scholarly journals An Optimal Classification Method for Biological and Medical Data

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Yao-Huei Huang ◽  
Yu-Chien Ko ◽  
Hao-Chun Lu
Keyword(s):  
Global Optimum ◽  
Medical Data ◽  
Classification Method ◽  
Mixed Integer ◽  
Nonlinear Program ◽  
Piecewise Linearization ◽  
Linearization Technique ◽  
Numerical Examples ◽  
Optimal Classification

This paper proposes a union of hyperspheres by the mixed-integer nonlinear program to classify biological and medical datasets. A classifying program with nonlinear terms uses piecewise linearization technique to obtain a global optimum. The numerical examples illustrate that the proposed method can obtain the global optimum more effectively than current methods.

scholarly journals Design Optimization of a Speed Reducer Using Deterministic Techniques

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Ming-Hua Lin ◽  
Jung-Fa Tsai ◽  
Nian-Ze Hu ◽  
Shu-Chuan Chang
Keyword(s):  
Programming Problem ◽  
Design Problem ◽  
Geometric Programming ◽  
Global Optimum ◽  
Mixed Integer ◽  
Piecewise Linearization ◽  
Design Problems ◽  
Acceptable Error ◽  
Generalized Geometric Programming ◽  
Speed Reducer

The optimal design problem of minimizing the total weight of a speed reducer under constraints is a generalized geometric programming problem. Since the metaheuristic approaches cannot guarantee to find the global optimum of a generalized geometric programming problem, this paper applies an efficient deterministic approach to globally solve speed reducer design problems. The original problem is converted by variable transformations and piecewise linearization techniques. The reformulated problem is a convex mixed-integer nonlinear programming problem solvable to reach an approximate global solution within an acceptable error. Experiment results from solving a practical speed reducer design problem indicate that this study obtains a better solution comparing with the other existing methods.

Transit Planning Optimization Under Ride-Hailing Competition and Traffic Congestion

2021 ◽  
Author(s):  
Keji Wei ◽  
Vikrant Vaze ◽  
Alexandre Jacquillat
Keyword(s):  
New York ◽  
Traffic Congestion ◽  
Service Providers ◽  
Public Transit ◽  
Mixed Integer ◽  
Nonlinear Program ◽  
Transit Planning ◽  
Planning Optimization ◽  
Transit Ridership ◽  
Transit Agencies

With the soaring popularity of ride-hailing, the interdependence between transit ridership, ride-hailing ridership, and urban congestion motivates the following question: can public transit and ride-hailing coexist and thrive in a way that enhances the urban transportation ecosystem as a whole? To answer this question, we develop a mathematical and computational framework that optimizes transit schedules while explicitly accounting for their impacts on road congestion and passengers’ mode choice between transit and ride-hailing. The problem is formulated as a mixed integer nonlinear program and solved using a bilevel decomposition algorithm. Based on computational case study experiments in New York City, our optimized transit schedules consistently lead to 0.4%–3% system-wide cost reduction. This amounts to rush-hour savings of millions of dollars per day while simultaneously reducing the costs to passengers and transportation service providers. These benefits are driven by a better alignment of available transportation options with passengers’ preferences—by redistributing public transit resources to where they provide the strongest societal benefits. These results are robust to underlying assumptions about passenger demand, transit level of service, the dynamics of ride-hailing operations, and transit fare structures. Ultimately, by explicitly accounting for ride-hailing competition, passenger preferences, and traffic congestion, transit agencies can develop schedules that lower costs for passengers, operators, and the system as a whole: a rare win–win–win outcome.

scholarly journals Integration of Mixed-Integer Nonlinear Program and Project Management Tool to Support Sustainable Cost-Optimal Construction Scheduling

2021 ◽  
Vol 13 (21) ◽  
pp. 12173
Author(s):  
Borna Dasović ◽  
Uroš Klanšek
Keyword(s):  
Project Management ◽  
Optimal Schedule ◽  
Indirect Costs ◽  
Management Tool ◽  
Mixed Integer ◽  
Task Completion ◽  
Nonlinear Program ◽  
Project Schedule ◽  
Construction Scheduling ◽  
Optimal Construction

This paper presents the integration of mixed-integer nonlinear program (MINLP) and project management tool (PMT) to support sustainable cost-optimal construction scheduling. An integrated structure of a high-level system for exact optimization and PMT was created. To ensure data compatibility between the optimization system and PMT and to automate the process of obtaining a cost-optimal schedule, a data transformation tool (DTT) was developed within a spreadsheet application. The suggested system can determine: (i) an optimal project schedule with associated network diagram and Gantt chart in continuous or discrete time units; (ii) optimal critical and non-critical activities, including their early start, late start, early finish, late finish along with total and free slack times; and (iii) minimum total project cost along with the allocation of direct and indirect costs. The system provides functionalities such as: (i) MINLP can be updated, and schedules can be re-optimized; (ii) the optimal schedule can be saved as a baseline to track changes; (iii) different optimization algorithms can be engaged whereby switching between them does not require model changes; (iv) PMT can be used to track task completion in the optimized schedule; (v) calendar settings can be changed; and (vi) visual reports can be generated to support efficient project management. Results of cost-optimal project scheduling are given in a conventional PMT environment, which raises the possibility that the proposed system will be more widely used in practice. Integration of MINLP and PMT allows each software to be used for what it was initially designed. Their combination leads to additional information and features of optimized construction schedules that would be significantly more difficult to achieve if used separately. Application examples are given in the paper to show the advantages of the proposed approach.

scholarly journals Optimal Operation of Critical Peak Pricing for an Energy Retailer Considering Balancing Costs

Energies ◽  
2019 ◽  
Vol 12 (24) ◽  
pp. 4658
Author(s):  
Hye Yoon Song ◽  
Gyu Sub Lee ◽  
Yong Tae Yoon
Keyword(s):  
Linear Programming ◽  
Deterministic Model ◽  
Renewable Energy Sources ◽  
Storage System ◽  
Energy Storage System ◽  
Global Optimum ◽  
Mean Value ◽  
Optimal Operation ◽  
Mixed Integer ◽  
Peak Pricing

Recently, there have been frequent fluctuations in the wholesale prices of electricity following the increased penetration of renewable energy sources. Therefore, retailers face price risks caused by differences between wholesale prices and retail rates. As a hedging against price risk, retailers can utilize critical peak pricing (CPP) in a price-based program. This study proposes a novel multi-stage stochastic programming (MSSP) model for a retailer with self-generation photovoltaic facility to optimize both its bidding strategy and the CPP operation, in the face of several uncertainties. Using MSSP, decisions can be determined sequentially with realization of the uncertainties over time. Furthermore, to ensure a global optimum, a mixed integer non-linear programming is transformed into mixed integer linear programming through three linearization steps. In a numerical simulation, the effectiveness of the proposed MSSP model is compared with that of a mean-value deterministic model based on a rolling horizon method. We also investigate the optimal strategy of a retailer by changing various input parameters and perform a sensitivity analysis to assess the impacts of different uncertain parameters on the retailer’s profit. Finally, the effect of the energy storage system on the proposed optimization problem is investigated.

scholarly journals Research on Two-stage Order Picking Sequencing for Intensive Shelf

2019 ◽  
Vol 296 ◽  
pp. 02003
Author(s):  
Xue Tian ◽  
Li Zhou ◽  
Jianglong Yang
Keyword(s):  
Mathematical Model ◽  
Global Optimum ◽  
Order Picking ◽  
Storage Space ◽  
Time Cost ◽  
Two Stage ◽  
Numerical Examples ◽  
Stage Order ◽  
Waiting Cost ◽  
The Law

The increasingly usage of Intensive shelves, greatly increase the utilization of storage space, but also is more demanding on order picking time . Based on the storage layout of intensive mobile shelves, this paper combines the time cost of shelf movement with the moving distance under the guidance of seeking global optimum. Transform the single order picking process into TSP problem, while considering the picking process. The waiting cost of the order, and the minimum of the picking cost and the waiting cost of the whole batch of orders requiring shelf movement, to establish a two-stage mathematical model of the order picking order. Then, the algorithm for solving the model is designed, and the simulation is carried out by numerical examples to illustrate the law and characteristics of the problem more vividly, in order to provide reference and reference for the order picking activities of intensive mobile shelves.

Flexible Synthesis of Heat Exchanger Network with Particle Swarm Optimization Algorithm

2011 ◽  
Vol 214 ◽  
pp. 569-572 ◽  
Author(s):  
Xio Ling Zhang ◽  
Hong Chao Yin ◽  
Zhao Yi Huo
Keyword(s):  
Particle Swarm Optimization ◽  
Heat Exchanger ◽  
Operating Cost ◽  
Particle Swarm ◽  
Optimal Solution ◽  
Mixed Integer ◽  
Optimization Approach ◽  
Nonlinear Program ◽  
Heat Exchanger Network ◽  
Swarm Optimization

In this paper, the flexible synthesis problem for heat exchanger network(HEN) is formulated to a mixed integer nonlinear program(MINLP) model. The objection function of the model consists of two components: First, a candidate HEN structure has to satisfy flexible criterion during input span. Second, a minimized annual cost consisting of investment cost and operating cost is investigated. The solution strategy based on particle swarm optimization(PSO) algorithm is proposed to obtain the optimal solution of the presented model. Finally, a four streams example is investigated to show the advantage of the whole proposed optimization approach.

scholarly journals A Robust Formulation Model for Multi-Period Failure Restoration Problems in Integrated Energy Systems

Energies ◽  
2019 ◽  
Vol 12 (19) ◽  
pp. 3673
Author(s):  
Chen ◽  
Lou ◽  
Guo
Keyword(s):  
Natural Disasters ◽  
High Efficiency ◽  
Storage System ◽  
Energy Systems ◽  
Mixed Integer ◽  
Level Energy ◽  
Piecewise Linearization ◽  
Integrated Energy Systems ◽  
Failure Restoration ◽  
Robust Formulation

The risks faced by modern energy systems are increasing, primarily caused by natural disasters. As a new form of multi-level energy complimentary utilization, integrated energy systems are attracting more and more attention for their high-efficiency and low-cost. However, due to the deep coupling relationship between systems, they are more susceptible to natural disasters, resulting in a cascading failure. To enhance the resilience of the integrated electricity-gas system, this paper proposes a failure restoration strategy after a natural disaster occurs. First, the temporal constraints of the dispatching model are considered, and the failure restoration problem is molded into a multi-period mixed-integer linear programme, aiming to recover the interrupted loads as much as possible. Second, since the uncertain output of distributed generation sources (DGs) such as wind turbines and photovoltaic systems will threat the reliability of restoration results, the robust formulation model is incorporated to cope with this problem. Third, we propose a new modeling method for radial topology constraints towards failure restoration. Moreover, the Column and Constraints Generation (C&CG) decomposition method is utilized to solve the robust model. Then, the piecewise linearization technique and the linear DistFlow equations are utilized to eliminate the nonlinear terms, providing a model that could be easily solved by an off-shelf commercial solver. The obtained results include the sequence of line/pipeline switchgear actions, the time-series dispatching results of electricity storage system, gas storage system, and the coupling devices including the gas-fired turbine, power to gas equipment. Finally, the effectiveness of the proposed restoration strategy is verified by numerical simulation on a 13-6 node integrated energy system.

scholarly journals An MI-SDP Model for Optimal Location and Sizing of Distributed Generators in DC Grids That Guarantees the Global Optimum

2020 ◽  
Vol 10 (21) ◽  
pp. 7681 ◽  
Author(s):  
Walter Gil-González ◽  
Alexander Molina-Cabrera ◽  
Oscar Danilo Montoya ◽  
Luis Fernando Grisales-Noreña
Keyword(s):  
Nonlinear Programming ◽  
Optimization Problem ◽  
System Analysis ◽  
Programming Model ◽  
Classical Problem ◽  
Distribution Networks ◽  
Global Optimum ◽  
Optimal Location ◽  
Mixed Integer ◽  
Distributed Generators

This paper deals with a classical problem in power system analysis regarding the optimal location and sizing of distributed generators (DGs) in direct current (DC) distribution networks using the mathematical optimization. This optimization problem is divided into two sub-problems as follows: the optimal location of DGs is a problem, with those with a binary structure being the first sub-problem; and the optimal sizing of DGs with a nonlinear programming (NLP) structure is the second sub-problem. These problems originate from a general mixed-integer nonlinear programming model (MINLP), which corresponds to an NP-hard optimization problem. It is not possible to provide the global optimum with conventional programming methods. A mixed-integer semidefinite programming (MI-SDP) model is proposed to address this problem, where the binary part is solved via the branch and bound (B&B) methods and the NLP part is solved via convex optimization (i.e., SDP). The main advantage of the proposed MI-SDP model is the possibility of guaranteeing a global optimum solution if each of the nodes in the B&B search is convex, as is ensured by the SDP method. Numerical validations in two test feeders composed of 21 and 69 nodes demonstrate that in all of these problems, the optimal global solution is reached by the MI-SDP approach, compared to the classical metaheuristic and hybrid programming models reported in the literature. All the simulations have been carried out using the MATLAB software with the CVX tool and the Mosek solver.

A Mixed Integer Nonlinear Program Based Power Load Estimator for Distribution Grid

2020 ◽  
Vol 14 (1) ◽  
pp. 842-851
Author(s):  
Yu Yang ◽  
Hen-Geul Yeh ◽  
Son H. Doan
Keyword(s):  
Mixed Integer ◽  
Nonlinear Program ◽  
Distribution Grid ◽  
Power Load
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