检索结果-内蒙古大学图书馆

Derivative-free methods for mixed-integer nonsmooth constrained optimization

COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2022年第2期82卷 293-327页

作者： Giovannelli, Tommaso Liuzzi, Giampaolo Lucidi, Stefano Rinaldi, Francesco Lehigh Univ Dept Ind & Syst Engn Bethlehem PA USA Sapienza Univ Roma Dipartimento Ingn Informat Automat & Gest Rome Italy Ist Anal Sistemi & Informat IASI CNR Rome Italy Univ Padua Dipartimento Matemat Tullio Levi Civita Padua Italy

In this paper, mixed-integer nonsmooth constrained optimization problems are considered, where objective/constraint functions are available only as the output of a black-box zeroth-order oracle that does not provide derivative information. A new derivative-free linesearch-based algorithmic framework is proposed to suitably handle those problems. First, a scheme for bound constrained problems that combines a dense sequence of directions to handle the nonsmoothness of the objective function with primitive directions to handle discrete variables is described. Then, an exact penalty approach is embedded in the scheme to suitably manage nonlinear (possibly nonsmooth) constraints. Global convergence properties of the proposed algorithms toward stationary points are analyzed and results of an extensive numerical experience on a set of mixed-integer test problems are reported.

关键词： Derivative-free optimization Nonsmooth optimization mixed-integer nonlinear programming

来源：评论

学校读者我要写书评

暂无评论

A two-time-level model for mission and flight planning of an inhomogeneous fleet of unmanned aerial vehicles

引用

COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2023年第1期85卷 293-335页

作者： Schmidt, Johannes Fuegenschuh, Armin Brandenburg Univ Technol Cottbus Senftenberg Pl Deutsch Einheit 1 D-03046 Cottbus Germany

We consider the mission and flight planning problem for an inhomogeneous fleet of unmanned aerial vehicles (UAVs). Therein, the mission planning problem of assigning targets to a fleet of UAVs and the flight planning problem of finding optimal flight trajectories between a given set of waypoints are combined into one model and solved simultaneously. Thus, trajectories of an inhomogeneous fleet of UAVs have to be specified such that the sum of waypoint-related scores is maximized, considering technical and environmental constraints. Several aspects of an existing basic model are expanded to achieve a more detailed solution. A two-level time grid approach is presented to smooth the computed trajectories. The three-dimensional mission area can contain convex-shaped restricted airspaces and convex subareas where wind affects the flight trajectories. Furthermore, the flight dynamics are related to the mass change, due to fuel consumption, and the operating range of every UAV is altitude-dependent. A class of benchmark instances for collision avoidance is adapted and expanded to fit our model and we prove an upper bound on its objective value. Finally, the presented features and results are tested and discussed on several test instances using GUROBI as a state-of-the-art numerical solver.

关键词： mixed-integer nonlinear programming Mission planning Inhomogeneous fleet Time windows Linearization methods

来源：评论

学校读者我要写书评

暂无评论

Integrative decision on new product development in configurable product family

引用

EUROPEAN JOURNAL OF INDUSTRIAL ENGINEERING 2024年第2期18卷 191-224页

作者： Ziaei, Mazaher Ketabi, Saeedeh Ghandehari, Mahsa Univ Isfahan Dept Management Esfahan Iran

Intensified competition leads companies to integrate decision-making on design, supply, and marketing policies for the new product development (NPD). This integration is more substantial for the manufacturers of configurable product families (CPF) such as cars. This study aims to develop a profit-maximisation model to concurrently optimise all main variables of configuration selection, components' supply policy, price, modules' warranty length, and launch time for NPD in CPF. The proposed model is a mixed-integer nonlinear program and is solved through an adapted differential evolution (DE) algorithm. Different numerical cases extracted from one automobile company are studied, and sensitivity analysis on the main parameters is performed. The results approve the significant effects of integrative decision-making based on new variables on the profit. Due to the diversity of the decision variables, the model can be applied in a wide range of situations. Furthermore, considering more realistic assumptions helps to achieve more practical solutions and applicable results.

关键词： configurable product family modules' warranty length launch time mixed-integer nonlinear programming differential evolution DE algorithm

来源：评论

学校读者我要写书评

暂无评论

Evaluation of isoflavone extraction options at commercial scale

引用

BIOFUELS BIOPRODUCTS & BIOREFINING-BIOFPR 2022年第6期16卷 1708-1725页

作者： Chea, John D. Lehr, Austin L. Stanzione, Joseph F. Yenkie, Kirti M. Rowan Univ Henry M Rowan Coll Engn Dept Chem Engn Glassboro NJ 08028 USA

Resource sustainability concerns keep increasing owing to the continuous use of natural materials without reclamation. Efforts are ongoing to find sustainable feedstocks for naturally derived products with competitive economics and properties. However, there is no established methodology for commercializing the extraction of chemicals from renewable sources. This work examined soybeans as a potential bio-based feedstock to generate isoflavones at a commercial scale. The isoflavone content in soybeans has proven beneficial in the nutraceuticals industry for its anti-inflammatory and cancer-inhibition properties and in the materials sector owing to their inherent chemical functionality and thermal resistance. Currently, isoflavone extraction is only optimized at lab scale. Thus, we present a superstructure-based framework to screen isoflavone extraction methods and assess their viability at a commercial scale. This allows the simultaneous comparison of alternative technologies using mixed-integer nonlinear programming optimization to determine the most economical pathway. Internal material recovery greatly enhances the viability at a commercial scale by reducing the annual operating cost and environmental footprint. Therefore, this work presents a powerful tool for systematically comparing extraction pathways and assessing their commercial feasibility. The successful implementation of commercial-scale extraction of isoflavone has tremendous potential for generating additional revenue for US soy farmers. Isoflavones can produce bio-based polymers and composites and are used in products such as dietary supplements, cosmetics and nutraceuticals. Similar works can be applied to extract other natural materials from renewable feedstocks and increase the production of bio-based products. (c) 2022 Society of Chemical Industry and John Wiley & Sons, Ltd.

关键词： phytoestrogens extraction mixed-integer nonlinear programming optimization

来源：评论

学校读者我要写书评

暂无评论

Global optimization methods for the discrete network design problem

引用

TRANSPORTATION RESEARCH PART B-METHODOLOGICAL 2013年第Apr.期50卷 42-60页

作者： Wang, Shuaian Meng, Qiang Yang, Hai Univ Wollongong Sch Math & Appl Stat Wollongong NSW 2522 Australia Natl Univ Singapore Dept Civil & Environm Engn Singapore 117576 Singapore Hong Kong Univ Sci & Technol Dept Civil & Environm Engn Kowloon Hong Kong Peoples R China

This paper addresses the discrete network design problem (DNDP) with multiple capacity levels, or multi-capacity DNDP for short, which determines the optimal number of lanes to add to each candidate link in a road network. We formulate the problem as a bi-level programming model, where the upper level aims to minimize the total travel time via adding new lanes to candidate links and the lower level is a traditional Wardrop user equilibrium (UE) problem. We propose two global optimization methods by taking advantage of the relationship between UE and system optimal (SO) traffic assignment principles. The first method, termed as SO-relaxation, exploits the property that an optimal network design solution under SO principle can be a good approximate solution under UE principle, and successively sorts the solutions in the order of increasing total travel time under SO principle. Optimality is guaranteed when the lower bound of the total travel time of the unexplored solutions under UE principle is not less than the total travel time of a known solution under UE principle. The second method, termed as UE-reduction, adds the objective function of the Beckmann-McGuire-Winsten transformation of UE traffic assignment to the constraints of the SO-relaxation formulation of the multi-capacity DNDP. This constraint is convex and strengthens the SO-relaxation formulation. We also develop a dynamic outer-approximation scheme to make use of the state-of-the-art mixed-integer linear programming solvers to solve the SO-relaxation formulation. Numerical experiments based on a two-link network and the Sioux-Falls network are conducted. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： Discrete network design problem Bi-level programming Traffic equilibrium Network optimization mixed-integer nonlinear programming

来源：评论

学校读者我要写书评

暂无评论

GLOBAL OPTIMIZATION ALGORITHMS FOR CHIP LAYOUT AND COMPACTION

引用

ENGINEERING OPTIMIZATION 1995年第2期25卷 131-154页

作者： DORNEICH, MC SAHINIDIS, NV UNIV ILLINOIS DEPT MECH & IND ENGN URBANA IL 61801 USA

The package planning (chip layout and compaction) problem can be stated in terms of an optimization problem. The goal is to find the relative placement and shapes of the chips in a way that minimizes the total chip area subject to linear and nonlinear constraints. The constraints arise from geometric design rules, distance and connectivity requirements between various components, area and communication costs and other designer-specified requirements. The problem has been addressed in various settings. It is of unusual computational difficulty due to the nonconvexities involved. This paper presents a new mixed-integer nonlinear programming formulation for simultaneous chip layout and two-dimensional compaction. Global optimization algorithms are developed for this model as well as for an existing formulation for the chip compaction problem. These algorithms are implemented with the global optimization software BARON and illustrated by solving several example problems.

关键词： CHIP LAYOUT AND COMPACTION PACKAGE PLANNING BRANCH-AND-REDUCE mixed-integer nonlinear programming

来源：评论

学校读者我要写书评

暂无评论

Inversion of convection-diffusion equation with discrete sources

引用

OPTIMIZATION AND ENGINEERING 2021年第3期22卷 1419-1457页

作者： Sharma, Meenarli Hahn, Mirko Leyffer, Sven Ruthotto, Lars Waanders, Bart van Bloemen Indian Inst Technol Powai 400076 Maharashtra India Otto von Guericke Univ Univ Pl 2 Magdeburg Germany Argonne Natl Lab 9700 South Cass Ave Lemont IL 50439 USA Emory Univ 400 Dowman Dr Atlanta GA 30322 USA Sandia Natl Labs POB 5800 Albuquerque NM 87185 USA

We present a convection-diffusion inverse problem that aims to identify an unknown number of sources and their locations. We model the sources using a binary function, and we show that the inverse problem can be formulated as a large-scale mixed-integer nonlinear optimization problem. We show empirically that current state-of-the-art mixed-integer solvers cannot solve this problem and that applying simple rounding heuristics to solutions of the relaxed problem can fail to identify the correct number and location of the sources. We develop two new rounding heuristics that exploit the value and a physical interpretation of the continuous relaxation solution, and we apply a steepest-descent improvement heuristic to obtain satisfactory solutions to both two- and three-dimensional inverse problems. We also provide the code used in our numerical experiments in open-source format.

关键词： mixed-integer optimization PDE-constrained optimization mixed-integer nonlinear programming Source inversion

来源：评论

学校读者我要写书评

暂无评论

Solving mixed-integer nonlinear optimization problems using simultaneous convexification: a case study for gas networks

引用

JOURNAL OF GLOBAL OPTIMIZATION 2021年第2期80卷 307-340页

作者： Liers, Frauke Martin, Alexander Merkert, Maximilian Mertens, Nick Michaels, Dennis Friedrich Alexander Univ Erlangen Nurnberg Dept Math Cauerstr 11 D-91058 Erlangen Germany Otto von Guericke Univ Dept Math Univ Pl 2 D-39106 Magdeburg Germany Tech Univ Dortmund Fac Math Dortmund Germany

Solving mixed-integer nonlinear optimization problems (MINLPs) to global optimality is extremely challenging. An important step for enabling their solution consists in the design of convex relaxations of the feasible set. Known solution approaches based on spatial branch-and-bound become more effective the tighter the used relaxations are. Relaxations are commonly established by convex underestimators, where each constraint function is considered separately. Instead, a considerably tighter relaxation can be found via so-called simultaneous convexification, where convex underestimators are derived for more than one constraint function at a time. In this work, we present a global solution approach for solving mixed-integer nonlinear problems that uses simultaneous convexification. We introduce a separation method that relies on determining the convex envelope of linear combinations of the constraint functions and on solving a nonsmooth convex problem. In particular, we apply the method to quadratic absolute value functions and derive their convex envelopes. The practicality of the proposed solution approach is demonstrated on several test instances from gas network optimization, where the method outperforms standard approaches that use separate convex relaxations.

关键词： mixed-integer nonlinear programming Simultaneous convexification Convex envelope Gas network optimization

来源：评论

学校读者我要写书评

暂无评论

A COMPARISON BETWEEN MILP AND MINLP APPROACHES TO OPTIMAL SOLUTION OF nonlinear DISCRETE TRANSPORTATION PROBLEM

引用

TRANSPORT 2015年第2期30卷 135-144页

作者： Klansek, Uros Univ Maribor Fac Civil Engn Maribor Slovenia

Finding an exact optimal solution of the nonlinear Discrete Transportation Problem (NDTP) represents a challenging task in transportation science. Development of an adequate model formulation and selection of an appropriate optimization method are thus significant for attaining valuable solution of the NDTP. When nonlinearities appear within the criterion of optimization, the NDTP can be formulated directly as a mixed-integer nonlinear programming (MINLP) task or it can be linearized and converted into a mixed-integer Linear programming (MILP) problem. This paper presents a comparison between MILP and MINLP approaches to exact optimal solution of the NDTP. The comparison is based on obtained results of experiments executed on a set of reference test problems. The paper discusses advantages and limitations of both optimization approaches.

关键词： transportation problems discrete transporting flows nonlinear costs optimization methods mixed-integer linear programming mixed-integer nonlinear programming

来源：评论

学校读者我要写书评

暂无评论

Sensitivity-Based Approaches for Handling Discrete Variables in Optimal Power Flow Computationse

引用

IEEE TRANSACTIONS ON POWER SYSTEMS 2010年第4期25卷 1780-1789页

作者： Capitanescu, Florin Wehenkel, Louis Univ Liege Dept Elect Engn & Comp Sci B-4000 Liege Belgium

This paper proposes and compares three iterative approaches for handling discrete variables in optimal power flow (OPF) computations. The first two approaches rely on the sensitivities of the objective and inequality constraints with respect to discrete variables. They set the discrete variables values either by solving a mixed-integer linear programming (MILP) problem or by using a simple procedure based on a merit function. The third approach relies on the use of Lagrange multipliers corresponding to the discrete variables bound constraints at the OPF solution. The classical round-off technique and a progressive round-off approach have been also used as a basis of comparison. We provide extensive numerical results with these approaches on four test systems with up to 1203 buses, and for two OPF problems: loss minimization and generation cost minimization, respectively. These results show that the sensitivity-based approach combined with the merit function clearly outperforms the other approaches in terms of: objective function quality, reliability, and computational times. Furthermore, the objective value obtained with this approach has been very close to that provided by the continuous relaxation OPF. This approach constitutes therefore a viable alternative to other methods dealing with discrete variables in an OPF.

关键词： Discrete variables mixed-integer linear programming mixed-integer nonlinear programming nonlinear programming optimal power flow

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：