clarify adjacent points feasible for LVA training. Results Both lymphatic vessels and veins were classified into four major courses: dorsal, medial, lateral, and plantar. The majority were dorsal vessels, both lymphatic vessels and veins. The adjacent points were always found in the distal dorsum center and were especially concentrated between the metacarpophalangeal (MP) joint and central interphalangeal crease, followed by the medial and lateral sides. Conclusion The most relevant point for LVA surgical training in the trotter was the dorsal center distal to the MP joint, where parallel vessels of similar sizes were found in all cases. This practical LVA surgical model would improve surgeon skills in not only anastomosis but also preoperative fluorescent lymphography.

Handling of Constraints in Efficient Global Optimization

Although the Efficient Global Optimization (EGO) algorithm has been widely used in multi-disciplinary optimization, it is still difficult to handle multiple constraint problems. In this study, to increase the accuracy of approximation, the Least Squares Support Vector Regression (LSSVR) is suggested to replace the kriging model for approximating both objective and constrained functions while the variances of these surrogate models are still obtained by kriging. To enhance the ability to search the feasible region, two criteria are suggested. First, a Maximize Probability of Feasibility (MPF) strategy to handle the infeasible initial sample points is suggested to generate feasible points. Second, a Multi-Constraint Parallel (MCP) criterion is suggested for multiple constraints handling, parallel computation and validation, respectively. To illustrate the efficiency of the suggested EGO-based method, several deterministic benchmarks are tested and the suggested methods demonstrate a superior performance compared with two other constrained algorithms. Finally, the suggested algorithm is successfully utilized to optimize the fiber path of variable-stiffness beam and lightweight B-pillar to demonstrate the performance for engineering applications.

Computing Feasible Points of Bilevel Problems with a Penalty Alternating Direction Method

Bilevel problems are highly challenging optimization problems that appear in many applications of energy market design, critical infrastructure defense, transportation, pricing, and so on. Often these bilevel models are equipped with integer decisions, which makes the problems even harder to solve. Typically, in such a setting in mathematical optimization, one develops primal heuristics in order to obtain feasible points of good quality quickly or to enhance the search process of exact global methods. However, there are comparably few heuristics for bilevel problems. In this paper, we develop such a primal heuristic for bilevel problems with a mixed-integer linear or quadratic upper level and a linear or quadratic lower level. The heuristic is based on a penalty alternating direction method, which allows for a theoretical analysis. We derive a convergence theory stating that the method converges to a stationary point of an equivalent single-level reformulation of the bilevel problem and extensively test the method on a test set of more than 2,800 instances—which is one of the largest computational test sets ever used in bilevel programming. The study illustrates the very good performance of the proposed method in terms of both running times and solution quality. This renders the method a suitable subroutine in global bilevel solvers as well as a reasonable standalone approach. Summary of Contribution: Bilevel optimization problems form a very important class of optimization problems in the field of operations research, which is mainly due to their capability of modeling hierarchical decision processes. However, real-world bilevel problems are usually very hard to solve—especially in the case in which additional mixed-integer aspects are included in the modeling. Hence, the development of fast and reliable primal heuristics for this class of problems is very important. This paper presents such a method.

Self-Regulating Artificial-Free Linear Programming Solver Using a Jump and Simplex Method

An enthusiastic artificial-free linear programming method based on a sequence of jumps and the simplex method is proposed in this paper. It performs in three phases. Starting with phase 1, it guarantees the existence of a feasible point by relaxing all non-acute constraints. With this initial starting feasible point, in phase 2, it sequentially jumps to the improved objective feasible points. The last phase reinstates the rest of the non-acute constraints and uses the dual simplex method to find the optimal point. The computation results show that this method is more efficient than the standard simplex method and the artificial-free simplex algorithm based on the non-acute constraint relaxation for 41 netlib problems and 280 simulated linear programs.

A Fixed-Point Subgradient Splitting Method for Solving Constrained Convex Optimization Problems

In this work, we consider a bilevel optimization problem consisting of the minimizing sum of two convex functions in which one of them is a composition of a convex function and a nonzero linear transformation subject to the set of all feasible points represented in the form of common fixed-point sets of nonlinear operators. To find an optimal solution to the problem, we present a fixed-point subgradient splitting method and analyze convergence properties of the proposed method provided that some additional assumptions are imposed. We investigate the solving of some well known problems by using the proposed method. Finally, we present some numerical experiments for showing the effectiveness of the obtained theoretical result.

Improved regularity assumptions for partial outer convexification of mixed-integer PDE-constrained optimization problems

Partial outer convexification is a relaxation technique for MIOCPs being constrained by time-dependent differential equations. Sum-Up-Rounding algorithms allow to approximate feasible points of the relaxed, convexified continuous problem with binary ones that are feasible up to an arbitrarily smallδ> 0. We show that this approximation property holds for ODEs and semilinear PDEs under mild regularity assumptions on the nonlinearity and the solution trajectory of the PDE. In particular, requirements of differentiability and uniformly bounded derivatives on the involved functions from previous work are not necessary to show convergence of the method.

AUTOMATING BACKHOE OPERATION USING FUZZY LOGIC

During the past decade, automation has significantly increased in all forms of engineering. With the fast-paced research and development in automation, it is expected that automation will be commonplace and many operations will be performed using robots. Automation of heavy construction equipment is in its early stages. Attempts are persistently made to push the frontiers of science and technology to automate heavy equipment but, limited progress has been made. This research presents a fuzzy logic modeling approach for moving a back-hoe bucket from a fill point to a dump point. The fuzzy logic model is designed to accept all feasible points formed by boom and stick movements in 3D space. Inputs to the model are coordinates of fill and dump spots, as well as stick and boom dimensions. The model provides output signals to automate the bucket movement by swinging the bucket, lowering (or raising) boom, and stretching (or retracting) stick. The paper also includes three site scenarios to demonstrate the performance of the model. The three scenarios are varied from a very basic to a very complex maneuver. All three scenarios are tested for error, and the errors are within acceptable limits.