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Optimization Problem - knapsack

مسألة الحقيبة - البرمجة الديناميكية ومسائل الأمثلة

2109   2   53   0 ( 0 )
 Publication date 2016
and research's language is العربية
 Created by Zein Shaheen




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Earthmoving is the process of moving and processing soil from one location to another to alter an existing land surface into a desired configuration. Highways, dams, and airports are typical examples of heavy earthmoving projects. Over the years, con struction managers have devised ways to determine the quantities of material to be moved from one place to another. Various types of soil (soft earth, sand, hard clay, …, etc.) create different level of difficulty of the problem. Earthmoving problem has traditionally been solved using mass diagram method or variety of operational research techniques. However, existing models do not present realistic solution for the problem. Multiple soil types are usually found in cut sections and specific types of soil are required in fill sections. Some soil types in cut sections are not suitable to be used in fill sections and must be disposed of. In this paper a new mathematical programming model is developed to find-out the optimum allocation of earthmoving works. In developing the proposed model, different soil types are considered as well as variation of unit cost with earth quantities moved. Suggested borrow pits and/or disposal sites are introduced to minimize the overall earthmoving cost. The proposed model is entirely formulated using the programming capabilities of VB6 while LINDO is used to solve the formulated model to get the optimum solution. An example project is presented to show how the developed model can be implemented.
Molecular docking is a hard optimization problem that has been tackled in the past, demonstrating new and challenging results when looking for one objective . However, only a few papers can be found in the literature that deal with this problem by means of a multi-objective approach, and no experimental comparisons have been made in order to clarify which of them has the best overall performance. In this research, we use and compare, a set of representative multi-objective optimization algorithms. The approach followed is focused on optimizing the inter-molecular and intra-molecular energies as two main objectives to minimize.
Linear programming (LP, or linear optimization) is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. Linear programming is a special case of mathematical programming (mathematical optimization). More formally, linear programming is a technique for the optimization of a linear objective function, subject to linear equality and linear inequality constraints. Its feasible region is a convex polyhedron, which is a set defined as the intersection of finitely many half spaces, each of which is defined by a linear inequality. Its objective function is a real-valued affine function defined on this polyhedron. A linear programming algorithm finds a point in the polyhedron where this function has the smallest (or largest) value if such a point exists.
Multi-objective evolutionary algorithms are used in a wide range of fields to solve the issues of optimization, which require several conflicting objectives to be considered together. Basic evolutionary algorithm algorithms have several drawbacks, such as lack of a good criterion for termination, and lack of evidence of good convergence. A multi-objective hybrid evolutionary algorithm is often used to overcome these defects.
In this research, we study the material point motion, in the field of a homogeneous and unbounded, material rod. so we present the Hamiltonian formalization of the problem and study the orbits located in the plans perpendicular to the rod. We reve al the proprieties of symmetry of those orbits, and present the conditions to its closure. We also study the material point motion, in the field of a homogeneous and bounded, material rod. We present the Hamiltonian formalization of the problem, reveal the practicality of the plan of symmetry, and we studied the motion in this plan. We reveal the existence of unbounded or bounded planar orbits; some of those are closed. We also reveal that when the angular velocity isn't null, there are not orbits leading to a collision with the rod.

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