scholarly journals Outcome space range reduction method for global optimization of sum of affine ratios problem

2016 ◽  
Vol 14 (1) ◽  
pp. 736-746 ◽  
Author(s):  
Hongwei Jiao ◽  
Sanyang Liu ◽  
Jingben Yin ◽  
Yingfeng Zhao
Keyword(s):  
Global Optimization ◽  
Reduction Method ◽  
Optimal Solution ◽  
Space Region ◽  
Equivalent Problem ◽  
Solution Quality ◽  
Range Reduction ◽  
Branching Rule ◽  
Outcome Space ◽  
Space Range

Abstract Many algorithms for globally solving sum of affine ratios problem (SAR) are based on equivalent problem and branch-and-bound framework. Since the exhaustiveness of branching rule leads to a significant increase in the computational burden for solving the equivalent problem. In this study, a new range reduction method for outcome space of the denominator is presented for globally solving the sum of affine ratios problem (SAR). The proposed range reduction method offers a possibility to delete a large part of the outcome space region of the denominators in which the global optimal solution of the equivalent problem does not exist, and which can be seen as an accelerating device for global optimization of the (SAR). Several numerical examples are presented to demonstrate the advantages of the proposed algorithm using new range reduction method in terms of both computational efficiency and solution quality.

scholarly journals An Effective Algorithm for Globally Solving Sum of Linear Ratios Problems

2017 ◽  
Vol 2017 ◽  
pp. 1-7
Author(s):  
Hongwei Jiao ◽  
Lei Cai ◽  
Zhisong Hou ◽  
Chunyang Bai
Keyword(s):  
Programming Problem ◽  
Computational Efficiency ◽  
Nonconvex Programming ◽  
Optimal Solution ◽  
Space Region ◽  
Effective Algorithm ◽  
Equivalent Problem ◽  
Solution Quality ◽  
Space Partition ◽  
Pruning Technique

In this study, we propose an effective algorithm for globally solving the sum of linear ratios problems. Firstly, by introducing new variables, we transform the initial problem into an equivalent nonconvex programming problem. Secondly, by utilizing direct relaxation, the linear relaxation programming problem of the equivalent problem can be constructed. Thirdly, in order to improve the computational efficiency of the algorithm, an out space pruning technique is derived, which offers a possibility of pruning a large part of the out space region which does not contain the optimal solution of the equivalent problem. Fourthly, based on out space partition, by combining bounding technique and pruning technique, a new out space branch-and-bound algorithm for globally solving the sum of linear ratios problems (SLRP) is designed. Finally, numerical experimental results are presented to demonstrate both computational efficiency and solution quality of the proposed algorithm.

scholarly journals Least-looping stepping-stone-based ASM approach for transportation and triangular intuitionistic fuzzy transportation problems

2021 ◽  
Author(s):  
Kedar Nath Das ◽  
Rajeev Das ◽  
Debi Prasanna Acharjya
Keyword(s):  
Optimal Solution ◽  
Transportation Engineering ◽  
Key Factors ◽  
Solution Quality ◽  
Transportation Problems ◽  
Stepping Stone ◽  
Intuitionistic Fuzzy ◽  
Real World Problem ◽  
Statistical Results ◽  
Made In

AbstractTransportation problem (TP) is a popular branch of Linear Programming Problem in the field of Transportation engineering. Over the years, attempts have been made in finding improved approaches to solve the TPs. Recently, in Quddoos et al. (Int J Comput Sci Eng (IJCSE) 4(7): 1271–1274, 2012), an efficient approach, namely ASM, is proposed for solving crisp TPs. However, it is found that ASM fails to provide better optimal solution in some cases. Therefore, a new and efficient ASM appoach is proposed in this paper to enhance the inherent mechanism of the existing ASM method to solve both crisp TPs and Triangular Intuitionistic Fuzzy Transportation Problems (TIFTPs). A least-looping stepping-stone method has been employed as one of the key factors to improve the solution quality, which is an improved version of the existing stepping-stone method (Roy and Hossain in, Operation research Titus Publication, 2015). Unlike stepping stone method, least-looping stepping-stone method only deals with few selected non-basic cells under some prescribed conditions and hence minimizes the computational burden. Therefore, the framework of the proposed method (namely LS-ASM) is a combination of ASM (Quddoos et al. 2012) and least-looping stepping-stone approach. To validate the performance of LS-ASM, a set of six case studies and a real-world problem (those include both crisp TPs and TIFTPs) have been solved. The statistical results obtained by LS-ASM have been well compared with the existing popular modified distribution (MODI) method and the original ASM method, as well. The statistical results confirm the superiority of the LS-ASM over other compared algorithms with a less computationl effort.

Predictive Search for Capacitated Multi-Item Lot Sizing Problems

2021 ◽  
Author(s):  
Tao Wu
Keyword(s):  
Mathematical Programming ◽  
Heuristic Search ◽  
Lot Sizing ◽  
Optimal Solution ◽  
Solution Space ◽  
Search Method ◽  
Benchmark Problems ◽  
Solution Quality ◽  
Programming Technique ◽  
Advanced Analytics

For capacitated multi-item lot sizing problems, we propose a predictive search method that integrates machine learning/advanced analytics, mathematical programming, and heuristic search into a single framework. Advanced analytics can predict the probability that an event will happen and has been applied to pressing industry issues, such as credit scoring, risk management, and default management. Although little research has applied such technique for lot sizing problems, we observe that advanced analytics can uncover optimal patterns of setup variables given properties associated with the problems, such as problem attributes, and solution values yielded by linear programming relaxation, column generation, and Lagrangian relaxation. We, therefore, build advanced analytics models that yield information about how likely a solution pattern is the same as the optimum, which is insightful information used to partition the solution space into incumbent, superincumbent, and nonincumbent regions where an analytics-driven heuristic search procedure is applied to build restricted subproblems. These subproblems are solved by a combined mathematical programming technique to improve solution quality iteratively. We prove that the predictive search method can converge to the global optimal solution point. The discussion is followed by computational tests, where comparisons with other methods indicate that our approach can obtain better results for the benchmark problems than other state-of-the-art methods. Summary of Contribution: In this study, we propose a predictive search method that integrates machine learning/advanced analytics, mathematical programming, and heuristic search into a single framework for capacitated multi-item lot sizing problems. The advanced analytics models are used to yield information about how likely a solution pattern is the same as the optimum, which is insightful information used to divide the solution space into incumbent, superincumbent, and nonincumbent regions where an analytics-driven heuristic search procedure is applied to build restricted subproblems. These subproblems are solved by a combined mathematical programming technique to improve solution quality iteratively. We prove that the predictive search method can converge to the global optimal solution point. Through computational tests based on benchmark problems, we observe that the proposed approach can obtain better results than other state-of-the-art methods.

Design Optimization of a 3D Parameterized Vane Cascade With Non-Axisymmetric Endwall Based on a Modified EGO Algorithm and Data Mining Techniques

2017 ◽  
Author(s):  
Chenxi Li ◽  
Zhendong Guo ◽  
Liming Song ◽  
Jun Li ◽  
Zhenping Feng
Keyword(s):  
Data Mining ◽  
Global Optimization ◽  
Design Space ◽  
Pressure Coefficient ◽  
Differential Evolution Algorithm ◽  
Optimal Solution ◽  
Efficient Global Optimization ◽  
Data Mining Techniques ◽  
Parallel Axis ◽  
Better Than

The design of turbomachinery cascades is a typical high dimensional and computationally expensive problem, a metamodel-based global optimization and data mining method is proposed to solve it. A modified Efficient Global Optimization (EGO) algorithm named Multi-Point Search based Efficient Global Optimization (MSEGO) is proposed, which is characterized by adding multiple samples at per iteration. By testing on typical mathematical functions, MSEGO outperforms EGO in accuracy and convergence rate. MSEGO is used for the optimization of a turbine vane with non-axisymmetric endwall contouring (NEC), the total pressure coefficient of the optimal vane is increased by 0.499%. Under the same settings, another two optimization processes are conducted by using the EGO and an Adaptive Range Differential Evolution algorithm (ARDE), respectively. The optimal solution of MSEGO is far better than EGO. While achieving similar optimal solutions, the cost of MSEGO is only 3% of ARDE. Further, data mining techniques are used to extract information of design space and analyze the influence of variables on design performance. Through the analysis of variance (ANOVA), the variables of section profile are found to have most significant effects on cascade loss performance. However, the NEC seems not so important through the ANOVA analysis. This is due to the fact the performance difference between different NEC designs is very small in our prescribed space. However, the designs with NEC are always much better than the reference design as shown by parallel axis, i.e., the NEC would significantly influence the cascade performance. Further, it indicates that the ensemble learning by combing results of ANOVA and parallel axis is very useful to gain full knowledge from the design space.

Cooperative Coevolution with Formula-Based Variable Grouping for Large-Scale Global Optimization

2018 ◽  
Vol 26 (4) ◽  
pp. 569-596 ◽  
Author(s):  
Yuping Wang ◽  
Haiyan Liu ◽  
Fei Wei ◽  
Tingting Zong ◽  
Xiaodong Li
Keyword(s):  
Global Optimization ◽  
Objective Function ◽  
Real World ◽  
Large Scale ◽  
Divide And Conquer ◽  
Group Method ◽  
Objective Functions ◽  
Elementary Functions ◽  
Cooperative Coevolution ◽  
Solution Quality

For a large-scale global optimization (LSGO) problem, divide-and-conquer is usually considered an effective strategy to decompose the problem into smaller subproblems, each of which can then be solved individually. Among these decomposition methods, variable grouping is shown to be promising in recent years. Existing variable grouping methods usually assume the problem to be black-box (i.e., assuming that an analytical model of the objective function is unknown), and they attempt to learn appropriate variable grouping that would allow for a better decomposition of the problem. In such cases, these variable grouping methods do not make a direct use of the formula of the objective function. However, it can be argued that many real-world problems are white-box problems, that is, the formulas of objective functions are often known a priori. These formulas of the objective functions provide rich information which can then be used to design an effective variable group method. In this article, a formula-based grouping strategy (FBG) for white-box problems is first proposed. It groups variables directly via the formula of an objective function which usually consists of a finite number of operations (i.e., four arithmetic operations “[Formula: see text]”, “[Formula: see text]”, “[Formula: see text]”, “[Formula: see text]” and composite operations of basic elementary functions). In FBG, the operations are classified into two classes: one resulting in nonseparable variables, and the other resulting in separable variables. In FBG, variables can be automatically grouped into a suitable number of non-interacting subcomponents, with variables in each subcomponent being interdependent. FBG can easily be applied to any white-box problem and can be integrated into a cooperative coevolution framework. Based on FBG, a novel cooperative coevolution algorithm with formula-based variable grouping (so-called CCF) is proposed in this article for decomposing a large-scale white-box problem into several smaller subproblems and optimizing them respectively. To further enhance the efficiency of CCF, a new local search scheme is designed to improve the solution quality. To verify the efficiency of CCF, experiments are conducted on the standard LSGO benchmark suites of CEC'2008, CEC'2010, CEC'2013, and a real-world problem. Our results suggest that the performance of CCF is very competitive when compared with those of the state-of-the-art LSGO algorithms.

scholarly journals A Novel Method for Economic Dispatch with Across Neighborhood Search: A Case Study in a Provincial Power Grid, China

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-18 ◽  
Author(s):  
Guojiang Xiong ◽  
Jing Zhang ◽  
Xufeng Yuan ◽  
Dongyuan Shi ◽  
Yu He ◽  
...  
Keyword(s):  
Power Grid ◽  
Economic Dispatch ◽  
Optimal Solution ◽  
Inequality Constraints ◽  
Search Space ◽  
Neighborhood Search ◽  
Solution Quality ◽  
Promising Alternative ◽  
Comparison Results ◽  
Population Based Algorithm

Economic dispatch (ED) is of cardinal significance for the power system operation. It is mathematically a typical complex nonlinear multivariable strongly coupled optimization problem with equality and inequality constraints, especially considering the valve-point effects. In order to effectively solve the problem, a simple yet very young and efficient population-based algorithm named across neighborhood search (ANS) is implemented in this paper. In ANS, a group of individuals collaboratively navigate through the search space for obtaining the optimal solution by simultaneously searching the neighborhoods of multiple superior solutions. Four benchmark test cases with diverse complexities and characteristics are firstly employed to comprehensively verify the feasibility and effectiveness of ANS. The experimental and comparison results fully demonstrate the superiority of ANS in terms of the final solution quality, convergence speed, robustness, and statistics. In addition, the sensitivities of ANS to variations of population size and across-search degree are studied. Furthermore, ANS is applied to a practical provincial power grid of China. All the comparison results consistently indicate that ANS is highly competitive and can be used as a promising alternative for ED problems.

scholarly journals Topology Optimization of Automotive sheet metal part using Altair Inspire

2020 ◽  
Vol 5 (3) ◽  
pp. 143-150
Author(s):  
Netsanet Ferede
Keyword(s):  
Topology Optimization ◽  
Sheet Metal ◽  
Optimization Problem ◽  
Optimal Solution ◽  
Sheet Metal Part ◽  
Metal Part ◽  
Solution Quality ◽  
Design Engineers ◽  
Automotive Sheet ◽  
Reduced Costs

In an optimization problem, different candidate solutions are compared with each other, and then the best or optimal solution is obtained which means that solution quality is fundamental. Topology optimization is used at the concept stage of design. It deals with the optimal distribution of material within the structure. Altair Inspire software is the industry's most powerful and easy-to-use Generative Design/Topology Optimization and rapid simulation solution for design engineers. In this paper Topology optimization is applied using Altair inspire to optimize the Sheet metal Angle bracket. Different results are conducted the better and final results are fulfilling the goal of the paper which is minimizing the mass of the sheet metal part by 65.9%  part and Maximizing the stiffness with Better Results of Von- Miss Stress Analysis,  Displacement, and comparison with different load cases.  This can lead to reduced costs, development time, material consumption, and product less weight.

MISSION-ADAPTABLE ROUTE PLANNING IN UNCERTAIN AND ADVERSARIAL ENVIRONMENT

2006 ◽  
Vol 15 (05) ◽  
pp. 803-821 ◽  
Author(s):  
PING YAN ◽  
MINGYUE DING ◽  
CHANGWEN ZHENG
Keyword(s):  
Real Time ◽  
A Priori ◽  
Route Planning ◽  
Optimal Solution ◽  
Dijkstra Algorithm ◽  
Solution Quality ◽  
Model Complex ◽  
Local Methods ◽  
Domain Specific Knowledge ◽  
Planning Algorithm

In this paper, the route-planning problems of Unmanned Aerial Vehicle (UAV) in uncertain and adversarial environment are addressed, including not only single-mission route planning in known a priori environment, but also the route replanning in partially known and mission-changeable environments. A mission-adaptable hybrid route-planning algorithm based on flight roadmap is proposed, which combines existing global and local methods (Dijkstra algorithm, SAS and D*) into a two-level framework. The environment information and constraints for UAV are integrated into the procedure of building flight roadmap and searching for routes. The route-planning algorithm utilizes domain-specific knowledge and operates in real time with near-optimal solution quality, which is important to uncertain and adversarial environment. Other planners do not provide all of the functionality, namely real-time planning and replanning, near-optimal solution quality, and the ability to model complex 3D constraints.

Multiobjective Programming

2014 ◽  
pp. 1585-1604
Author(s):  
Minghe Sun
Keyword(s):  
Programming Problem ◽  
Multiobjective Programming ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Objective Functions ◽  
Solution Quality ◽  
Solution Methods ◽  
Multiobjective Programming Problem ◽  
Feasible Solutions ◽  
Multiobjective Programming Problems

Optimization problems with multiple criteria measuring solution quality can be modeled as multiobjective programming problems. Because the objective functions are usually in conflict, there is not a single feasible solution that can optimize all objective functions simultaneously. An optimal solution is one that is most preferred by the decision maker (DM) among all feasible solutions. An optimal solution must be nondominated but a multiobjective programming problem may have, possibly infinitely, many nondominated solutions. Therefore, tradeoffs must be made in searching for an optimal solution. Hence, the DM's preference information is elicited and used when a multiobjective programming problem is solved. The model, concepts and definitions of multiobjective programming are presented and solution methods are briefly discussed. Examples are used to demonstrate the concepts and solution methods. Graphics are used in these examples to facilitate understanding.

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