The real world optimization problems are often very challenging to solve, and many applications have to deal with NP-hard problems [1]. To solve such problems, optimization tools have to be used even though there is no guarantee that the optimal solution can be obtained. In fact, for NP problems, there are no efficient algorithms at all. As a result of this, many problems have to be solved by trial and errors using various optimization techniques [2]. In addition, new algorithms have been developed to see if they can cope with these challenging optimization problems. Among these new algorithms, many algorithms such as particle swarm optimization, cuckoo search and firefly algorithm, have gained popularity due to their high efficiency. In this paper we have used IBACH algorithm for solving integer programming problems. Integer programming is NP-hard problems[3-10].The name “linear integer programming “is referred” to the class of combinatorial constrained optimization problems with integer variables, where the objective function is a linear function and the constraints are linear inequalities.” The Linear Integer Programming (also known as LIP) optimization problem can be stated in the following general form:
Max cx (1)
s.t. Ax ≤ b, (2) xZn (3) where the solution x∈ Zn is a vector of n integer variables: x = (x1, x2 , …, xn)T and the data are rational and are given by the m×n matrix A, the 1×n matrix c, and the m×1 matrix b. This formulation includes also equality constraints, because each equality constraint can be represented by means of two inequality constraints like those included in eq. (2).
Integer programming addresses the problem raised by non-intege...
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... of particle swarm optimization (PSO), Standard harmony search algorithm (HS) standard bat algorithm and improved harmony search algorithm (IHS). In comparison with exact values we find that the results of IBACH algorithm are very close to the exact values of selected problems under the study. If a large number of variables are to be found, then it is hard to go past the classical methods. More usually, though, users will choose to use the proposed algorithm, to save their own time and to gain reliability. for example when we solved test problem number 6 by proposed algorithm it took time 7 seconds ,but when we solved it by branch and bound(exact method) it took time 396 seconds .
The reason for getting better results than the other algorithms considered is that the search power of bat algorithm. Adding to this, using chaos improves the performance of the algorithm.
Noori, S., Feylizadeh, M. R., Bagherpour, M., Zorriassatine, F., & Parkin, R. M. (2008). Optimization of material requirement planning by fuzzy multi-objective linear programming. Proceedings of the Institution of Mechanical Engineers, 222, 887-900. Retrieved from http://search.proquest.com/docview/195144743?accountid=32521
Abstract—Most Independent System Operators (ISOs) adopt the Bid Cost Minimization (BCM) to select offers and their respective generation levels while minimizing the total bid cost. It was shown that the customer payment costs that result from selected offers can differ significantly from the customer payments resulting from the Payment Cost Minimization (PCM), under which payment costs are minimized directly. In order to solve the PCM in the dual space, the Lagrangian relaxation and surrogate optimization approach is frequently used. When standard optimization methods, such as branch-and-cut, become ineffective due to the large size of a problem, the Lagrangian relaxation and surrogate optimization approach provides a good feasible solution within a reasonable CPU time. The convergence of the standard Lagrangian relaxation and surrogate subgradient approach depends on the optimal dual value, which is usually unknown. Furthermore, when using the surrogate subgradient approach, the upper bound property is lost, so additional conditions are needed to ensure convergence. The main goal of this paper is to develop a convergent variation of the surrogate subgradient method without invoking the optimal dual value, and show the relevance and effectiveness of the new method for solving large constrained optimization problems, such as the PCM.
In order to minimize the total shipping costs in the Darby distribution system, linear programming can be used.
I am ready to go back to my home school because I haved worked on my childish ways, worked on my behavior plus I don't like being at the bonds alternative program. The old me had this problem talking,laughing,arguing,and being disrespectful. The new me is not going to talk when not told, known when there's a time and a place to laugh, and stop arguing with teachers because I am not always right. There are some problems that I have but i push myself that I can do better.
Genetic Algorithms provide a holistic search process based on principles of natural genetics and survivals of the fittest……
Usually different optimization methods are used to solve the TEP: genetic algorithm (GA), Tabu search (TS) and several heuristic and metaheuristic techniques. Those are called static scenarios. Dynamic scenarios are the one based on game theory which represents the behavior of different participants in the electricity market. Different games and models like cournot, Stackelberg, bargaining etc.. are recently used to obtain an optimal decision concerning TEP.
Cormen T. H, Leiserson C. E., Rivest R. L. and Stein C. [1990] (2001). “Introduction to Algorithms”, 2nd edition, MIT Press and McGraw-Hill, ISBN 0-262-03293-7, pp. 27–37. Section 2.3: Designing algorithms..
...ithms can be integrated with neural networks to solve the complex problems in machine learning, such systems are called hybrid intelligent systems. Neural networks are very powerful tools for Intelligence Systems. Although there are some limitations in terms of the complexity of the neural circuit and the lack of representation in very complex systems, there is an ongoing research to improve performance and capabilities of neural networks.
There are a lot of searching algorithms, from which Linear Search Algorithm is one of the simple and easy algorithm, but it also have complexity, which we discuss here,
[2]S.M Mohd, I.Zuwairie, U.Satomi, O.Osamu, K. Marzuki(2005). DNA Computing for Complex Scheduling Problem[Online]. Available : http://www.isc.meiji.ac.jp/~onosemi/IADC/ICNCSaufee.pdf
The range of task environments that can be characterized by well - defined problems is vast. We can distinguish between so - called, toy problems, which are intended to illustrate or exercise various problem - solving methods, and so - called real - world problems, which tend to be more difficult and whose solutions people actually care about. In this section, we will give examples of both. By nature, toy problems can be given a concise, exact descri ption. This means that they can be easily used by different researchers to compare the performance of algorithms. Real - world problems, on the other hand, tend not to have a single agreed - upon description, but we will attempt to give the general flavor of t heir formulations.
Linear programming uses a mathematical model to describe the problem of concern. Linear programming is used in many practical applications, such as transportation, production planning, etc. It is also the building block for combinatorial optimization. One aspect of linear programming which is often forgotten is the fact that it is also a useful proof technique. A linear programming problem may be defined as the problem of maximizing or minimizing a linear function subject to linear constraints. The constraints may be equalities or inequalities. All linear programming problems have four main elements in common: decision variables, objective function, constraints and variable
The field of neural networks involves a new approach to computing that uses mathematical structures with the ability to learn (Zsolutions). These methods were inspired by investigations into modeling nervous system learning (Zsolutions). For example, neurons in the human brain are used to transmit data back and forth to each other. Artificial neural networks use this same technique to process various kinds of information (Fu, p 4).
Constrained Maximisation is a term in economics used to refer to and is concerned with the restrictions imposed on the availabilty of resources and other requirements.( ) it tries to explain using prescribed forumlae such as the langarian method how firms can solve issues to do with constrained maximisation. In this context however we are more interested in the maximisation of profits in firms, we are interested in the contraints imposed on managers that limit their options when making decisions.
Fortunately, during under-graduation, I got an opportunity to detect the optimum path of a process through my project “Design and Development of PCB Dual Head Drilling Machine”. Additionally, I became aware of a new subject called Six Sigma which aided me in intertwining new optimization techniques into my project to make the process effective. I optimized the creation...