Recently, Pinar Civicioglu [2] developed a new metaheuristic **search** **algorithm** called **Differential** **Search** **Algorithm** (DSA) for uni-objective optimization. DSA simulates a superorganism migrating between the two stopovers sites. DSA has unique mutation and crossover operators. DSA has only two control parameters that are used for controlling the movement of superorgnisms. DSA has been applied for a variety of applications. Till now, it had not been extended to solve multiple objectives. DSA appears more suitable for **multiobjective** **problems** as high speed of convergence and less overhead of parameters setting. In this paper, a novel approach named **multiobjective** **differential** **search** **algorithm** (MODSA), which allows the DSA to deal with **multiobjective** optimization **problems**. MODSA is based on non-dominated sorting strategy. The concept of Pareto dominance is incorporated in MODSA to determine which solution is better. The constraint handling mechanism is added in the MODSA to increase the ability of exploration of DSA. MODSA has been compared with other recently proposed **multiobjective** metaheuristic algorithms and validated on benchmark test functions.

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In this paper, we have introduced a new **multiobjective** **algorithm** for portfolio optimization: DEMPO - **Differential** Evolution for **Multiobjective** Portfolio Optimization. Perhaps the most important result is that the new **algorithm** has the great advantage of full generality, i.e.: the ability to tackle a problem as it is without requiring rigid assumptions about convexity and linearity, while obtaining highly accurate results in very reasonable runtime. The **algorithm** allows considering different objective functions, such as value at risk and expected shortfall, and typical real world constraints that managers have often to satisfy. The comparison with quadratic programming for the standard mean-variance portfolio optimization problem shows that DEMPO can reach comparable results with the same runtime for high dimensional problem. The main drawback of DEMPO with respect to QP seems to be the inability of identifying solutions over the frontier as spread out as the QP solutions. We are currently working on this problem and preliminary results suggest that by using an ad-hoc initialization scheme this drawback does not exist any longer. Moreover, to our knowledge there has not been a comparison with a QP approach to portfolio optimization yet that has demonstrated that the quality of results obtained with a DE based approach and the required runtime is comparable for high dimensional **problems**.

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[1] Goldberg, and David E., “Genetic **Algorithm** in **Search**, Optimization and Machine Learning”, Addison Wesley, 1989. [2] K. Deep and M. Thakur, “A new mutation operator for real coded genetic algorithms”, Applied mathematics and computation, volume 193, issue 1, pp. 211-230, 2007. [3] L.J. Eshelman, and J.D. Schaffer, “Real-Coded Genetic

generate sub-population, a crowding-based technique to maintain the diversity and local information, and a new crowding based archive to help the **algorithm** adapt to a dynamically changing environment. Das et al. (2014) suggested a dynamic DE **algorithm** where they used the popular multi-population approach accompanied with two special types of individuals in each subpopulation to maintain the diversity known as Quantum or Brownian individuals and do not follow the DE rules. The **algorithm** also employs a neighbourhood-driven double mutation strategy to control the perturbation and thereby prevents the population from converging too quickly with the hope to avoid premature convergence. In addition, an exclusion rule is used to spread the subpopulations over a larger portion of the **search** space as this enhances the optima tracking ability of the **algorithm**. Furthermore, an aging mechanism is incorporated to prevent the **algorithm** from stagnating at any local optimum.

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Many methods were originally proposed for unconstrained optimization **problems**, and were improved later by means of constraint-handling techniques for more difficult constrained optimization **problems** [7]. Original DE is one of those methods, which has been proposed and generally considered as a reliable, accurate, robust and fast optimization method for unconstrained continuous optimization **problems** [5] and since then it has attracted much attention and many new versions of it have been proposed and applied to practical optimization **problems**. Liu and Lampinen [8] reported that the effectiveness, efficiency and robustness of the DE **algorithm** are sensitive to the settings of the control parameters, and hence introduced a fuzzy adaptive **differential** evolution **algorithm** by using fuzzy logic controllers to adapt the **search** parameters for the mutation operator and crossover operator. Ali and Törn [9] introduced new versions of DE **algorithm** and suggested some modifications to the classical DE in order to improve its efficiency and robustness. They introduced an auxiliary population of individuals alongside the original population. Sun et al. [10] proposed a combination of DE **algorithm** and the estimation of distribution **algorithm** (EDA), which tries to guide the **search** towards a promising area by sampling new solutions from a probability model. Based on experimental results it has been demonstrated that the DE/EDA **algorithm** outperforms both DE and EDA algorithms.

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Further, in the line of ‘‘no-free-lunch” theorem, there is no optimization technique which is well defined for all type of opti- mization **problems**. This motivate us to propose a new **algorithm**, especially input control parameters free, with the hope to solve a wider range of unsolved problem. Therefore, it is justified to pro- pose a new optimization method to explore the LFC performance so as to ameliorate the degree of stability of power system. The main motivation for the expansion of **differential** **search** **algorithm** (DSA) is to achieve a simpler and effective solution of LFC problem. DSA is a recently introduced population based stochastic optimiza- tion method proposed by Civicioglu in 2012, which is inspired by the Brownian-like-random-walk used by an organism to migrate [34]. It is an iterative process which tries to minimize the selected objective function. Additionally, authors have introduced quasi- oppositional based learning (QOBL) mechanism into the original DSA to accelerate the convergence speed and to improve the com- putational efficiency of same. The proposed quasi-oppositional DSA (QODSA) method is tested on four well-known interconnected power systems and established its superiority over some recently published control algorithms for the identical test system by the transient analysis method. Two types of random load perturbation (RLP) are projected in this article to verify the robustness of the designed controllers. Finally, parametric uncertainties are considered for sensitivity analysis of the designed controllers.

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Abstract—Combining ideas from evolutionary algorithms, de- composition approaches and Pareto local **search**, this paper sug- gests a simple yet efficient memetic **algorithm** for combinatorial **multiobjective** optimization **problems**: MoMad. It decomposes a combinatorial **multiobjective** problem into a number of single objective optimization **problems** using an aggregation method. MoMad evolves three populations: population P L for recording the current solution to each subproblem, population P P for storing starting solutions for Pareto local **search**, and an external population P E for maintaining all the nondominated solutions found so far during the **search**. A problem-specific single objective heuristic can be applied to these subproblems to initialize the three populations. At each generation, a Pareto local **search** method is first applied to **search** a neighborhood of each solution in P P to update P L and P E . Then a single objective local **search** is applied to each perturbed solution in P L for improving P L and P E , and re-initializing P P . The procedure is repeated until a stopping condition is met. MoMad provides a generic hybrid algorithmic framework to use problem specific knowledge and employ well developed single objective local **search** and heuristics, and Pareto local **search** methods for dealing with combinatorial **multiobjective** **problems**. It is a population based iteration method and thus an anytime **algorithm**. Extensive experiments have been conducted in this paper to study MoMad and compare it with some other state of the art algorithms on the **multiobjective** traveling salesman problem and the **multiobjective** knapsack problem. The experimental results show that our proposed **algorithm** outperforms or performs similarly to the best so far heuristics on these two **problems**.

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[2, 3]. In the last decade, population based methods have proven to be to be successful in tackling dynamic optimisation **problems** [4-6] and such achievements have not considered to be surprising as they deal with a population of solutions that are scattered over the whole **search** space [7]. However, population based methods that were developed to solve static optimisation **problems** are considered as infeasible options when it co mes to handling dynamic optimisation proble ms. Over the years, it has become ev ident that in order to cope with problem dynamis m, population -based methods have to integrate some mechanisms that would adaptively modify their behaviours to accommodate changes in the **problems**. One of the most notable example in literature is to increase the population diversity when the changes are detected [8, 9]. A number of population-based methods, such as Genetic Algorith m (GA) [10], Particle Swarm Optimisation **Algorithm** (PSO) [11, 12] and **Differential** Evolution (DE) [13] have been employed for dynamic optimisation **problems**.

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Tizhoosh introduced the concept of opposition-based learn- ing (OBL) in [12] . This notion has been applied to accelerate the reinforcement learning [13,14] and the back propagation learning [15] in neural networks. The main idea behind OBL is the simultaneous consideration of an estimate and its corre- sponding opposite estimate (i.e., guess and opposite guess) in order to achieve a better approximation for the current candi- date solution. In the recent literature, the concept of opposite numbers has been utilized to speed up the convergence rate of an optimization **algorithm**, e.g., opposition-based **differential** evolution (ODE) [16] . This idea of opposite number may be incorporated during the harmony memory (HM) initialization and also for generating the new harmony vectors during the process of HS. In this paper, OBL has been utilized to accelerate the convergence rate of the HS **algorithm**. Hence, the proposed approach of this paper has been called as opposition-based HS (OHS). OHS uses opposite numbers during HM initialization and also for generating the new HM during the evolutionary process of HS.

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Unit commitment (UC) is the problem of formative schedule of generating units within a power system subject to device and operating constraints. This means the resultant UC schedule should get the most out of the profit, which can be regarded as to implying the minimization of the system production cost as well, during the period, given for a day and so longer time, while simultaneously satisfying the constraints of individual generator [1]. UC is a large scale optimization problem since it involves a large number of 0/1 scheduling variables that represent up/down time status of generators. Some techniques already have been applied to this problem [2-3], such as branch and bound [4], dynamic programming [5], lagrangian programming [6], genetic **algorithm** [7], **differential** evolution [8], hybrid methods [9-10].recently a new heuristic **search** **algorithm** namely gravitational **search** **algorithm**(GSA) motivated by gravitational law and law of motion have been proposed[11-12]. In this paper GSA method has been proposed for solving unit commitment problem.

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PDE is also a back propagation optimization approach[2]. The main points of this **algorithm** are: the **algorithm** generate an initial population according to Gaussian distribution N (.5,.15), then all dominated solutions are removed from the population, carry out crossover only with non-dominated solu- tions at each generation, if the number of non-dominated solu- tions exceeds the limit, then find out distance metric relation D(x) between non-dominated solutions in order to remove one which is closer to any of the non-dominated solution in the set and for producing new child, randomly select three parents from the population. The newly generated child replaces the main parent in the population only if it dominates the main parent. The **algorithm** was tested on two bench mark **problems** which contain two objective function and thirty variables. The solutions of the two test problem, provided by PDE **algorithm**, are compared with 12 other multi objective evolutionary algo- rithms (MEAs). Out of 12 algorithms no **algorithm** produces optimal result. PDE is significantly better than some of the MEAs. But there is no single crossover rate for which PDE is superior than all other algorithms.

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Many **search** techniques required auxiliary information in order to work properly. For e.g. Gradient techniques need derivative in order to chain the current peak and other procedures like greedy technique requires access to most tabular parameters whereas genetic algorithms do not require all these auxiliary information. GA is blind to perform an effective **search** for better and better structures they only require objective function values associated with the individual strings. A genetic **algorithm** (or GA) is categorized as global **search** heuristics used in computing to find true or approximate solutions to optimization **problems**. Genetic algorithms is a particular class of evolutionary algorithms that use techniques inspired by evolutionary biology such as inheritance, mutation, selection, and crossover (also called recombination). Genetic algorithms are implemented as a computer simulation in which a population of abstract representations (called chromosomes or the genotype or the genome) of candidate solutions (called individuals, creatures, or phenotypes) to an optimization problem evolves toward better solutions. [1] Traditionally, solutions are represented in binary as strings of 0s and 1s, but other encodings are also possible. The evolution usually starts from a population of randomly generated individuals and happens in generations. In each generation, the fitness of every individual in the population is evaluated, multiple individuals are selected from the current population (based on their fitness), and modified (recombined and possibly mutated) to form a new population. The new population is then used in the next iteration of the **algorithm**. Commonly,

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In the domain of science and engineering, most of the **problems** are attributed to constrained **multiobjective** opti- mization **problems** (CMOPs), which need to optimize mul- tiple conflicting objectives subject to various inequality and equality constraints. So the algorithms of solving CMOPs have to **search** the set of nondominated feasible solutions fulfilling all constraints. It is desirable that those gained solutions can approximate the true Pareto front with better diversity and even distribution. Evolutionary algorithms (EAs) are population-based **search** algorithms and can find multiple optimal solutions in one single run, and they are suitable to solve **multiobjective** **problems** (MOPs). But for the specific application of solving CMOPs, we find that most of the existing constrained **multiobjective** EAs (MOEAs) cannot effectively exploit the population because their obtained con- vergence and diversity are not acceptable.

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The researchers have used many methods to solve **problems**, various algorithms were create for solve the facility layout **problems** such as CRAFT, ALDEP and CORELAP and develop the algorithms for solving the multi floor facility layout such as SPACECRAFT, MULTIPLE, SABLE, STAGE, etc. Moreover, using mathematics with exact methods (Patsiatzis and Papageorgiou, 2002; Afrazeh et al., 2010) for finding the optimal solutions, spent more time for calculation with more variables and limitations. The optimal solution is not easy to reaching, therefore, many heuristic approacheshave been developed to get the near-optimal solutions such as simulated annealing (Meller and Bozer, 1996; Xiaoning and Weina, 2011) Genetic algorithms (Kochhar, 1998 ; Kochhar and Heragu, 1999; Lee et al., 2005), Tabu **search** (Abdinnour-Helm and Hadley, 2000). But not found yet the **differential** evolution **algorithm** used to solve the MFLPwith multi objective, so in this research will present the DE method for solving the MFLPs with the objectivesare minimize the transporting material costand maximize adjacency requirement between the facility.

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MOEA/D with Tabu **Search** for **Multiobjective** Permutation Flow Shop Scheduling **Problems**
Ahmad Alhindi, Student Member, IEEE, and Qingfu Zhang, Senior Member, IEEE,
Abstract— **Multiobjective** Evolutionary **Algorithm** based on Decomposition (MOEA/D) decomposes a **multiobjective** opti- misation problem into a number of single-objective **problems** and optimises them in a collaborative manner. This paper investigates how to use Tabu **Search** (TS), a well-studied single objective heuristic to enhance MOEA/D performance. In our proposed approach, the TS is applied to these subproblems with the aim to escape from local optimal solutions. The experimental studies have shown that MOEA/D with TS outperforms the classical MOEA/D on **multiobjective** permutation flow shop scheduling **problems**. It also have demonstrated that use of problem specific knowledge can significantly improve the algo- rithm performance.

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for continuous and discrete functions **problems**. However, a simple GA may suffer from slow convergence, and instability of results [11,12]. GAs’ problem solution power can be increased by local searching. In this study a new local random **search** **algorithm** in order to reach a quick and closer result to the optimum solution. Local **search** techniques have long been used to attack many recent optimization **problems** [13-15]. The basic idea is to start from an initial solution and to **search** for succes- sive improvements by examining neighboring solutions. The proposed local **search** technique is based on a dy- namic version of pattern **search** technique. Pattern **search** technique is a popular paradigm in Direct **Search** (DS) methods [16].

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Cuckoo **search** **algorithm** (CSA) [8] - [9] is a successful evolutionary optimization method which has been used in a large amount of numerical optimization **problems** [10]. CSA was first proposed by Xin-She Yang in [8], who described the basic framework and internal approaches of CSA. Afterward, Milan Tuba developed CSA with an a more sophisticated method for searching step [10]. CSA was based on the biological fact that some cuckoo species has a special natural habit of parasitic breeding [10]. For example, the Guira and Ani, will lay their eggs in shared nests, and they may even take others’ eggs away so that their own eggs would have more chance to be hatched [11]. CSA was soon implemented on practical engineering **problems** that its excellent performance on several types of test functions was then presented in [12]. Considering other evolutionary algorithms such as Genetic **Algorithm** and Particle Swarm Optimization, comparison shows that CSA is superior to these existing algorithms for multimodal objective functions. On one hand, there are fewer parameters to be pre-determined in CSA than in GA and PSO [8]. On the other hand, by implementing a combination of global **search** and local **search**, CSA is capable of efficiently traversing the whole searching space and accurately locating the local minima around a local space. Recently, CSA and some other evolutionary algorithms have been successfully applied to the designs of some typical types of FIR digital filters [13] - [15], which has raised people’s research interest in this field.

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1 Introduction and Related Work
General iterative heuristics such as tabu **search** and genetic algorithms (GAs) have been widely used to solve numerous hard **problems** [1]. This interest is attributed to their generality, ease of implementation, and ability to reach near optimal solutions by escaping from local minima. However, depending on size of a problem, such heuristics may have huge runtime requirements. This is also true for VLSI placement problem of modern industry-size circuits for which, iterative heuristics require huge run times to reach near optimal solutions [2, 3]. With rapidly increasing density of VLSI circuits, the run time dilemma of iterative techniques is aggravating and hence there is a need of accelerating their **search** process.

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the proposed **algorithm** operates in two Phases. In the first one, **multiobjective** version of genetic **algorithm** is used as **search** engine in order to generate approximate true Pareto front. This **algorithm** is based on concept of co-evo- lution and repair **algorithm**. Also it maintains a finite-sized archive of nondominated solutions which gets iteratively updated in the presence of new solutions based on the concept of ε-dominance. Then in the second phase, rough set theory is adopted as local **search** engine in order to improve the spread of the solutions found so far. Our proposed approach keeps track of all the feasible solutions found during the optimization. The results, provided by the proposed **algorithm** for benchmark **problems** and engineering applications, are promis- ing when compared with exiting well-known algorithms. Also, our results suggest that our **algorithm** is better applicable for solving real-world application **problems**.

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