Figure 2: Non simultaneous orders can share stack space This means that it is natural to associate the lifetime of a costumers’ **order** **in** the solution with intervals of time measured not **in** minutes or hours but measured **in** terms of the number of diﬀerent products **in** the manufactur- ing sequence. We have seen that we can start solving a MOSP **problem** with a graph, and that **in** the solution of the **problem** we can consider **an** **interval** for the time that each stack is open. We will see that **an** **interval** graph can be associated to the set of intervals **in** the solution and we will also use some properties of **interval** **graphs** to ﬁnd the solution of MOSP instances.

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applied to non-differentiable objective functions. Recently, Genetic Algorithm (GA) technique appeared as a promising algorithm for handling the **optimization** problems. GA can be viewed as a general-purpose search method, **an** **optimization** method, or a learning mechanism, based loosely on Darwinian principles of biological evolution, reproduction and ‘‘the survival of the fittest’’ [10]. GA maintains a set of candidate solutions called population and repeatedly modifies them. At each step, the GA selects individuals from the current population to be parents and uses them to produce the children for the next generation. **In** general, the fittest individuals of any population tend to reproduce and survive to the next generation, thus improving successive generations. However, inferior individuals can, by chance, survive and also reproduce. GA is well suited and has been extensively applied to solve complex design **optimization** problems because it can handle both discrete and continuous variables, non-linear objective and constrained functions without requiring gradient information

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The scientific computing represents the design and analysis activity for the nu- meric solving of mathematical problems **in** science and engineering, and tradition- ally this activity is called numeric analysis. The scientific computing is used **in** **order** to simulate natural phenomena, **using** virtual prototypes of models **in** engineering [7]. The general strategy is to replace a difficult **problem** with **an** easier one having the same solution, or a very similar solution, that is, they wish to replace **an** infinite **problem** with a finite **problem**, the differential one with the algebraically one, the non-linear with the linear, and eventually, a complicated one with a simple one, and the solution obtained can only approximate the solution of the original prob- lem.

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Abstract. **In** this paper we consider **an** **optimization** **problem** applying the metaheuristic Firefly algorithm (FY) to weight **an** ensemble of rainfall forecasts from daily precipitation simulations with the Brazilian developments on the Regional Atmospheric Modeling System (BRAMS) over South Amer- ica during January 2006. The method is addressed as a pa- rameter estimation **problem** to weight the ensemble of pre- cipitation forecasts carried out **using** different options of the convective parameterization scheme. Ensemble simulations were performed **using** different choices of closures, repre- senting different formulations of dynamic control (the mod- ulation of convection by the environment) **in** a deep convec- tion scheme. The **optimization** **problem** is solved as **an** **in**- verse **problem** of parameter estimation. The application and validation of the methodology is carried out **using** daily pre- cipitation fields, defined over South America and obtained by merging remote sensing estimations with rain gauge ob- servations. The quadratic difference between the model and observed data was used as the objective function to deter- mine the best combination of the ensemble members to re- produce the observations. To reduce the model rainfall bi- ases, the set of weights determined by the algorithm is used to weight members of **an** ensemble of model simulations **in** **order** to compute a new precipitation field that represents the observed precipitation as closely as possible. The validation of the methodology is carried out **using** classical statistical scores. The algorithm has produced the best combination of the weights, resulting **in** a new precipitation field closest to the observations.

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Genetic algorithms were formally introduced **in** the United States **in** the 1970s by John Holland at University of Michigan. Genetic algorithm is based on the mechanics of natural selection and natural genetics [7].Its fundamental principle is that the fittest member of population has the highest probability for survival. The genetic algorithm, works only with objective function information **in** a search for **an** optimal parameter set. **In** particular, genetic algorithms work very well on mixed (continuous and discrete), combinatorial problems. They are less susceptible to getting 'stuck' at local optima than gradient search methods. But they tend to be computationally expensive. To use a genetic algorithm, it must represent a solution to your **problem** as a genome (or chromosome)[6] The genetic algorithm then creates a population of solutions and applies genetic operators such as mutation and crossover to evolve the solutions **in** **order** to find the best one(s) which is shown **in** Fig:2, as no of iteration increased the value of fitness function(objective function) improves.

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The core abstraction of Spark is the resilient distributed dataset (RDD), which is a distributed collection of elements. Instead of immediately executing **an** operation on **an** RDD, Spark instead builds **an** execution graph until it encounters **an** operation, known as **an** action, to force the graph to be executed. This allows the actual execution to be optimized based on succeeding operations. For example, instead of reading **an** entire file, Spark may read only those parts that will be processed **in** succeeding steps. Spark has also introduced the DataFrames application program- ming interface (API), which essentially wraps **an** RDD into SQL- like tables. This API also eases **optimization** by adding more con- text to the desired action. Another benefit of the API is that the methods are implemented **in** Java and Scala, the native languages of Spark, regardless of the language used by the user. This is a major boost for Python and R users, which are typically executed more slowly than Java or Scala.

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Sometimes we have to solve small and median size combinatorial **optimization** problems **using** commercial codes of mixed linear integer programming as CPLEX, LINDO, OSL, XPRESS, etc. The use of branch and cut techniques to solve these problems needs a hard work of implementation. For the traveling salesman **problem** (TSP) and the Steiner tree **problem** (STP) **in** **graphs** one uses mathematical models with **an** exponential number of constraints to avoid subtours, these constraints are implicitly considered. The aim of this paper is to present 0-1 mixed linear programs with a polynomial number of variables and constraints to solve some combinatorial **optimization** problems **using** commercial codes. When we solve integer linear programming by column generation techniques, we have to generate paths, cycles and trees with additional constraints **in** small **graphs**, 40 to 60 nodes, 120 to 180 edges, at each iteration. For this we can use a commercial code to solve the master **problem** and the same code to solve the **optimization** **problem** which generates at each iteration a new column.

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Lamarckian learning: The Lamarckian approach is based on the inheritance of acquired characteristics obtained through learning. This approach forces the genetic structure to reflect the result of local search. The genetic structure of **an** individual and its fitness are changed to match the solution found by a local search method. **In** the Lamarckian approach, the local search method is used as a refinement operator that modifies the genetic structure of **an** individual and places it back. Lamarckian evolution can accelerate the search process of genetic algorithm (Whiteley et al., 1994), on the other hands can disrupt the schema **processing** which can badly affect the exploring abilities of genetic algorithm, which may lead to premature convergence. Most of the hybrid genetic algorithms that repair chromosomes to satisfy constraints are Lamarckian and

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3.2 Fuzzy decision making **using** fuzzy **optimization** – flexible **optimization** Fuzzy decision making **using** fuzzy **optimization** was first operationalized by Tanaka, Okuda, and Asai [31, 32], and then by Zimmermann [38]. This approach, based on Bellman and Zadeh [1], transforms systems of inequalities Ax ≤ b and the objective function into aspirations. The results are what is commonly called soft constraints, where the number b to the right of the inequality is a target such that, if the constraint is less than or equal to b, the membership value is one (the constraint is satisfied with certainty), and, if the constraint is greater than b + d, (for **an** a-priori given d ≥ 0), the membership is zero (the constraint is not satisfied with certainty). Here, the objective function is translated into a target, say z = f (x, c) ≥ t ∗ , and t ∗ translated into **an** aspiration. **In** between, the membership function is interpolated so that it is consistent with the definition of a fuzzy **interval** membership function **in** the context of the **problem**. Linear interpolation was the original form [38]. This models a fuzzy meaning of inequality that is translated into a fuzzy membership function and is the source of our use of the designation of flexible programming for these classes of **optimization** problems. The α-level represents the degree of feasibility of the constraints, consistent with the aspiration that the inequality be less than b but definitely not more than b + d. Thus, the objective, according to [38], is to simultaneously satisfy all constraints at the highest possible level of preference as measured by the α-levels of the membership functions. The approach of [38] is not always Pareto optimal. It must be iterated – fix the constraints at bounds and re-optimize.

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This paper presents a fuzzy switching controller for uncer- tain nonlinear systems which are represented by a class of TS fuzzy systems with uncertainties. The controller pro- posed uses local guaranteed cost control laws and a switching scheme based on local quadratic Lyapunov functions when the state is on the boundary of defined subspaces of the state space. A sufficient condition for the stability of the uncertain nonlinear system with state feedback is given **in** terms of a piecewise quadratic Lyapunov function. This approach pro-

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Electrical power plays a pivotal role **in** the modern world to satisfy various needs. It is therefore very important that the electrical power generated is transmitted and distributed efficiently **in** **order** to satisfy the power requirement. Electrical power is generated **in** several ways. The economic scheduling of all generators **in** a system to meet desired demand is important **problem** **in** operation and planning of power system. The Economic Load Dispatch (ELD) **problem** is the most significant **optimization** **problem** **in** scheduling the generation of thermal generators **in** power system. **In** ELD **problem**, ultimate goal is to decrease the operation cost of the power generation system, while supplying the required power demanded. **In** addition to this, the various operational constraints of the system should also be satisfied. Traditional methods to solve ELD **problem** include the linear programming method, gradient method, lambda iteration method and Newton‟s method [1].

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39 Edge-Clique Graphs and the l- Coloring Problem Tiziana Calamoneri, Rossella Petreschi... 40.[r]

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A computer network is **an** interconnected group of computers with the ability to exchange data. Today, computer networks are the core of modern communication. Routing **problem** is one of the important research issues **in** communication networks (Jayakumar and Gopinath, 2008). **An** ideal routing algorithm should strive to find **an** optimal path for packet transmission within a specified time so as to satisfy the Quality of Service (QoS). The objective functions related to cost, time, reliability and risk are appropriated for selecting the most satisfactory route **in** many communication network **optimization** problems. Traditionally, the routing **problem** has been a single-objective **problem** of minimization of either cost or delay. However, it is necessary to take into account that many real world problems are multi-objective **in** nature and so is the shortest path routing **problem** **in** computer networks.

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important advantage of the combination of these three controls is the large decrease **in** the popu- lation of natural mosquitoes, (Figure 11e), which minimizes the risk of diseases outbreak. The summer **in** Brazil occurs **in** the first four months of the year (January-April), it is a hot and humid period presenting optimal conditions for the growth of the Aedes aegypti mosquito population, and represents the time of the year when the greatest number of mosquito transmitted diseases takes place. For this reason there is frequent need for sanitary surveillance authorities to apply vector controls **in** this period. **In** this context and **in** **order** to conduct sensitivity analysis with respect to the duration of **an** outbreak, we also investigate some instances **in** which control was applied during part or throughout the year, beginning **in** the summer period, during which the population is at high levels.

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The global search optimization method, Genetic Algorithm, used for the automatic interpretation of Semblance, randomly generates an initial population of time interval velocities models [r]

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Abstract—Wireless data usage is growing now faster than ever before. **In** **order** to attend the increasing demand for wireless services and considering that frequency spectrum is a scarce and expensive resource, wireless are required to operate as efficiently as possible. **In** this context, the application of mathematical **optimization** methods **in** the study and design of key function- alities of wireless systems has acquired great relevance. This papers surveys some applications of **optimization** methods to wireless communications problems. Among them, game theory and majorization theory have got increasing attention **in** the last few years and are described **in** some more details. **An** application of **optimization** methods to solve a concrete **problem** **in** modern wireless communications, namely, the maximization of the ergodic capacity of a Coordinated Multi-Point system with statistical Channel State Information at the Transmitter is also provided.

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Furthermore, non-spherical celestial bodies such as planets, physical satellites, asteroids and comets can be modeled by a triaxial ellipsoid. Also, the present day accuracy requirements and the modern computational capabilities push toward the study on the triaxial ellipsoid as a geometrical and a physical model **in** geodesy and related interdisciplinary sciences Panou et al (2013).

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This paper is devoted to investigation of the hat **problem** on **graphs** with exactly three cycles. **In** the hat **problem**, each of n players is randomly fitted with a blue or red hat. Everybody can try to guess simultaneously his own hat color by looking at the hat colors of the other players. The team wins if at least one player guesses his hat color correctly, and no one guesses his hat color wrong; otherwise the team loses. The aim is to maximize the probability of winning. Note that every player can see everybody excluding himself. This **problem** has been considered on a graph, where the vertices correspond to the players, and a player can see each player to whom he is connected by **an** edge. We show that the hat number of a graph with exactly three cycles is 3

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