Recently, Pinar Civicioglu  developed a new metaheuristic searchalgorithm called DifferentialSearchAlgorithm (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 multiobjectiveproblems as high speed of convergence and less overhead of parameters setting. In this paper, a novel approach named multiobjectivedifferentialsearchalgorithm (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.
In this paper, we have introduced a new multiobjectivealgorithm 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.
 Goldberg, and David E., “Genetic Algorithm in Search, Optimization and Machine Learning”, Addison Wesley, 1989.  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.  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.
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 . 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  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  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  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.  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.
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 differentialsearchalgorithm (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 . 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.
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 multiobjectiveproblems. 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.
[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 . 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) , Particle Swarm Optimisation Algorithm (PSO) [11, 12] and Differential Evolution (DE)  have been employed for dynamic optimisation problems.
Tizhoosh introduced the concept of opposition-based learn- ing (OBL) in  . This notion has been applied to accelerate the reinforcement learning [13,14] and the back propagation learning  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)  . 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.
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 . 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 , dynamic programming , lagrangian programming , genetic algorithm , differential evolution , hybrid methods [9-10].recently a new heuristic searchalgorithm namely gravitational searchalgorithm(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.
PDE is also a back propagation optimization approach. 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.
multiobjective optimization problem (MOP) difficult for multi- objective evolutionary algorithms (MOEAs). To deal with this problem feature, an algorithm should carefully balance between exploration and exploitation. The decomposition-based MOEA decomposes an MOP into a number of single objective subprob- lems and solves them in a collaborative manner. Single objective optimizers can be easily used in this algorithm framework. Covariance matrix adaptation evolution strategy (CMA-ES) has proven to be able to strike good balance between the explo- ration and the exploitation of search space. This paper proposes a scheme to use both differential evolution (DE) and covariance matrix adaptation in the MOEA based on decomposition. In this scheme, single objective optimization problems are clustered into several groups. To reduce the computational overhead, only one subproblem from each group is selected to optimize by CMA-ES while other subproblems are optimized by DE. When an evo- lution strategy procedure meets some stopping criteria, it will be reinitialized and used for solving another subproblem in the same group. A set of new multiobjective test problems with bias features are constructed in this paper. Extensive experimental studies show that our proposed algorithm is suitable for dealing with problems with biases.
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.  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,
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 multiobjectiveproblems (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.
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.
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.
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 searchalgorithm 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 .
Cuckoo searchalgorithm (CSA)  -  is a successful evolutionary optimization method which has been used in a large amount of numerical optimization problems . CSA was first proposed by Xin-She Yang in , who described the basic framework and internal approaches of CSA. Afterward, Milan Tuba developed CSA with an a more sophisticated method for searching step . CSA was based on the biological fact that some cuckoo species has a special natural habit of parasitic breeding . 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 . CSA was soon implemented on practical engineering problems that its excellent performance on several types of test functions was then presented in . 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 . 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  - , which has raised people’s research interest in this field.
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 . 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.
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.