We present a toolchain for solving path planning problems for concentric tube robots through obstacle fields. First, ellipsoidal sets representing the target area and obstacles are constructed from labelled point clou...
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We present a toolchain for solving path planning problems for concentric tube robots through obstacle fields. First, ellipsoidal sets representing the target area and obstacles are constructed from labelled point clouds. Then, the nonlinear and highly nonconvex optimal control problem is solved by introducing a homotopy on the obstacle positions where at one extreme of the parameter the obstacles are removed from the operating space, and at the other extreme they are located at their intended positions. We present a detailed example (with more than a thousand obstacles) from stereotactic neurosurgery with real-world data obtained from labelled MRI scans.
In this paper, a new algorithm has been introduced to construct the membership function and non-membership function of uncertain reliability of a series system via non-linear programming techniques, which having compo...
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ISBN:
(纸本)9783037855744
In this paper, a new algorithm has been introduced to construct the membership function and non-membership function of uncertain reliability of a series system via non-linear programming techniques, which having components following different types of intuitionistic uncertain failure rates.
We introduce a method which based on Bell inequalities, to study quantum phase transitions. By using the non-linear programming, we compare two different kinds of Bell inequalities, the original Bell inequality and Cl...
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We introduce a method which based on Bell inequalities, to study quantum phase transitions. By using the non-linear programming, we compare two different kinds of Bell inequalities, the original Bell inequality and Clauser-Horne-Shimony-Holt (CHSH) inequality. And we find that the original Bell inequality is more accurate in detecting the Bell non-locality. By defining the maximal violation of Bell inequalities, we calculate two kinds of transitions, the one is magnetic transition in the spin- 1/2 XX model and the other is topological transition in the Kitaev honeycomb model. The critical points are detected successfully. Compared with traditional methods, our method requires no prior knowledge of order parameters and it is base-free.
In this paper, a bi-objective priority based assignment problem (BPBAP) related to an industrial project, is considered in which, depending upon the work breakdown structure, the n tasks involved in the project are di...
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In this paper, a bi-objective priority based assignment problem (BPBAP) related to an industrial project, is considered in which, depending upon the work breakdown structure, the n tasks involved in the project are divided into two categories. One of the categories consists of m primary tasks and the other one consists of ( n - m) secondary tasks (for m < n). The project is such that the secondary tasks can be executed only after the primary tasks are finished, however, the tasks within each category may be executed simultaneously. This problem is a special case of categorized assignment scheduling problem, discussed extensively in literature. The BPBAP is studied with the objective of minimizing simultaneously, the two criteria namely, total execution time and total assignment cost of the project which are equal to the sum of execution times and assignment costs respectively, of primary and secondary tasks. Generally, it is not possible to optimize both the objectives simultaneously, therefore, there is a need to do time-cost trade-off analysis of the problem. Since, the present problem is based on two-stage execution of the project (one stage for each category of tasks), therefore, a criteria based iterative algorithm considering all the possible combinations of the parameters of both the categories, is developed that finds all the non-dominated points of BPBAP in a polynomial time. Numerical illustrations are provided in the support of theory.
As the share of variable renewable energy increases, adequate prices on electricity spot markets become increasingly important as they set signals for scarcity, investment, or demand response. Market prices are derive...
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As the share of variable renewable energy increases, adequate prices on electricity spot markets become increasingly important as they set signals for scarcity, investment, or demand response. Market prices are derived from the underlying welfare maximization problem. On electricity spot markets, this optimization problem is based on the non-convex and non-linear Alternating Current Optimal Power Flow (ACOPF) model. Since the ACOPF is intractable, electricity markets around the world use a linear approximation, the Direct Current Optimal Power Flow (DCOPF) model. Recent research has led to better non-linear relaxations of the ACOPF. We show that these non-linear relaxations increase welfare and imply significantly lower redispatch costs and side-payments. Most importantly, we show that the price signals obtained from non-linear relaxations are much improved. The DCOPF often yields high price differences between nodes when there is no line congestion in the AC-feasible solution or vice versa. Such biased price signals pose a significant problem in practice as they lead to inefficient demand response, distorted investment signals, and incorrect congestion incomes. The use of non-linear relaxations mitigates this problem and provides an important advantage of the resulting prices over prices based on the DCOPF.
Engineering optimization is the subject of interest for many scientific research teams on a global scale;it is a part of today's mathematical modelling and control of processes and systems. The attention in this a...
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Engineering optimization is the subject of interest for many scientific research teams on a global scale;it is a part of today's mathematical modelling and control of processes and systems. The attention in this article is focused on optimization modelling of technological processes of surface treatment. To date, a multitude of articles are devoted to the applications of mathematical optimization methods to control technological processes, but the situation is different for surface treatment processes, especially for anodizing. We perceive their lack more, so this state has stimulated our interest, and the article contributes to filling the gap in scientific research in this area. The article deals with the application of non-linear programming (NLP) methods to optimise the process of anodic oxidation of aluminium using MATLAB toolboxes. The implementation of optimization methods is illustrated by solving a specific problem from engineering practice. The novelty of this article lies in the selection of effective approaches to the statement of optimal process conditions for anodizing. To solve this complex problem, a solving strategy based on the design of experiments approach (for five factors), exploratory data analysis, confirmatory analysis, and optimization modelling is proposed. The original results have been obtained through the experiment (performed by using the DOE approach), statistical analysis, and optimization procedure. The main contribution of this study is the developed mathematical-statistical computational (MSC) model predicting the thickness of the resulting aluminium anodic oxide layer (AOL). Based on the MSC model, the main goal has been achieved-the statement of optimal values of factors acting during the anodizing process to achieve the thickness of the protective layer required by clients, namely, for 5, 7, 10, and 15 [mu m].
In the just-in-time (JIT) manufacturing system, the vendors ship in small batch sizes. Hence the buyers are at an advantageous position as they can reduce their inventory holding costs. The practice of shipping in sma...
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In the just-in-time (JIT) manufacturing system, the vendors ship in small batch sizes. Hence the buyers are at an advantageous position as they can reduce their inventory holding costs. The practice of shipping in smaller batch sizes often results in the vendors incurring high costs as the number of production setups and the number of shipments increases for the vendors. The vendors could only switch to JIT mode when there is an assurance from the buyer of providing some compensation for the increased costs. This compensation from the buyer to the vendors is called 'surcharge price'. In our work, we have studied the surcharge pricing mechanism in the presence of backorder when there is a powerful vendor and have shown that the it can coordinate a decentralized supply chain. Our study incorporates both the cases of the buyer holding full information about the vendors' costs as well as the case of information asymmetry. In the case of full information, we have shown that the optimal order quantity in the presence of surcharge pricing is less than that of the vendor dominated scenario. At the same time, the optimal order quantity is higher than that in the buyer dominated scenario. Further, the total supply chain costs are also minimized when a surcharge pricing contract is offered in comparison to both the buyer and the vendor dominated scenarios. For the information asymmetry case, we have framed the optimal set of screening contracts and have shown that an optimal surcharge pricing contract to the vendor is free from the probability distribution of the vendor type.
The brilliant method due to Good and Turing allows for estimating objects not occurring in a sample. The problem, known under names "sample coverage" or "missing mass" goes back to their cryptograp...
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ISBN:
(纸本)9781538682098
The brilliant method due to Good and Turing allows for estimating objects not occurring in a sample. The problem, known under names "sample coverage" or "missing mass" goes back to their cryptographic work during WWII, but over years has found has many applications, including language modeling, inference in ecology and estimation of distribution properties. This work characterizes the maximal mean-squared error of the Good-Turing estimator, for any sample and alphabet size.
The suitability of agents for tasks and ranked preference of tasks for agents play a significant role in problems where several agents are available to perform various tasks. The agents should be allocated to various ...
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This paper presents a two-stage method for simultaneous least-cost design and operation of looped water distribution systems (WDSs). After partitioning the network into a chord and spanning trees, in the first stage, ...
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This paper presents a two-stage method for simultaneous least-cost design and operation of looped water distribution systems (WDSs). After partitioning the network into a chord and spanning trees, in the first stage, a reformulated linearprogramming (LP) method is used to find the least cost design of a WDS for a given set of flow distribution. In the second stage, a non-linear programming (NLP) method is used to find a new flow distribution that reduces the cost of the WDS operation given the WDS design obtained in stage one. The following features of the proposed two-stage method make it more appealing compared to other methods: (1) the reformulated LP stage can consistently reduce the penalty cost when designing a WDS under multiple loading conditions;(2) robustness as the number of loading conditions increases;(3) parameter tuning is not required;(4) the method reduces the computational burden significantly when compared to meta-heuristic methods;and (5) in oppose to an evolutionary "black box" based methodology such as a genetic algorithm, insights through analytical sensitivity analysis, while the algorithm progresses, are handy. The efficacy of the proposed methodology is demonstrated using two WDSs case studies.
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