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An Improved Bernstein Global Optimization Algorithm for MINLP Problems with Application in Process Industry

MATHEMATICS IN COMPUTER SCIENCE 2014年第3-4期8卷 357-377页

作者： Patil, Bhagyesh V. Nataraj, P. S. V. Lab Informat Nantes Atlant BP 92208 F-44322 Nantes France Indian Inst Technol Syst & Control Engn Grp Bombay 400076 Maharashtra India

We present an improved Bernstein global optimization algorithm to solve polynomial mixed-integer nonlinear programming (MINLP) problems. The algorithm is of branch-and-bound type, and uses the Bernstein form of the polynomials for the global optimization. The new ingredients in the algorithm include a modified subdivision procedure, a vectorized Bernstein cut-off test and a new branching rule for the decision variables. The performance of the improved algorithm is tested and compared with earlier reported Bernstein global optimization algorithm (to solve polynomial MINLPs) and with several state-of-the-art MINLP solvers on a set of 19 test problems. The results of the tests show the superiority of the improved algorithm over the earlier reported Bernstein algorithm and the state-of-the-art solvers in terms of the chosen performance metrics. Similarly, efficacy of the improved algorithm in handling a real-world MINLP problem is brought out via a trim-loss minimization problem from the process industry.

关键词： Bernstein polynomials Branch-and-bound Global optimization mixed-integer nonlinear programming Trim-loss problem

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An Analysis of Decision to Retrofit Coal Based Power Plant with Carbon Capture Technology Having Uncertain Parameters

An Analysis of Decision to Retrofit Coal Based Power Plant w...

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IEEE International Conference on Industrial Engineering and Engineering Management (IEEM)

作者： Kumari, Shalini Bera, Sasadhar Indian Inst Management Ranchi Dept Operat Management Ranchi Bihar India

ISBN: (纸本)9781538672204

The increasing industrialization since its inception has drawn attention towards the impact of industrial activities on the global environment. The increasing concern of global warming and rising earth's temperature has driven the institution of the Paris Agreement to examine the threshold limit of emission of carbon dioxide, which is the major component of greenhouse gases (GHG). Carbon capture and storage (CCS) technologies play a vital role in achieving net-zero carbon emission. The motivation behind this paper is to review the execution of CCS innovation in thermal power plants with the help of a mixed-integer nonlinear programming model. The problem of uncertainty of emission information in the thermal power plant is solved using the fuzzy technique. The results presented here demonstrate the option of selection of technology in a coalfired power plant.

关键词： Carbon capture and storage Fuzzy optimization Greenhouse gases mixed-integer nonlinear programming

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A Hybrid Tabu Search Heuristic for a Bilevel Competitive Facility Location Model

A Hybrid Tabu Search Heuristic for a Bilevel Competitive Fac...

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7th International Workshop on Hybrid Metaheuristics

作者： Kucukaydin, Hande Aras, Necati Altinel, I. Kuban Bogazici Univ Dept Ind Eng Istanbul Turkey

ISBN: (纸本)9783642160530

We consider a problem in which a firm or franchise enters a market by locating new facilities where there are existing facilities belonging to a competitor. The firm aims at finding the location and attractiveness of each facility to be opened so as to maximize its profit. The competitor, on the other hand, can react by adjusting the attractiveness of its existing facilities, opening new facilities and/or closing existing ones with the objective of maximizing its own profit. The demand is assumed to be aggregated at certain points in the plane and the facilities of the firm can be located at prespecified candidate sites. We employ Huff's gravity-based rule in modeling the behavior of the customers where the fraction of customers at a demand point that visit a certain facility is proportional to the facility attractiveness and inversely proportional to the distance between the facility site and demand point. We formulate a bilevel mixed-integer nonlinear programming model where the firm entering the market is the leader and the competitor is the follower. In order to find a feasible solution of this model, we develop a hybrid tabu search heuristic which makes use of two exact methods as subroutines: a gradient ascent method and a branch-and-bound algorithm with nonlinear programming relaxation.

关键词： Tabu search competitive facility location bilevel programming mixed-integer nonlinear programming

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Improving sustainability in a two-level pharmaceutical supply chain through Vendor-Managed Inventory system

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OPERATIONS RESEARCH FOR HEALTH CARE 2019年 21卷 44-55页

作者： Weraikat, Dua Zanjani, Masoumeh Kazemi Lehoux, Nadia Rochester Inst Technol Dubai Dept Mech & Ind Engn POB 341055 Dubai U Arab Emirates Concordia Univ Dept Mech & Ind Engn Montreal PQ H3G 1M8 Canada Univ Laval Dept Genie Mecan Quebec City PQ G1V 0A6 Canada

Hospitals, as the main customers of medications, typically adopt conservative inventory control policies by keeping large quantities of drugs in stock. Given the perishable nature of medications, such strategies lead to the expiration of excess inventory in the absence of patients' demand. Consequently, producers are faced with governmental penalties and environmental reputation forfeit due to the negative impact that disposing expired medications pose to the environment. This article aims to improve the sustainability of a pharmaceutical supply chain using a real case study. An analytical model is proposed to explore the effect of implementing a Vendor-Managed Inventory (VMI) system in minimizing the quantity of the expired medications at hospitals. Further, a set of Monte-Carlo simulation tests are conducted to investigate the robustness of the VMI model under demand uncertainty. Experimental results on a real case study under deterministic demand show the efficiency of the VMI model in eliminating the amount of expired medications without compromising customer's satisfaction. The results also demonstrate that the safety stock (SS) level and the capacity assigned to the customer are crucial factors in the overall cost of the pharmaceutical supply chain (PSC). The PSC cost could be reduced by 19% when reducing the SS level by 50%. Moreover, the producer is recommended to increase the capacity assigned to the customer by a factor of 1.5 so as to fully satisfy the customer's demand. Finally, the simulation results confirm the efficiency and robustness of embracing a VMI system under random demand scenarios. More precisely, zero amount of expired medications is obtained in 93% of cases. Thus, adopting this strategy could minimize drug wastage and ultimately improve the reputation of the producer in the market in terms of implementing Lean and sustainable practices. (C) 2019 Elsevier Ltd. All rights reserved.

关键词： Supply Chain Vendor-Managed Inventory Pharmaceutical Industry mixed-integer nonlinear programming

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Mitigating Anomalies in Parallel Branch-and-Bound Based Algorithms for mixed-integer nonlinear Optimization 7th

Mitigating Anomalies in Parallel Branch-and-Bound Based Algo...

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7th International Symposium on Combinatorial Optimization (ISCO)

作者： Palkar, Prashant Mahajan, Ashutosh Univ Augsburg Inst Math D-86159 Augsburg Germany Indian Inst Technol Ind Engn & Operat Res Mumbai 400076 India

ISBN: (纸本)9783031185298;9783031185304

We address detrimental anomalies in parallel versions of two state-of-the-art algorithms for convex mixed-integer nonlinear programs (MINLPs): nonlinear branch-and-bound (NLP-BB) and the LP/NLP based branch-and-bound (QG). A detrimental anomaly is when a parallel algorithm performs worse than its sequential counterpart. Unambiguous node selection functions have been developed in the past to avoid these anomalies. We extend this notion of unambiguity to subroutines for branching and generating linearization cuts. We implement the proposed unambiguous branching and cut generation strategies alongside unambiguous node selection in NLP-BB and QG in the open-source MINLP solver Minotaur. Our computational experiments on convex instances from the MINLPLib library show that detrimental anomalies can be reduced to a great extent in practical algorithms. We also compare these algorithms with opportunistic parallel versions. Our results highlight that opportunistic versions perform better in terms of wall clock times, while the deterministic versions avoid detrimental anomalies with theoretically established guarantees and also provide reproducible results, a feature that is desirable while developing parallel algorithms. We recommend settings in Minotaur that yield opportunistic or deterministic runs for the parallel NLP-BB and QG algorithms.

关键词： mixed-integer nonlinear programming Parallel branch-and-bound Anomalies LP/NLP based branch-and-bound

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Discrete flow pooling problems in coal supply chains 21

Discrete flow pooling problems in coal supply chains

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21st International Congress on Modelling and Simulation (MODSIM) held jointly with the 23rd National Conference of the Australian-Society-for-Operations-Research / DSTO led Defence Operations Research Symposium (DORS

作者： Boland, N. Kalinowski, T. Rigterink, F. Georgia Inst Technol H Milton Stewart Sch Ind & Syst Engn Atlanta GA 30332 USA Univ Newcastle Sch Math & Phys Sci Callaghan NSW Australia

ISBN: (纸本)9780987214355

The pooling problem is a nonconvex nonlinear programming problem (NLP) with applications in the refining and petrochemical industries, but also the coal mining industry. The problem can be stated as follows: given a set of raw material suppliers (inputs) and qualities of the supplies, find a cost-minimising way of blending these raw materials in intermediate pools and outputs so as to satisfy requirements on the output qualities. The blending in two stages (in pools and outputs) introduces bilinear constraints. The pooling problem can alternatively be described as a minimum cost network flow problem with additional bilinear constraints to capture the blending of raw materials. In this paper we study a variation of the pooling problem that arises naturally in the coal mining industry and is sometimes referred to as grade targeting. Coal is made-to-order according to customers' desired product qualities. Deviations from these target qualities result in contractually agreed bonuses and penalties. In the pooling problem variation we study, costs are associated with these bonuses and penalties instead of network flows. While in the original pooling problem we have hard bounds on the qualities and unmet demand is penalised in the objective function, in our coal mining variation we have hard demand constraints and deviations from target qualities are penalised. This makes finding a feasible solution easy, while in the pooling problem finding a nontrivial feasible solution that satisfies the quality requirements is already hard. An implication of this is that we are able to solve larger problem instances than those typically studied in the pooling problem literature. To model the coal blending process accurately, we define a time-expanded network where the intermediate pools represent coal stockpiles over time. Since coal is transported in large quantities, we study the trade-off between continuous and discretized flows in coal blending, i.e., solving a continuous flow prob

关键词： Coal blending pooling problem mixed-integer nonlinear programming mixed-integer linear programming

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Security-Constrained Energy Management System for Microgrids Under Uncertainty

Security-Constrained Energy Management System for Microgrids...

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IEEE PES Transmission and Distribution Conference and Exhibition - Latin America (T and D LA)

作者： Alves da Silva, Jessica Alice Lopez, Juan Camilo Arias, Nataly Banol Rider, Marcos Julio Pereira da Silva, Luiz Carlos Univ Estadual Campinas Dept Syst & Energy DSE UNICAMP Campinas SP Brazil

ISBN: (纸本)9781728141558

This paper presents a stochastic mixed-integer nonlinear programming model (MINLP) for the security-constrained energy management system (EMS) of microgrids under demand and renewable generation uncertainties. Considering a balanced single-phase representation of the network, the proposed MINLP model is transformed into a mixed-integer second-order cone programming (MISOCP) model that can be solved via off-the-shelf convex programming solvers. The proposed formulation considers photovoltaic (PV) generation, energy storage systems (ESS), direct load control (DLC) and a diesel generator (genset), which can be turned on when the microgrid is operating in isolated mode. The proposed model minimizes the average operational costs for the day-ahead scheduling. Constraints consider the operation in either grid-connected or isolated mode due to a predefined set of plausible contingencies, hence the term security-constrained. The proposed model is tested using data of the real microgrid Laboratory of Intelligent Electrical Networks (LabREI), located at the UNICAMP facilities. Results show that the proposed model is suitable for real-world applications since it provides cost-efficient and contingency-robust solutions.

关键词： Microgrids mixed-integer nonlinear programming mixed-integer second-order cone programming security-constrained energy management system

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The two-level strategy for MINLP synthesis of process flowsheets under uncertainty

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COMPUTERS & CHEMICAL ENGINEERING 2000年第2-7期24卷 195-201页

作者： Pintaric, ZN Kravanja, Z Univ Maribor Fac Chem & Chem Engn SI-2000 Maribor Slovenia

This paper presents a two-level strategy for stochastic synthesis of chemical processes under uncertainty with a fixed degree of flexibility by using the mixed-integer nonlinear programming (MINLP) approach. The objective is to develop an automated and robust strategy which could handle nontrivial optimization problems (about 1000 equations and variables with a considerable number of uncertain parameters - up to 30) that, at the present, cannot be solved in a reasonable period of time by using rigorous stochastic optimization methods. To accomplish the task, the nonlinear subproblems at fixed structures have been decomposed into design and operating optimization levels, the former being facilitated by using a direct search method and the latter by using the reduced dimensional stochastic procedure. Two examples are presented to illustrate the robustness and efficiency of the proposed strategy at solving medium- and large-scale problems. (C) 2000 Elsevier Science Ltd. All rights reserved.

关键词： mixed-integer nonlinear programming synthesis process two-stage two level uncertainty flexibility

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A genetic algorithm to integrate a comprehensive dynamic cellular manufacturing system with aggregate planning decisions

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INTERNATIONAL JOURNAL OF MANAGEMENT SCIENCE AND ENGINEERING MANAGEMENT 2020年第2期15卷 138-154页

作者： Kia, Reza German Univ Technol GUtech Fac Business & Econ Dept Logist Tourism & Serv Management Muscat Iran Islamic Azad Univ Dept Ind Engn Firoozkooh Branch Firoozkooh Iran

In this paper, to design a Cellular Manufacturing System (CMS) under a dynamic situation and make Aggregate Planning (AP) decisions simultaneously, a mixed-integer nonlinear programming (MINLP) model is designed. The distinctive features of the comprehensive Dynamic CMS (DCMS) model under consideration are: i) an extensive coverage of significant manufacturing characteristics in designing a DCMS in addition to the main strategies of AP, ii) integration of cost elements addressing structural, operational and planning issues in the design of DCMS, and iii) capable of developing better DCMS design decisions by incorporating more detailed and realistic parameters when compared to the literature. An illustrative numerical example is solved by CPLEX 12.6 to demonstrate the achievements obtained by the integrated model. Since the proposed model belongs to NP-hard category, a Genetic Algorithm (GA) improved by an elaborately designed matrix-based chromosome representation to represent all decision variables, as well as a sequential procedure generating initial solutions is developed. Several test problems either generated randomly or taken from the literature with various sizes are solved and the results are compared with the solutions gained using CPLEX solver. The comparisons results show that the designed GA is capable of evolving optimal or near-optimal solutions with relative gap less than 1% in a computationally satisfactory manner.

关键词： Dynamic cellular manufacturing system mixed-integer nonlinear programming aggregate planning genetic algorithm

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Power System Restoration Planning with Standing Phase Angle and Voltage Difference Constraints

Power System Restoration Planning with Standing Phase Angle ...

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2014 Power Systems Computation Conference (PSCC)

作者： Mak, Terrence W. K. Coffrin, Carleton Van Hentenryck, Pascal Hiskens, Ian A. Hill, David NICTA Sydney NSW Australia Univ Melbourne Melbourne Vic 3010 Australia Australian Natl Univ Canberra ACT 0200 Australia Univ Michigan Ann Arbor MI 48109 USA Univ Hong Kong Central Hong Kong Peoples R China

ISBN: (纸本)9788393580132

This paper considers the restoration of a transmission system after a significant disruption such as a natural disaster. It considers the Restoration Order Problem (ROP) that jointly considers generator dispatch, load pickups, and restoration prioritization to minimize the size of the blackout while satisfying the network operational constraints. The paper examines transient effects in power restoration and generalizes the ROP formulation with standing phase angle and voltage difference constraints in order to minimize rotor swings. Case studies indicated that the novel ROP-SPASVD formulation reduces rotor swings of synchronous generators by over 50%, while having a negligible impact on the blackout size (i.e., <= 1.5% increase), which is still optimized holistically.

关键词： Power System Restoration Standing Phase Angle Generator Dynamics DC Power Flow LPAC Power Flow mixed-integer nonlinear programming

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