scholarly journals SOLVING THE NONLINEAR DISCRETE TRANSPORTATION PROBLEM BY MINLP OPTIMIZATION

Transport ◽  
2013 ◽  
Vol 29 (1) ◽  
pp. 1-11 ◽  
Author(s):  
Uroš Klanšek
Keyword(s):  
Transportation Problem ◽  
Optimization Problems ◽  
Relaxation Method ◽  
Optimization Method ◽  
Critical Issue ◽  
Branch And Cut ◽  
Mixed Integer ◽  
Cut Method ◽  
Optimum Solution ◽  
Selection Of

The Nonlinear Discrete Transportation Problem (NDTP) belongs to the class of the optimization problems that are generally difficult to solve. The selection of a suitable optimization method by which a specific NDTP can be appropriately solved is frequently a critical issue in obtaining valuable results. The aim of this paper is to present the suitability of five different Mixed-Integer Nonlinear Programming (MINLP) methods, specifically for the exact optimum solution of the NDTP. The evaluated MINLP methods include the extended cutting plane method, the branch and reduce method, the augmented penalty/outer-approximation/equality-relaxation method, the branch and cut method, and the simple branch and bound method. The MINLP methods were tested on a set of NDTPs from the literature. The gained solutions were compared and a correlative evaluation of the considered MINLP methods is shown to demonstrate their suitability for solving the NDTPs.

scholarly journals SOLVING THE NONLINEAR TRANSPORTATION PROBLEM BY GLOBAL OPTIMIZATION

Transport ◽  
2010 ◽  
Vol 25 (3) ◽  
pp. 314-324 ◽  
Author(s):  
Uroš Klanšek ◽  
Mirko Pšunder
Keyword(s):  
Global Optimization ◽  
Transportation Problem ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Branch And Cut ◽  
Cut Method ◽  
Global Optimization Methods ◽  
Optimum Solution ◽  
Global And Local ◽  
Branch And Cut Method

The aim of this paper is to present the suitability of three different global optimization methods for specifically the exact optimum solution of the nonlinear transportation problem (NTP). The evaluated global optimization methods include the branch and reduce method, the branch and cut method and the combination of global and local search strategies. The considered global optimization methods were applied to solve NTPs with reference to literature. NTPs were formulated as nonlinear programming (NLP) optimization problems. The obtained optimal results were compared with those got from literature. A comparative evaluation of global optimization methods is presented at the end of the paper to show their suitability for solving NTPs.

scholarly journals Exit lane allocation with the lane-based signal optimization method at isolated intersections

2020 ◽  
Vol 47 (12) ◽  
pp. 1345-1358
Author(s):  
Qinrui Tang ◽  
Alexander Sohr
Keyword(s):  
Optimization Problems ◽  
Signal Sequence ◽  
Optimization Method ◽  
Signalized Intersections ◽  
Branch And Cut ◽  
Mixed Integer ◽  
Auxiliary Variables ◽  
Signal Optimization ◽  
Pavement Markings ◽  
Lane Based

In signal optimization problems, incompatible movements are usually in either of two states: predecessor or successor. However, if the exit lane is well allocated, the incompatible movements merging at the same destination arm can exist in parallel. The corresponding longer green duration is expected to increase the capacity of intersections. This paper aims to solve the exit lane allocation problem with the lane-based method by applying the three states among incompatible movements at conventional signalized intersections. After introducing auxiliary variables, the problem is formulated as a mixed integer programming and can be solved using a standard branch-and-cut algorithm. In addition to the exit lane allocation results, this proposed method can also determine the cycle length, green duration, start of green, and signal sequence. The results show that the proposed method can obtain a higher capacity than that without the exit lane allocation. The pavement markings are further suggested for safety.

scholarly journals A COMPARISON BETWEEN MILP AND MINLP APPROACHES TO OPTIMAL SOLUTION OF NONLINEAR DISCRETE TRANSPORTATION PROBLEM

Transport ◽  
2014 ◽  
Vol 30 (2) ◽  
pp. 135-144 ◽  
Author(s):  
Uroš Klanšek
Keyword(s):  
Transportation Problem ◽  
Optimal Solution ◽  
Optimization Method ◽  
Mixed Integer ◽  
Test Problems ◽  
Model Formulation ◽  
Reference Test ◽  
Adequate Model ◽  
Integer Nonlinear Programming ◽  
Selection Of

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.

scholarly journals Hierarchical Optimization Method for Energy Scheduling of Multiple Microgrids

2019 ◽  
Vol 9 (4) ◽  
pp. 624 ◽  
Author(s):  
Tao Rui ◽  
Guoli Li ◽  
Qunjing Wang ◽  
Cungang Hu ◽  
Weixiang Shen ◽  
...  
Keyword(s):  
Optimization Problems ◽  
Stackelberg Game ◽  
Optimization Method ◽  
Economic Benefits ◽  
Power Grids ◽  
Mixed Integer ◽  
Hierarchical Optimization ◽  
Load Demand ◽  
Control Framework ◽  
Two Stages

This paper proposes a hierarchical optimization method for the energy scheduling of multiple microgrids (MMGs) in the distribution network of power grids. An energy market operator (EMO) is constructed to regulate energy storage systems (ESSs) and load demands in MMGs. The optimization process is divided into two stages. In the first stage, each MG optimizes the scheduling of its own ESS within a rolling horizon control framework based on a long-term forecast of the local photovoltaic (PV) output, the local load demand and the price sent by the EMO. In the second stage, the EMO establishes an internal price incentive mechanism to maximize its own profits based on the load demand of each MG. The optimization problems in these two stages are solved using mixed integer programming (MIP) and Stackelberg game theory, respectively. Simulation results verified the effectiveness of the proposed method in terms of the promotion of energy trading and improvement of economic benefits of MMGs.

Hierarchical Arrangement of Characteristics in Product Design Optimization

2005 ◽  
Vol 128 (4) ◽  
pp. 701-709 ◽  
Author(s):  
Masataka Yoshimura ◽  
Masahiko Taniguchi ◽  
Kazuhiro Izui ◽  
Shinji Nishiwaki
Keyword(s):  
Design Optimization ◽  
Product Design ◽  
Optimization Problems ◽  
Optimization Method ◽  
Hierarchical Level ◽  
Specific Design ◽  
Design Problems ◽  
Hierarchical Arrangement ◽  
Optimum Solution ◽  
Insight Into

This paper proposes a machine product design optimization method based on the decomposition of performance characteristics, or alternatively, extraction of simpler characteristics, that is especially responsive to the detailed features or difficulties presented by specific design problems. The optimization problems examined here are expressed using hierarchical constructions of the decomposed and extracted characteristics and the optimizations are sequentially repeated, starting with groups of characteristics having conflicting characteristics at the lowest hierarchical level and proceeding to higher levels. The proposed method not only effectively provides optimum design solutions, but also facilitates deeper insight into the design optimization results, so that ideas for optimum solution breakthroughs are more easily obtained. An applied example is given to demonstrate the effectiveness of the proposed method.

scholarly journals Closing the gap in linear bilevel optimization: a new valid primal-dual inequality

2020 ◽  
Author(s):  
Thomas Kleinert ◽  
Martine Labbé ◽  
Fränk Plein ◽  
Martin Schmidt
Keyword(s):  
Branch And Bound ◽  
Optimization Problems ◽  
Valid Inequalities ◽  
Bilevel Optimization ◽  
Branch And Cut ◽  
Mixed Integer ◽  
Valid Inequality ◽  
Single Level ◽  
Primal Dual ◽  
Level Problem

Abstract Linear bilevel optimization problems are often tackled by replacing the linear lower-level problem with its Karush–Kuhn–Tucker conditions. The resulting single-level problem can be solved in a branch-and-bound fashion by branching on the complementarity constraints of the lower-level problem’s optimality conditions. While in mixed-integer single-level optimization branch-and-cut has proven to be a powerful extension of branch-and-bound, in linear bilevel optimization not too many bilevel-tailored valid inequalities exist. In this paper, we briefly review existing cuts for linear bilevel problems and introduce a new valid inequality that exploits the strong duality condition of the lower level. We further discuss strengthened variants of the inequality that can be derived from McCormick envelopes. In a computational study, we show that the new valid inequalities can help to close the optimality gap very effectively on a large test set of linear bilevel instances.

scholarly journals Robust operation of microgrid energy system under uncertainties and demand response program

2020 ◽  
Vol 17 (2) ◽  
pp. 1005
Author(s):  
Sahar Seyyedeh Barhagh ◽  
Amin Mohammadpour Shotorbani ◽  
Behnam Mohammadi-Ivatloo ◽  
Kazem Zare ◽  
Ali Farzamnia
Keyword(s):  
Power Systems ◽  
Demand Response ◽  
Optimization Problems ◽  
Energy Systems ◽  
Stochastic Scheduling ◽  
Energy System ◽  
Optimization Method ◽  
Operating Conditions ◽  
Mixed Integer ◽  
Demand Response Program

<span>Microgrid energy systems are one of suitable solutions to the available problems in power systems such as energy losses, and resiliency issues. Local generation by these energy systems can reduce the role of the upstream network, which is a challenge in risky conditions. Also, uncertain behavior of electricity consumers and generating units can make the optimization problems sophisticated. So, uncertainty modeling seems to be necessary. In this paper, in order to model the uncertainty of generation of photovoltaic systems, a scenario-based model is used, while the robust optimization method is used to study the uncertainty of load. Moreover, the stochastic scheduling is performed to model the uncertain nature of renewable generation units. Time-of–use rates of demand response program (DRP) is also utilized to improve the system economic performance in different operating conditions. Studied problem is modeled using a mixed-integer linear programming (MILP). The general algebraic modeling system (GAMS) package is used to solve the proposed problem. A sample microgrid is studied and the results with DRP and without DRP are compared. It is shown that same robustness is achieved with a lower increase in the operation cost using DRP.</span>

scholarly journals STPGA: Selection of training populations with a genetic algorithm

2017 ◽  
Author(s):  
Deniz Akdemir
Keyword(s):  
Genetic Algorithm ◽  
Variable Selection ◽  
Optimization Problems ◽  
Subset Selection ◽  
Breeding Population ◽  
Mixed Integer ◽  
Optimal Subset ◽  
Look Ahead ◽  
Selection Of ◽  
The Ideal

AbstractOptimal subset selection is an important task that has numerous algorithms designed for it and has many application areas. STPGA contains a special genetic algorithm supplemented with a tabu memory property (that keeps track of previously tried solutions and their fitness for a number of iterations), and with a regression of the fitness of the solutions on their coding that is used to form the ideal estimated solution (look ahead property) to search for solutions of generic optimal subset selection problems. I have initially developed the programs for the specific problem of selecting training populations for genomic prediction or association problems, therefore I give discussion of the theory behind optimal design of experiments to explain the default optimization criteria in STPGA, and illustrate the use of the programs in this endeavor. Nevertheless, I have picked a few other areas of application: supervised and unsupervised variable selection based on kernel alignment, supervised variable selection with design criteria, influential observation identification for regression, solving mixed integer quadratic optimization problems, balancing gains and inbreeding in a breeding population. Some of these illustrations pertain new statistical approaches.

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