# Genetic Algorithms And Simulated Annealing Pdf

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- Combined Simulated Annealing Algorithm for the Discrete Facility Location Problem
- HillClimbing, Simulated Annealing and Genetic Algorithms
- An enhanced genetic algorithm with simulated annealing for job-shop scheduling

## Combined Simulated Annealing Algorithm for the Discrete Facility Location Problem

IT outsourcing is an effective way to enhance the core competitiveness for many enterprises. But the schedule risk of IT outsourcing project may cause enormous economic loss to enterprise. In this paper, the Distributed Decision Making DDM theory and the principal-agent theory are used to build a model for schedule risk management of IT outsourcing project.

In addition, a hybrid algorithm combining simulated annealing SA and genetic algorithm GA is designed, namely, simulated annealing genetic algorithm SAGA. The effect of the proposed model on the schedule risk management problem is analyzed in the simulation experiment. Consequently, this paper provides the scientific quantitative proposal for the decision maker who needs to manage the schedule risk of IT outsourcing project.

With the increasing development of information technology, IT outsourcing has been developing rapidly. It is currently being used as an important strategy by many companies to focus on the core competency, reduce cost, and increase profit. In Europe and other developed countries, either small businesses or large multinational companies always give the noncore business to external professional company [ 1 — 4 ].

Although IT outsourcing has many advantages including reducing cost and enhancing the core competence, there also exist some problems that need to be solved urgently, especially the problem of managing the schedule risk of IT outsourcing, which may bring about huge loss to company. Consequently, it is very vital to research how to manage the schedule risk of IT outsourcing. Researchers have done a lot of related research [ 6 — 12 ].

But most methods and models proposed in the literature only discuss the risk management issues on project itself and ignore the cooperation between principal and agent and the distribution characteristics of the IT outsourcing activities.

In recent years, principal-agent theory has been widely employed to solve the problem of risk management of IT outsourcing and good results have been achieved through these studies.

Earl et al. Then, he argued that the risk of IT outsourcing came from enterprises, agents, and the process of IT activities and proposed corresponding risk management measures based on principal-agent theory [ 17 — 19 ]. Bahli and Rivard proposed a scenario-based conceptualization of the IT outsourcing risk and applied it to the specific context of IT outsourcing using transaction cost and agency theory [ 20 ].

Osei-Bryson and Ngwenyama offered a method and some mathematical models for analyzing risks and constructing incentive contracts for information system outsourcing [ 21 ]. Sanfa et al. Xianli et al. In this paper, we build a two-level principal-agent model combined with reward and punishment mechanism for schedule risk management of IT outsourcing project based on the Distributed Decision Making DDM theory and principal-agent theory [ 24 — 26 ].

According to the feature of problem, the SAGA is designed to solve the proposed model and the optimal plan of managing schedule risk is given based on the simulation analysis. The purpose of this paper is to provide crucial decision support for the people who need to manage the schedule risk of IT outsourcing project. The remainder of this paper is structured as follows. Section 1 presents the schedule risk management model of IT outsourcing project.

In Section 2 , the design of algorithm is given. In addition, numerical examples and results analyzed are depicted in Section 3. Finally, conclusion is given in Section 4. For IT outsourcing, principal divides a whole project into some serial subprojects in the IT developing process, as shown in Figure 1.

The definition of serial subprojects is that subproject is performed after completion of subproject. The schedule risk is reflected in two aspects of duration and risk loss. Each subproject has an initial duration and initial risk loss. In order to effectively manage the schedule risk, the reward and punishment mechanism is added in outsourcing contract; that is, if the project is completed in advance, the agent is rewarded; otherwise the agent is punished.

Each subproject will be contracted with different agents, and a typical principal-agent relationship between principal and agent will be generated. For the relationship between principal and agents, see Figure 2. The optimal solution of top-level model is the optimal combination of risk management capital, and the optimal solution of base-level model is the optimal combination of risk management measure of subproject.

In the decision making process, the principal transfers risk management capital to the predicted base-level model. The optimal solution of top-level model is obtained based on the goal of maximizing the profit of the principal and the information returned from the predicted base-level model.

Then, the optimal solution of top-level model is transferred to the real base-level model. Under the constraint of risk management capital, the agents obtain the best control measure combination of the subproject according to the goal of maximizing the profit. The information exchange process between the principal and the agents is shown in Figure 3. For the IT development, the duration of the subproject is determined by the duration of the activities on the critical path. Hence we only consider the schedule of the activities on the critical path.

Figure 4 shows the network diagram of subproject , in which the critical path is 1—— So agent only allocates risk management capital to activities 1, 2, 3, 6, 8, and 9. Based on the DDM theory and principal-agent theory, a two-level schedule risk management model of IT outsourcing project is built [ 27 , 28 ]. In the top-level, the decision maker is the principal who determines how to allocate the risk management capital among agents.

The objective of top-level is to maximize the profit of principal, and the reward and punishment mechanism is introduced into the model. In the base-level, the decision maker is the agents who determine the best combination of risk management measure of subproject. The objective of top-level shown in formula 1 is to maximize the profit of principal; the reward and punishment mechanism is fulfilled by item. The operation is defined as. Formula 2 indicates participation constraint; formula 3 indicates incentive compatibility constraint; formula 4 indicates risk management capital constraint; formula 5 indicates that the risk management capital is a natural integer, which is the decision variable in the top-level model.

In the predicted base-level, the decision makers are the agents, and there are agents. Take agent , for example. Formula 8 indicates chance constraint. Formula 9 indicates the reward and penalty function based on the duration. Formula 10 indicates the saved risk loss of subproject; the operation is defined as.

Formula 11 indicates that the sum of used risk management capital is not greater than the risk management capital which is allocated to subproject; formula 13 represents a set of the predicted base-level variables; formula 14 represents the value range of that is the decision variable in the predicted base-level model.

In the real base-level, the decision makers are the agents, and there are agents. The top-level model is an integer programming problem, and the base-level model including the predicted base-level model is a combinatorial optimization problem.

The whole problem is a NP hard problem, because the base-level is embedded in the top-level. So, we use genetic algorithm GA to solve the problem in this paper. It is well known that GA that was first introduced by Holland is very effective for solving combinatorial optimization problems.

For example, GA has been successfully applied in solving traveling salesman problem, knapsack problem, bin packing problem, and so on.

However, the disadvantage of GA is that the local search capability is not strong [ 29 — 33 ]. Simulated annealing SA is a general random search algorithm, which is an extension of the local search algorithm [ 34 — 37 ]. The overall thought of SAGA is simple. Firstly, some initial solutions of GA are generated randomly.

After a period of iteration, some superior solutions are produced. Then, sort the corresponding fitness value of these superior solutions in descending order. We try to find the best solution of the proposed problem around these superior solutions.

In top-level, each chromosome represented by real number is a combination of risk management capital and the length of chromosome represents the number of agents. In base-level, each chromosome represented by real number is a combination of risk management capital and the length of chromosome represents the number of the activities on the critical path.

Take the base-level encoding scheme shown in Figure 6 as example; it can be seen that there are 5 activities on the critical path, and measure 2 is used to manage the risk of activity 1, measure 4 is used to manage the risk of activity 2, and so on. Initial population is generated randomly. Punishment strategy is adopted to deal with the constraints, so we do not have to judge whether the initial solution meets the constraint conditions. Considering the proposed optimization problems with constraints, we set up a fitness function with punishment term to evaluate individuals.

The top-level fitness function is given as where Function 24 is top-level objective function; and are punishment coefficients, respectively.

The base-level fitness function is given as where Function 25 is base-level objective function; and are punishment coefficients, respectively. The Monte Carlo Simulation method is used to deal with the random variable [ 37 — 40 ]. The process of calculating the fitness of the predicted base-level model by Monte Carlo Simulation is shown as follows. Step 1. Set is equal to [ ]; is sampling number. Step 2.

Samples are generated by normal distribution function. Step 3. Calculate that is the fitness value of the predicted base-level model by formula 26 ,. Step 4. The th biggest element of can be used as the fitness value of the th predicted base-level model, which can be seen by the law of large numbers. This paper takes proportional selection strategy [ 41 , 42 ].

Then, the probability of selected individual is given by where is the fitness of individual and NP is the population size.

Here, we adopt well-known Roulette Wheel scheme. In order to prevent the best individual in each generation from being destroyed, elite-preservation strategy is also used.

That is to say, the best individual of each generation directly becomes one of individuals in the next generation without crossover and mutation operation. Double-point crossover is adopted in this paper, which is beneficial for keeping excellent individual. Figure 7 shows the example of the double-point crossover operator, where and are parent chromosomes. So, the generated children chromosomes are and. Reversal mutation is adopted in this paper [ 35 ].

Under the condition of satisfying the mutation rate, randomly select two points in the parent and sort the genes between these two points in reverse order.

## HillClimbing, Simulated Annealing and Genetic Algorithms

IT outsourcing is an effective way to enhance the core competitiveness for many enterprises. But the schedule risk of IT outsourcing project may cause enormous economic loss to enterprise. In this paper, the Distributed Decision Making DDM theory and the principal-agent theory are used to build a model for schedule risk management of IT outsourcing project. In addition, a hybrid algorithm combining simulated annealing SA and genetic algorithm GA is designed, namely, simulated annealing genetic algorithm SAGA. The effect of the proposed model on the schedule risk management problem is analyzed in the simulation experiment.

Skip to search form Skip to main content You are currently offline. Some features of the site may not work correctly. This paper theoretically compares the performance of simulated annealing and evolutionary algorithms. Our main result is that under mild conditions a wide variety of evolutionary algorithms can be shown to have greater performance than simulated annealing after a sufficiently large number of function evaluations. Save to Library. Create Alert. Launch Research Feed.

Genetic Algorithm (GA) and Simulated Annealing (SA) have been used to solve optimization problems. Both GA and SA search a solution space throughout a.

## An enhanced genetic algorithm with simulated annealing for job-shop scheduling

The method is a two-layer algorithm, in which the external subalgorithm optimizes the decision of the facility location decision while the internal subalgorithm optimizes the decision of the allocation of customer's demand under the determined location decision. The performance of the CSA is tested by 30 instances with different sizes. The computational results show that CSA works much better than the previous algorithm on DFLP and offers a new reasonable alternative solution method to it. The classical facility location problem FLP is one of the most important models in combinatorial optimization, which is to determine the number and locations of the facilities and allocate customers to these facilities in such a way that the total cost is minimized. The FLP may be the most critical and most difficult decision in the designing of an efficient supply chain for the facilities are costly and difficult to reverse after being located.

This chapter introduces the basic concepts and notation of genetic algorithms and simulated annealing, which are two basic search methodologies that can be used for modelling and simulation of complex non-linear dynamical systems. Since both techniques can be considered as general purpose optimization methodologies, we can use them to find the mathematical model which minimizes the fitting errors for a specific problem. On the other hand, we can also use any of these techniques for simulation if we exploit their efficient search capabilities to find the appropriate parameter values for a specific mathematical model. We also describe in this chapter the application of genetic algorithms to the problem of finding the best neural network or fuzzy system for a particular problem.

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* - Идея неплохая, но на каждое послание Танкадо, увы, поступает ответ. Танкадо пишет, его партнер отвечает.*

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Вирусы. Холод пронзил все ее тело. Но как мог вирус проникнуть в ТРАНСТЕКСТ. Ответ, уже из могилы, дал Чатрукьян. Стратмор отключил программу Сквозь строй.

Потом, всего через несколько секунд, он должен был включить основные генераторы, и сразу же восстановились бы все функции дверных электронных замков, заработали фреоновые охладители и ТРАНСТЕКСТ оказался бы в полной безопасности. Но, приближаясь к рубильнику, Стратмор понял, что ему необходимо преодолеть еще одно препятствие - тело Чатрукьяна на ребрах охлаждения генератора. Вырубить электропитание и снова его включить значило лишь вызвать повторное замыкание. Труп надо передвинуть. Стратмор медленно приближался к застывшему в гротескной лозе телу, не сводя с него глаз.

Хорошенькое зрелище, - подумал Беккер. - Где, черт возьми, регистратура. За едва заметным изгибом коридора Беккер услышал голоса.

*Только его собственные утверждения в электронных посланиях. И конечно… ТРАНСТЕКСТ. Компьютер висел уже почти двадцать часов.*

## 4 Comments

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HeartlownewatchThis chapter introduces the basic concepts and notation of genetic algorithms and simulated annealing, which are two basic search methodologies that can be.

NetdylibenKeywords: Heuristics, Simulated Annealing, Genetic Algorithms, Facility Layout Problem,. Parallel Algorithms, Combinatorial Optimization. 1.