Homotopy continuation enhanced branch and bound algorithms for strongly nonconvex mixed-integer nonlinear optimization

Large-scale strongly nonlinear and nonconvex mixed-integer nonlinear programming (MINLP) models frequently appear in optimization-based process synthesis, integration, intensification, and process control. However, they are usually difficult to solve by existing algorithms within acceptable time. In this study, we propose two robust homotopy continuation enhanced branch and bound (HCBB) algorithms (denoted as HCBB-FP and HCBB-RB) where the homotopy continuation method is employed to gradually approach the optimum of the NLP subproblem at a node from the solution at its parent node. A variable step length is adapted to effectively balance feasibility and computational efficiency. The computational results from solving four existing process synthesis problems demonstrate that the proposed HCBB algorithms can find the same optimal solution from different initial points, while the existing MINLP algorithms fail or find much worse solutions. In addition, HCBB-RB is superior to HCBB-FP due to much lower computational effort required for the same locally optimal solution.     

基于分支定界法的相控阵雷达事件调度算法

为解决相控阵雷达事件调度问题中调度成功率、时间偏移率与算法时效性三者之间的矛盾，本文提出一种基于分支定界法的调度算法；该算法首先在现有调度结果上调取所有可执行事件，即获得若干"节点"，多步递推后由多"层"节点形成若干条备选"分支"，扩大解空间范围，提高算法性能；然后通过"删减"操作删减掉收益较低分支，将解空间控制在一适当范围内，减小搜索盲目性，降低算法计算量.仿真实验表明，与基于综合优先级算法的调度结果相比，利用本文算法调度时调度成功率提升了52%；与基于时间指针算法的调度结果相比，本身算法时间偏移率降低了61%；与基于遗传算法的调度结果相比，本文算法调度耗时仅为前者1~2%.     

Determination of a suitable index for a solvent via two-column extractive distillation using a heuristic method

The traditional approach to solvent selection in the extractive distillation process strictly focuses on the change in the relative volatility of light-heavy components induced by the solvent. However, the total annual cost of the process may not be minimal when the solvent induces the largest change in relative volatility. This work presents a heuristic method for selecting the optimal solvent to minimize the total annual cost. The functional relationship between the relative volatility and the total annual cost is established, where the main factors, such as the relative volatility of the light-heavy components and the relative volatility of the heavy-component solvent, are taken into account. Binary azeotropic mixtures of methanol-toluene and methanol-acetone are separated to verify the feasibility of the model. The results show that using the solvent with the minimal two-column extractive distillation index, the process achieves a minimal total annual cost. The method is conducive for sustainable advancements in chemistry and engineering because a suitable solvent can be selected without simulation verification.     

p-Median and p-dispersion problems: A bi-criteria analysis

Given a collection of n locations and a symmetric measure of distance (difference) between each pair of locations, we seek to identify (select) a subset of p locations so as to achieve two distinct objectives. The first objective is to use the selected locations as centers (medians) of p groups that would partition the entire collection and minimize the total distance between the locations and their respective group medians. The second objective is to maximize the minimum distance (diversity) among the selected locations themselves. We study this problem as a multi-objective optimization problem and propose an iterative algorithm to obtain its non-dominated frontier. At each iteration we construct and solve a 0–1 integer programming problem. Through a computational experiment we show that this algorithm is computationally effective for small to medium size instances of the problem. We also propose a Lagrangian heuristic algorithm for solving larger instances of this problem.     

An optimization algorithm for the workforce management in a retail chain

This work proposes a scheduling problem for the workforce management in a chain of supermarkets operating in Italy. We focus on determining the ideal mix of full-time and part-time workers which are needed every week to guarantee a satisfactory service level during the check-out operations. The generation of working shifts, to be assigned to retail workers, is subject to several constraints imposed by both labour laws and enterprise bargaining agreements.We present a mathematical formulation of the problem followed by an exact solution approach which relies on the definition of feasible daily working shifts. The number of feasible daily shifts, that are combined to determine feasible weekly shifts, could drastically increase, depending on the selected planning interval. In addition, there may exist additional constraints, that are difficult to incorporate into the mathematical model. For these reasons, a hybrid heuristic, which does not require the generation of all feasible weekly shifts, is proposed in this paper.Using appropriate statistical techniques, a sensitivity analysis is performed to test the design of the hybrid heuristic. Computational tests are carried out by solving several real instances provided by the retail firm. The results obtained by the heuristic are compared both with an exact approach and with the solutions adopted by the retail company, which have been determined by using a naïf approach. Our hybrid heuristic exhibits excellent performance finding optimal or near optimal solutions in a very limited CPU time.     

基于弱变异准则的测试用例约简方法

针对为数较多的测试用例增加了回归测试成本的问题，提出一种基于弱变异准则的测试用例约简方法。首先，基于弱变异准则获得测试用例和变异分支关系矩阵；然后，重复约简4种无效测试需求和子集测试用例；最后，结合人工鱼群算法选择当前最优测试用例，并且交替执行简化和测试用例选择操作直至覆盖所有测试需求。该方法针对6个经典程序与贪心算法和HGS算法相比，基于弱变异准则并且不改变或稍微改变变异评分的条件下，约简率分别提高了73.4%和8.2%，且耗时分别降低了25.3%和56.1%。实验结果表明，所提方法在回归测试中可有效约简测试用例，降低测试代价。     

An energy-efficient two-stage hybrid flow shop scheduling problem in a glass production

Energy-efficient scheduling is highly necessary for energy-intensive industries, such as glass, mould or chemical production. Inspired by a real-world glass-ceramics production process, this paper investigates a bi-criteria energy-efficient two-stage hybrid flow shop scheduling problem, in which parallel machines with eligibility are at stage 1 and a batch machine is at stage 2. The performance measures considered are makespan and total energy consumption. Time-of-use (TOU) electricity prices and different states of machines (working, idle and turnoff) are integrated. To tackle this problem, a mixed integer programming (MIP) is formulated, based on which an augmented ε-constraint (AUGMECON) method is adopted to obtain the exact Pareto front. A problem-tailored constructive heuristic method with local search strategy, a bi-objective tabu search algorithm and a bi-objective ant colony optimisation algorithm are developed to deal with medium- and large-scale problems. Extensive computational experiments are conducted, and a real-world case is solved. The results show effectiveness of the proposed methods, in particular the bi-objective tabu search.     

新型树启发式搜索算法的机器人路径规划

面对三维空间移动机器人从起始点到终止点的最短路径问题,提出一种新型的边缘点树启发式搜索(TreeEP)算法,该方法将地图空间进行密度可调的三维离散化处理,根据障碍安全距离筛选出障碍物的可靠边缘点信息,再利用树扩散架构选出最能引导搜索方向的潜力点进行扩散搜索,最终得出最短路径。提出局部调整策略,得到改进的Tree-EP算法。实验结果表明,在带障碍复杂地形最短路径搜索应用中,提出的Tree-EP算法与已有方法相比,能找到更短的移动路径。     

A fast branch,bound and remember algorithm for disassembly line balancing problem

In recent years, the interests of disassembly line have increased owing to economic reasons and the increase of environmental awareness. Effective line can provide many advantages in terms of economic aspect and it facilitates competition the companies with others. This study contributes to the relevant literature by a branch, bound and remember algorithm for disassembly line balancing problem with AND/OR precedence. The proposed exact solution method employs the memory-based dominance rule to eliminate the reduplicated sub-problems by storing all the searched sub-problems and to utilise cyclic best-first search strategy to obtain high-quality complete solutions fast. In this paper, minimising the number of stations is taken as the performance measure. The proposed methodology is tested on a set of 260 instances and compared with the mathematical model using CPLEX solver and five well-known metaheuristics. Computational results show that the proposed method is capable of obtaining the optimal solutions for all the tested instances with less than 0.1?seconds on average. Additionally, comparative study demonstrates that the proposed method is the state-of-the-art algorithm and outperforms the CPLEX solver and metaheuristics in terms of both solution quality and search speed aspects.     

Efficient recursive least squares parameter estimation algorithm for accurate nanoCMOS variable gain amplifier performances

ABSTRACT

With the aggressive scaling of integrated circuit technology, parametric estimation is a critical task for designers who looked for solutions to the challenges of some Nanoscale CMOS parameters. This paper presented the prediction of primary parameters of CMOS transistor for 16 nm to 10 nm process nodes using both of Bisquare Weights (BW) method and a novel recursive least squares (RLS) parameter estimation algorithm. The proposed RLS algorithm consists of the minimisation of a quadratic criterion relating to the prediction error in order to attain the best estimated parameters of the developed mathematical model. The obtained results thanks to the proposed RLS algorithm were better than those reached using the BW method. Comparisons between Predictive Technology Model (PTM) data and parameters estimated with RLS algorithm were made to check the validity and the consistency of the proposed algorithm. These predicted primary parameters were helpful to estimate and to optimise the performances of the Variable Gain Amplifier (VGA) which was a basic circuit element with a key role in the design of new upcoming receivers.