A suggested algorithm to solve triangular fuzzy rough integer linear programming (TFRILP) problems with alpha-level is introduced in this paper in order to find rough value optimal solutions and decision rough integer...
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A suggested algorithm to solve triangular fuzzy rough integer linear programming (TFRILP) problems with alpha-level is introduced in this paper in order to find rough value optimal solutions and decision rough integer variables, where all parameters and decision variables in the constraints and the objective function are triangular fuzzy rough numbers. In real-life situations, the parameters of a linearprogramming problem model may not be defined precisely, because of the current market globalization and some other uncontrollable factors. In order to solve this problem, a proper methodology is adopted to solve the TFRILP problems by the slice-sum method with the branch-and-bound technique, through which two fuzzy integers linearprogramming (FILP) problems with triangular fuzzy interval coefficients and variables were constructed. One of these problems is an FILP problem, where all of its coefficients are the upper approximation interval and represent rather satisfactory solutions;the other is an FILP problem, where all of its coefficients are the lower approximation interval and represent completely satisfactory solutions. Moreover, alpha-level at alpha = 0.5 is adopted to find some other rough value optimal solutions and decision rough integer variables. integerprogramming is used, since a lot of the linearprogramming problems require that the decision variables be integers. In addition, the motivation behind this study is to enable the decision makers to make the right decision considering the proposed solutions, while dealing with the uncertain and imprecise data. A flowchart is also provided to illustrate the problem-solving steps. Finally, two numerical examples are given to clarify the obtained results.
A vector (multicriterion) problem of integer linear programming is considered on a finite set of feasible solutions. A metric l(p), 1 <= p <=infinity, is defined on the parameter space of the problem. A formula ...
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A vector (multicriterion) problem of integer linear programming is considered on a finite set of feasible solutions. A metric l(p), 1 <= p <=infinity, is defined on the parameter space of the problem. A formula of the maximum permissible level of perturbations is obtained for the parameters that preserve the efficiency (Pareto optimality) of a given solution. Necessary and sufficient conditions of two types of stability of the problem are obtained as corollaries.
It is not known if planar integer linear programming is P-complete or if it is in NC, and the same can be said about the computation of the remainder sequence of the Euclidean algorithm applied to two integers. Howeve...
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It is not known if planar integer linear programming is P-complete or if it is in NC, and the same can be said about the computation of the remainder sequence of the Euclidean algorithm applied to two integers. However, both computations are NC equivalent. The latter computational problem was reduced in NC to the former one by Deng [Mathematical programming: Complexity and Application, Ph.D. dissertation, Stanford University, Stanford, CA, 1989;Proc. ACM Symp. on Parallel Algorithms and Architectures, 1989, pp. 110-116]. We now prove the converse NC-reduction.
Generation of orthogonal fractional factorial designs (OFFDs) is an important and extensively studied subject in applied statistics. In this paper we show how searching for an OFFD that satisfies a set of constraints,...
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Generation of orthogonal fractional factorial designs (OFFDs) is an important and extensively studied subject in applied statistics. In this paper we show how searching for an OFFD that satisfies a set of constraints, expressed in terms of orthogonality between simple and interaction effects, is, in many applications, equivalent to solving an integer linear programming problem. We use a recent methodology, based on polynomial counting functions and strata, that represents OFFDs as the positive integer solutions of a system of linear equations. We use this system to set up an optimization problem where the cost function to be minimized is the size of the OFFD and the constraints are represented by the system itself. Finally we search for a solution using standard integerprogramming techniques. Some applications are also presented in the computational results section. It is worth noting that the methodology does not put any restriction either on the number of levels of each factor or on the orthogonality constraints and so it can be applied to a very wide range of designs, including mixed orthogonal arrays.
We consider a multicriteria integer linear programming problem with a targeting set of optimal solutions given by the set of all individual criterion minimizers (extrema). In this study, the lower and upper attainable...
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We consider a multicriteria integer linear programming problem with a targeting set of optimal solutions given by the set of all individual criterion minimizers (extrema). In this study, the lower and upper attainable bounds on the quasistability radius of the set of extremum solutions are obtained when solution and criterion spaces are endowed with different Holder's norms. As a corollary, an analytical formula for the quasistability radius is obtained for the case when the criterion space is endowed with Chebyshev's norm. Some computational challenges are also discussed.
Static multi-issue machines, such as traditional Very Long Instructional Word (VLIW) architectures, move complexity from the hardware to the compiler. This is motivated by the ability to support high degrees of instru...
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Static multi-issue machines, such as traditional Very Long Instructional Word (VLIW) architectures, move complexity from the hardware to the compiler. This is motivated by the ability to support high degrees of instruction-level parallelism without requiring complicated scheduling logic in the processor hardware. The simpler-control hardware results in reduced area and power consumption, but leads to a challenge of engineering a compiler with good code-generation quality. Transport triggered architectures (TTA), and other so-called exposed datapath architectures, take the compiler-oriented philosophy even further by pushing more details of the datapath under software control. The main benefit of this is the reduced register file pressure, with a drawback of adding even more complexity to the compiler side. In this article, we propose an integer linear programming (ILP)-based instruction scheduling model for TTAs. The model describes the architecture characteristics, the particular processor resource constraints, and the operation dependencies of the scheduled program. The model is validated and measured by compiling application kernels to various TTAs with a different number of datapath components and connectivity. In the best case, the cycle count is reduced to 52% when compared to a heuristic scheduler. In addition to producing shorter schedules, the number of register accesses in the compiled programs is generally notably less than those with the heuristic scheduler;in the best case, the ILP scheduler reduced the number of register file reads to 33% of the heuristic results and register file writes to 18%. On the other hand, as expected, the ILP-based scheduler uses distinctly more time to produce a schedule than the heuristic scheduler, but the compilation time is within tolerable limits for production-code generation.
A combinatorial description of the minimal free resolution of a lattice ideal allows us to the connection of integer linear programming and Algebra. The non null reduced homology spaces of some simplicial complexes ar...
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A combinatorial description of the minimal free resolution of a lattice ideal allows us to the connection of integer linear programming and Algebra. The non null reduced homology spaces of some simplicial complexes are the key. The extremal rays of the associated cone reduce the number of variables.
In the Tutor Allocation Problem, the objective is to assign a set of tutors to a set of workshops in order to maximize tutors' preferences. The problem is solved every year by many universities, each having its ow...
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In the Tutor Allocation Problem, the objective is to assign a set of tutors to a set of workshops in order to maximize tutors' preferences. The problem is solved every year by many universities, each having its own specific set of constraints. In this work, we study the tutor allocation in the School of Mathematics at the University of Edinburgh, and solve it with an integer linear programming model. We tested the model on the 2019/2020 case, obtaining a significant improvement with respect to the manual assignment in use and we showed that such improvement could be maintained while optimizing other key metrics such as load balance among groups of tutors and total number of courses assigned. Further tests on randomly created instances show that the model can be used to address cases of broad interest. We also provide meaningful insights on how input parameters, such as the number of workshop locations and the length of the tutors' preference list, might affect the performance of the model and the average number of preferences satisfied.
The drainage area maximization problem for an unconventional hydrocarbon field is addressed with the objective of designing a development plan that optimizes total production while satisfying environmental and operati...
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The drainage area maximization problem for an unconventional hydrocarbon field is addressed with the objective of designing a development plan that optimizes total production while satisfying environmental and operating constraints. The various characteristics of the problem are presented and a solution approach is developed around an integer linear programming model applied to a discretisation of the field's geographical area. Computational experiments show that the approach provides a practical response to the problem, generating solutions that comply with all of the constraints. The algorithm implemented under this approach has been incorporated into a software tool for planning and managing unconventional hydrocarbon operations and has been used since 2018 by two leading petroleum companies in Argentina to improve unconventional development plans for the country's "Vaca Muerta" geological formation.
With the increasing design complexities, the design of pin-constrained digital microfluidic biochips (PDMFBs) is of practical importance for the emerging marketplace. However, solutions of current pin-count reduction ...
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With the increasing design complexities, the design of pin-constrained digital microfluidic biochips (PDMFBs) is of practical importance for the emerging marketplace. However, solutions of current pin-count reduction are inevitably limited by simply adopting it after the droplet routing stage. In this paper, we propose the first droplet routing algorithm for PDMFBs that can integrate pin-count reduction with droplet routing stage. Furthermore, our algorithm is capable of minimizing the number of control pins, the number of used cells, and the droplet routing time. We first present a basic integer linear programming (ILP) formulation to optimally solve the droplet routing problem for PDMFBs with simultaneous multiobjective optimization. Due to the complexity of this ILP formulation, we also propose a two-stage technique of global routing followed by incremental ILP-based routing to reduce the solution space. To further reduce the runtime, we present a deterministic ILP formulation that casts the original routing optimization problem into a decision problem, and solve it by a binary solution search method that searches in logarithmic time. Extensive experiments demonstrate that in terms of the number of the control pins, the number of the used cells, and the routing time, we obtain much better achievement than all the state-of-the-art algorithms in any aspect.
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