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Abstract: Enhanced index tracking is a popular strategy in portfolio management that focuses on adding reliable value relative to the index on the basis of mimicking the behavior of the benchmark index. In this paper, we propose a multi-objective optimization scheme for the enhanced index tracking problem, which provides the framework of defining the objectives as both maximizing the degree of beating the benchmark index and minimizing the accumulated error of underperforming the benchmark. Transaction costs are limited in the constraints. An immunity-based multi-objective optimization algorithm is presented to search for the solution of the enhanced index tracking problem. Treatment of infeasibility and solution selection are also presented. Our proposed approach is implemented to five data sets drawn from major world markets. The computational results compared with other published results show that our method has superior performance. [ABSTRACT FROM AUTHOR]

Abstract: The permutation flow shop scheduling problem is addressed in this paper. Two objectives, minimization of makespan and total flow time, are considered. We propose a memetic algorithm, called NNMA, by integrating a general multiobjective evolutionary algorithm (NSGA-II) with a problem-specific heuristic (NEH). We take NEH as a local improving procedure in NNMA and propose several adaptations including the acceptance criterion and job-insertion ordering to deal with multiple objectives and to improve its performance. We test the performance of NNMA using 90 public problem instances with different problem scales, and compare its performance with 23 algorithms. The experimental results show that our NNMA provides close performance for 30 small-scale instances and better performance for 50 medium- and large-scale instances. Furthermore, more than 70% of the net set of non-dominated solutions is updated by NNMA for these 50 instances. [ABSTRACT FROM AUTHOR]

Abstract: This paper introduces a new stochastic approach for assisted history matching based on a continuous ant colony optimization algorithm. Ant Colony Optimization (ACO) is a multi-agent optimization algorithm inspired by the behavior of real ants. ACO is able to solve difficult optimization problems in both discrete and continuous variables. In the ACO algorithm, each artificial ant in the colony searches for good models in different regions of parameter space and shares information about the quality of the models with other agents. This gradually guides the colony towards models that match the desired behavior — in our case the production history of the reservoir. The use of ACO for history matching has been illustrated on two reservoir simulation cases. The first case is Teal South model which is a real reservoir with a simple structure and a single producing well. History matching of this model is a low dimensional problem with eight parameters. The second case study is PUNQ-S3 reservoir which has a more complex geological structure than Teal South model. This problem entails solving a high dimensional optimization problem. [Copyright &y& Elsevier]

Abstract: Many real life problems can be stated as a minimax optimization problem, such as the problems in economics, finance, management, engineering and other fields. In this paper, we present an algorithm with nonmonotone strategy and second-order correction technique for minimax optimization problems. Using this scheme, the new algorithm can overcome the difficulties of the Maratos effect occurred in the nonsmooth optimization, and the global and superlinear convergence of the algorithm can be achieved accordingly. Numerical experiments indicate some advantages of this scheme. [Copyright &y& Elsevier]

Abstract: In this paper, we first investigate the invertibility of a class of matrices. Based on the obtained results, we then discuss the solvability of Newton equations appearing in the smoothing-type algorithm for solving the second-order cone complementarity problem (SOCCP). A condition ensuring the solvability of such a system of Newton equations is given. In addition, our results also show that the assumption that the Jacobian matrix of the function involved in the SOCCP is a -matrix is not enough for ensuring the solvability of such a system of Newton equations, which is different from the one of smoothing-type algorithms for solving many traditional optimization problems in . [ABSTRACT FROM AUTHOR]

Simulated Annealing (SA) has been adopted by many Ensemble Clustering methods to achieve global combinational optimisation. However the performance of SA is sensitive to the settings of its parameters. Much work has been done for optimising the settings of these parameters over the last two decades, but few of them analysed the behaviour of different cooling functions for Ensemble Clustering. Our work has demonstrated that the clustering results could be invalid if we use SA for Ensemble Clustering without a good understanding of the behaviour of cooling functions. Therefore this paper aims to present the findings of how different cooling functions may affect the performance of Ensemble Clustering methods that use SA. We analyse the effect of cooling functions from three aspects: the convergence rate, the final value of the objective function, and the accuracy of results. Ten different cooling functions are tested on two Ensemble Clustering methods, and thirteen different datasets have been used for the experiments. The findings are particularly helpful for those who are interested in Ensemble Clustering methods as well as those who want to obtain a deep understanding of the behaviour of the cooling functions. [ABSTRACT FROM AUTHOR]

This paper proposes an improved subspace-based optimization method (SOM) by using a new construction method for the ambiguous part of the induced current. The new current construction method reduces not only the computational complexity of the current construction in every iteration of the optimization but also the computational complexity of the singular-value decomposition of the mapping from the induced current to scattered fields. Thus, the improved SOM is able to deal with the 3-D inverse-scattering problems. Numerical tests validate the algorithm. [ABSTRACT FROM AUTHOR]

Abstract: This paper proposes new Differential Evolution (DE) algorithm, named as Chaotically Initialized Differential Evolution (CIDE), that uses chaotic maps with certainty, ergodicity, unpredictability, non-periodicity, complex temporal behavior and the stochastic property for initial population generation. This has been done by using of different chaotic number generators each time a random number is needed by the classical DE algorithm in its initial step. Seven chaotic maps have been analyzed in the benchmark functions. It has been detected that coupling emergent results in different areas, like those of DE and complex dynamics, can improve the quality of results in some optimization problems and also that chaos may be a desired process. It has been also shown that, Sinus map and Circle map have somewhat increased the solution quality, that is in some cases they improved the global searching capability by escaping the local solutions. [Copyright &y& Elsevier]

Abstract: Kernelization is a strong and widely-applied technique in parameterized complexity. A kernelization algorithm, or simply a kernel, is a polynomial-time transformation that transforms any given parameterized instance to an equivalent instance of the same problem, with size and parameter bounded by a function of the parameter in the input. A kernel is polynomial if the size and parameter of the output are polynomially-bounded by the parameter of the input. In this paper we develop a framework which allows showing that a wide range of FPT problems do not have polynomial kernels. Our evidence relies on hypothesis made in the classical world (i.e. non-parametric complexity), and revolves around a new type of algorithm for classical decision problems, called a distillation algorithm, which is of independent interest. Using the notion of distillation algorithms, we develop a generic lower-bound engine that allows us to show that a variety of FPT problems, fulfilling certain criteria, cannot have polynomial kernels unless the polynomial hierarchy collapses. These problems include k-Path, k-Cycle, k-Exact Cycle, k-Short Cheap Tour, k-Graph Minor Order Test, k-Cutwidth, k-Search Number, k-Pathwidth, k-Treewidth, k-Branchwidth, and several optimization problems parameterized by treewidth and other structural parameters. [Copyright &y& Elsevier]

Abstract: In this paper, we study the inverse sorting problem with bound constraints under the -norm and the Hamming distance. For the problem under the -norm, an -time algorithm is presented. For the problem under the Hamming distance, we first show that it has an -time lower bound in the comparison model; and then, we present an -time algorithm. Both of the presented algorithms improve the previous upper bounds from . [Copyright &y& Elsevier]

In this paper, we study the quadratic model updating problems by using symmetric low-rank correcting, which incorporates the measured model data into the analytical quadratic model to produce an adjusted model that matches the experimental model data, and minimizes the distance between the analytical and updated models. We give a necessary and sufficient condition on the existence of solutions to the symmetric low-rank correcting problems under some mild conditions, and propose two algorithms for finding approximate solutions to the corresponding optimization problems. The good performance of the two algorithms is illustrated by numerical examples. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper introduces the algorithm portfolio concept to solve a combinatorial optimization problem pertaining to a supply chain. The supply chain problem is modeled with capacity constraints and demand variations over different time periods to minimize the total supply chain configuration cost. The algorithm portfolio is implemented over various problem instances to inspect and alleviate the computational expensiveness of a solution strategy. A bunch of five algorithms are utilized hereby viz. AIS, GA, Endosymbiotic Optimization, PSO and Psychoclonal algorithm. The observations reflect the appropriateness and effect of algorithm portfolios over the adopted supply chain, and viability over other optimization problems. [Copyright &y& Elsevier]

Recent research shows that simulated annealing with orthogonal array based neighbourhood functions can help in the search for a solution to a parametrical problem which is closer to an optimum when compared with conventional simulated annealing. Previous studies of simulated annealing analyzed only the main effects of variables of parametrical problems. In fact, both main effects of variables and interactions between variables should be considered, since interactions between variables exist in many parametrical problems. In this paper, an improved orthogonal array based neighbourhood function (IONF) for simulated annealing with the consideration of interaction effects between variables is described. After solving a set of parametrical benchmark function problems where interaction effects between variables exist, results of the benchmark tests show that the proposed simulated annealing algorithm with the IONF outperforms significantly both the simulated annealing algorithms with the existing orthogonal array based neighbourhood functions and the standard neighbourhood functions. Finally, the improved orthogonal array based simulated annealing was applied on the optimization of emulsified dynamite packing-machine design by which the applicability of the algorithm in real world problems can be evaluated and its effectiveness can be further validated. [Copyright &y& Elsevier]

This paper presents an algorithm for solving global optimization problems with bounded variables. The algorithm is a modification of the electromagnetism-like mechanism proposed by Birbil and Fang [An electromagnetism-like mechanism for global optimization, J. Global Optim. 25 (2003), pp. 263-282]. The differences are mainly on the local search procedure and on the force vector used to move each point in the population. Several widely-used benchmark problems were solved in a performance evaluation of the new algorithm when compared with the original one. A comparison with other stochastic methods is also included. The algorithm seems appropriate for large dimension problems. [ABSTRACT FROM AUTHOR]

This paper aims to study distribution system operations by the ant colony search algorithm (ACSA). The objective of this study is to present new algorithms for solving the optimal feeder reconfiguration problem, the optimal capacitor placement problem, and the problem of a combination of the two. The ACSA is a relatively new and powerful swarm intelligence method for solving optimization problems. It is a population-based approach that uses exploration of positive feedback as well as "greedy" search. The ACSA was inspired from the natural behavior of ants in locating food sources and bring them back to their colony by the formation of unique trails. Therefore, through a collection of cooperative agents called "ants," the near-optimal solution to the feeder reconfiguration and capacitor placement problems can be effectively achieved. In addition, the ACSA applies the state transition, local pheromone-updating, and global pheromone-updating rules to facilitate the computation. Through simultaneous operation of population agents, process stagnation can be effectively prevented. Optimization capability can be significantly enhanced. The proposed approach is demonstrated using two example systems from the literature. Computational results show that simultaneously taking into account both feeder reconfiguration and capacitor placement is more effective than considering them separately. [ABSTRACT FROM AUTHOR]

• The proposed ADMM-based algorithm can accelerate the solving of beam pattern synthesis problem. • The proposed element pattern selection scheme is able to greatly shrink the possible pattern combination search space. • The proposed pattern selection and optimization algorithm can further suppress the peak sidelobe level about 0 dB to 4 dB. The paper considers the array beam pattern synthesis (BPS) problem with reconfigurable pattern elements (RPE). Both the array weight and the array pattern are optimized, which further suppresses the peak sidelobe level (PSLL) compared with the fixed pattern array. For the array pattern optimization, the conventional selecting of appropriate N elements from K radiation patterns requires to evaluate all possible K N choices, resulting in the non-deterministic polynomial-hard RPE selection problem. In this work, this problem is solved through investigating different element pattern combinations with randomly arranged pattern locations. In such way, the possible solutions to the RPE selection problem has an overall choices of C N + K − 1 K − 1 = (N + K − 1) ! N ! (K − 1) ! , which extremely shrinks the solution space. An algorithm with the RPE selection and array weight optimization is proposed for the BPS problem. Furthermore, the alterative direction method of multipliers (ADMM) framework is introduced to accelerate the computation speed. The proposed algorithm provides an effective scheme for generating appropriate RPE combinations for PSLL suppression, resulting in a wider-angular scanning ability for array antenna. Simulation results demonstrate 0 dB to 4 dB lower PSLL can be obtained compared with the algorithms based on the fixed element pattern. [ABSTRACT FROM AUTHOR]

The problems of fuel reloading optimization is a complex multi-objective discrete optimization problem with multiple local optimums. In recent years, great process has been made in solving these problems by using meta-heuristic optimization algorithms. Teaching-learning based optimization algorithm (TLBO) is one kind of novel meta-heuristic optimization algorithms. However, it is seldom used to solve the problems of fuel reloading optimization, because its original purpose is to solve continuous optimization problems. In this paper, a hybrid teaching-learning genetic algorithm (HTLGA) is developed, which could be directly applied to solve the problems of fuel reloading optimization. This hybrid algorithm takes TLBO as main part, combines three operators of genetic algorithms (GA) which are coding, crossover and mutation. The optimization solutions which are represented as students in TLBO are further divided into top students, ordinary students and poor students in HTLGA. The calculation phases "Teacher phase" and "Learner phase" in TLBO are improved into "Teacher phase", "Discussion phase" and "Self-study phase" in HTLGA. For testing the optimization ability of HTLGA, it is applied to solve the problems of fuel reloading optimization for the 1/6 core of thorium-based block-type HTGRs. The results showed that the developed HTLGA has more powerful optimization ability than TLBO and GA. • By combining TLBO and GA, the hybrid teaching-learning genetic algorithm (HTLGA) was developed. • The correctness of developed optimization program based on HTLGA was proved. • For solving the problems of fuel reloading optimization, the optimization ability of HTLGA, TLBO and GA was compared. [ABSTRACT FROM AUTHOR]

Tree-Seed Algorithm (TSA) is a meta-heuristic optimization algorithm with good performance in solving continuous optimization problems. However, there is an imbalance between its exploration and exploitation when solving complex problems, mainly lack exploration. To overcome this problem, this paper proposes two tree migration mechanisms: triple-learning-based migration mechanism and sine-random-distribution migration mechanism. The target tree position is migrated by learning from the first three trees in the current iteration. The sine function is added to the tree migration formula to enhance the randomness of tree distribution. In order to verify these migration mechanisms, Triple Tree-Seed Algorithm (TriTSA) has been proposed and compared with TSA on 30 well-known test functions from IEEE CEC 2014. In addition, STSA, SCA, PSO, ABC, Jaya, and TLBO are adopted in some comparative experiments on different dimensions. The experiments show that the tree migration mechanism can improve the optimization capability of the original algorithm effectively. On all 30 benchmark test functions, TriTSA outperforms TSA on 10, 30, 50, and 100 dimensions by 70%, 90%, 90%, and 97% respectively. Finally, the proposed TriTSA is compared with TSA, ABC, PSO, and SCA on solving two classical engineering design problems. It is proved that the proposed algorithm is more applicable in solving practical problems. [ABSTRACT FROM AUTHOR]

The decomposition-based multi-objective evolutionary algorithm (MOEA/D) has shown remarkable effectiveness in solving multi-objective problems (MOPs). In this paper, we integrate the quantum-behaved particle swarm optimization (QPSO) algorithm with the MOEA/D framework in order to make the QPSO be able to solve MOPs effectively, with the advantage of the QPSO being fully used. We also employ a diversity controlling mechanism to avoid the premature convergence especially at the later stage of the search process, and thus further improve the performance of our proposed algorithm. In addition, we introduce a number of nondominated solutions to generate the global best for guiding other particles in the swarm. Experiments are conducted to compare the proposed algorithm, DMO-QPSO, with four multi-objective particle swarm optimization algorithms and one multi-objective evolutionary algorithm on 15 test functions, including both bi-objective and tri-objective problems. The results show that the performance of the proposed DMO-QPSO is better than other five algorithms in solving most of these test problems. Moreover, we further study the impact of two different decomposition approaches, i.e., the penalty-based boundary intersection (PBI) and Tchebycheff (TCH) approaches, as well as the polynomial mutation operator on the algorithmic performance of DMO-QPSO. [ABSTRACT FROM AUTHOR]

This paper proposes a hybrid algorithm based on particle swarm optimization (PSO) for a multiobjective permutation flow shop scheduling problem, which is a typical NP-hard combinatorial optimization problem with strong engineering backgrounds. Not only does the proposed multiobjective algorithm (named MOPSO) apply the parallel evolution mechanism of PSO characterized by individual improvement, population cooperation, and competition to effectively perform exploration but it also utilizes several adaptive local search methods to perform exploitation. First, to make PSO suitable for solving scheduling problems, a ranked-order value (ROV) rule based on a random key technique to convert the continuous position values of particles to job permutations is presented. Second, a multiobjective local search based on the Nawaz-Enscore-Ham heuristic is applied to good solutions with a specified probability to enhance the exploitation ability. Third, to enrich the searching behavior and to avoid premature convergence, a multiobjective local search based on simulated annealing with multiple different neighborhoods is designed, and an adaptive meta-Lamarckian learning strategy is employed to decide which neighborhood will be used. Due to the fusion of multiple different searching operations, good solutions approximating the real Pareto front can be obtained. In addition, MOPSO adopts a random weighted linear sum function to aggregate multiple objectives to a single one for solution evaluation and for guiding the evolution process in the multiobjective sense. Due to the randomness of weights, searching direction can be enriched, and solutions with good diversity can be obtained. Simulation resuIts and comparisons based on a variety of instances demonstrate the effectiveness, efficiency, and robustness of the proposed hybrid algorithm. [ABSTRACT FROM AUTHOR]

We consider the problem of computing the smallest contact forces, with point-contact friction model, that can hold an object in equilibrium against a known external applied force and torque. It is known that the force optimization problem (FOP) can be formulated as a semidefinite programming problem (SDP) or a second-order cone problem (SOCP), and thus, can be solved using several standard algorithms for these problem classes. In this paper, we describe a custom interior-point algorithm for solving the FOP that exploits the specific structure of the problem, and is much faster than these standard methods. Our method has a complexity that is linear in the number of contact forces, whereas methods based on generic SDP or SOCP algorithms have complexity that is cubic in the number of forces. Our method is also much faster for smaller problems. We derive a compact dual problem for the FOP, which allows us to rapidly compute lower bounds on the minimum contact force and certify the infeasibility of a FOP. We use this dual problem to terminate our optimization method with a guaranteed accuracy. Finally, we consider the problem of solving a family of FOPs that are related. This occurs, for example, in determining whether force closure occurs, in analyzing the worst case contact force required over a set of, external forces and torques, and in the problem of choosing contact points on an object so as to minimize the required contact force. Using dual bounds, and a warm-start version of our FOP method, we show how such families of FOPs can be solved very efficiently. [ABSTRACT FROM AUTHOR]

In the last two decades, a number of algorithms for the linear single-commodity min-cost flow (MCF) problem have been proposed, and several efficient codes are available that implement different variants of the algorithms. The practical significance of the algorithms has been tested by comparing the time required by their implementations for solving "from-scratch" instances of MCF, of different classes, as the size of the problem (number of nodes and arcs) increases. However, in many applications several closely related instances of MCF have to be sequentially solved, so that reoptimization techniques can be used to speed up computations, and the most attractive algorithm is the one that minimizes the total time required to solve all the instances in the sequence. In this paper we compare the performances of four different efficient implementations of algorithms for MCF under cost reoptimization in the context of decomposition algorithms for the multicommodity min-cost flow (MMCF) problem, showing that for some classes of instances the relative performances of the codes doing "from-scratch" optimization do not accurately predict the relative performances when reoptimization is used. Because the best solver depends both on the class and on the size of the instance, this work also shows the usefulness of a standard interface for MCF problem solvers that we have proposed and implemented. [ABSTRACT FROM AUTHOR]

This paper is concerned with the solution of a linear system with multiple right-hand sides. Such problems arise from nonlinear, time-dependent, inverse, or optimization problems. In order to solve these problems efficiently we use block variants of the conjugate gradient method and combine them with cache aware algorithms. Further, we describe the acceleration of algebraic multigrid (AMG) methods by using such cache aware algorithms. Finally, numerical studies are presented that show the high efficiency of the proposed methods. [ABSTRACT FROM AUTHOR]

The optimization of difference patterns of monopulse antennas is considered. The synthesis problem is recast as an optimization problem by defining a suitable cost function. In particular, in this paper, the cost function is based on constraints on the side-lobe levels. A subarray configuration is adopted and the ex- citations of the difference pattern are approximately determined. The optimization problem is efficiently solved by a differential evolution algorithm, which is able to contemporarily handle real and integer unknowns. Numerical results are reported concerning classical array configurations previously considered in the literature. [ABSTRACT FROM AUTHOR]

Accurate nonlinear dynamic models of process operations such as start-ups and shut-downs include state-dependent events that trigger discrete changes to the describing equations, and are best analyzed within a hybrid systems framework. The automated design of an optimal process operation can thus be formulated as a dynamic optimization problem with a hybrid system embedded. This paper describes recent progress on the development of suitable deterministic algorithms for the global solution of these problems. A method for constructing convex relaxations of general nonconvex nonlinear programming (NLP) problems with linear dynamic systems embedded is presented. These convex relaxations are then extended to multistage problems with model switches between the stages. Finally, integer variables are introduced to represent alternative sequences of model switches. The ability to construct convex relaxations enables existing nonconvex mixed nonlinear programming (MINLP) algorithms to be applied to find the global solution of the resulting mixed integer dynamic optimization (MIDO) problems. [Copyright &y& Elsevier]

Repair-based search algorithms start with an initial solution and attempt to improve it by iteratively applying repair operators. Such algorithms can often handle large-scale problems that may be difficult for systematic search algorithms. Nevertheless, the computational cost of solving such problems is still very high. We observed that many of the repair steps applied by such algorithms are redundant in the sense that they do not eventually contribute to finding a solution. Such redundant steps are particularly harmful in repair-based search, where each step carries high cost due to the very high branching factor typically associated with it. Accurately identifying and avoiding such redundant steps would result in faster local search without harming the algorithm's problem-solving ability. In this paper we propose a speedup learning methodology for attaining this goal. It consists of the following steps: defining the concept of a redundant step; acquiring this concept during off-line learning by analyzing solution paths for training problems, tagging all the steps along the paths according to the redundancy definition and using an induction algorithm to infer a classifier based on the tagged examples; and using the acquired classifier to filter out redundant steps while solving unseen problems. Our algorithm was empirically tested on instances of real-world employee timetabling problems (ETP). The problem solver to be improved is based on one of the best methods for solving some large ETP instances. Our results show a significant improvement in speed for test problems that are similar to the given example problems. [ABSTRACT FROM AUTHOR]

This paper presents a new distributed algorithm based on Ant System (AS) concepts called combinatorial Ant System (CAS). It is oriented to solve static discrete-state combinatorial optimization problems. Our approach consists of mapping the solution space of the combinatorial optimization problem in the space where the ants will walk, and defining the transition probability and the pheromone update formula of the Ant System, according to the objective function of the combinatorial Optimization Problem. We test our approach on the graph partitioning, graph coloring and traveling salesman problems. [ABSTRACT FROM AUTHOR]

The main point of this paper is to provide a simple and efficient threshold value for the threshold accepting (TA) algorithm to attempt an optimal solution for the regular grid travelling salesman problems (TSPs) in a reliable way. This new algorithm is named the single value threshold accepting algorithm (SVTA). The number of the threshold value is one and its value is: [(2-√2)g*10,0001/10,000 where g is the grid size and [x] is the smallest integer not less than a real number x. For the regular-grid TSPs, g can be set as 1/√n where n is the problem size. It is shown empirically, with 100 independent simulations performed with 441 cities, in 16 different cases, that the SVTA is far superior to (at least five times faster on average than) the previous double threshold accepting (DTA) with respect to the speed of finding a global optimal reliably. Particularly in the case of the 441 cities, the proposed algorithm is at least 21 times faster and rises up to 96 times on average and optimistically 284 times faster than the previous one. Important insight is provided that reveals how the formula works and why it works successfully. [ABSTRACT FROM AUTHOR]

This paper proposes a hybrid whale optimization algorithm (WOA) that is derived from the genetic and thermal exchange optimization-based whale optimization algorithm (GWOA-TEO) to enhance global optimization capability. First, the high-quality initial population is generated to improve the performance of GWOA-TEO. Then, thermal exchange optimization (TEO) is applied to improve exploitation performance. Next, a memory is considered that can store historical best-so-far solutions, achieving higher performance without adding additional computational costs. Finally, a crossover operator based on the memory and a position update mechanism of the leading solution based on the memory are proposed to improve the exploration performance. The GWOA-TEO algorithm is then compared with five state-of-the-art optimization algorithms on CEC 2017 benchmark test functions and 8 UCI repository datasets. The statistical results of the CEC 2017 benchmark test functions show that the GWOA-TEO algorithm has good accuracy for global optimization. The classification results of 8 UCI repository datasets also show that the GWOA-TEO algorithm has competitive results with regard to comparison algorithms in recognition rate. Thus, the proposed algorithm is proven to execute excellent performance in solving optimization problems. [ABSTRACT FROM AUTHOR]

In practical applications, solving multimodal multiobjective optimization problems (MMOPs), which have multiple Pareto optimal sets (PSs) in the decision space mapping to the same Pareto front (PF) in the objective space, has great significance for decision makers. The issue of how to maintain diversity in both decision space and objective space remains a key problem for existing multimodal multiobjective evolutionary algorithms. To address this issue, a novel grey prediction evolution algorithm for multimodal multiobjective optimization, termed MMGPE, is proposed in this paper. This is the first time that the grey prediction evolution algorithm (GPE), which is a recently proposed competitive optimization algorithm with strong exploration capability, is improved for MMOPs. These improvements are conducted in the following four aspects: (1) an initialization operator based on particle swarm optimization, (2) an adaptive parameter setting strategy depending on the domain of decision variables of MMOPs, (3) an accelerating convergence mechanism inspired by the niche principle, and (4) an environmental selection operator based on a nondominated sorting mechanism and a special crowding distance approach. The performance of MMGPE is compared with two state-of-the-art multiobjective evolutionary algorithms and four multimodal multiobjective evolutionary algorithms on 11 multimodal multiobjective test functions. MMGPE is also applied to solve a practical problem. The results show the MMGPE's effectiveness and superiority in achieving the goal of finding multiple PSs while obtaining a well-distributed PF. [ABSTRACT FROM AUTHOR]

Several population-based metaheuristic optimization algorithms have been proposed in the last decades, none of which are able either to outperform all existing algorithms or to solve all optimization problems according to the No Free Lunch (NFL) theorem. Many of these algorithms behave effectively, under a correct setting of the control parameter(s), when solving different engineering problems. The optimization behavior of these algorithms is boosted by applying various strategies, which include the hybridization technique and the use of chaotic maps instead of the pseudo-random number generators (PRNGs). The hybrid algorithms are suitable for a large number of engineering applications in which they behave more effectively than the thoroughbred optimization algorithms. However, they increase the difficulty of correctly setting control parameters, and sometimes they are designed to solve particular problems. This paper presents three hybridizations dubbed HYBPOP, HYBSUBPOP, and HYBIND of up to seven algorithms free of control parameters. Each hybrid proposal uses a different strategy to switch the algorithm charged with generating each new individual. These algorithms are Jaya, sine cosine algorithm (SCA), Rao's algorithms, teaching-learning-based optimization (TLBO), and chaotic Jaya. The experimental results show that the proposed algorithms perform better than the original algorithms, which implies the optimal use of these algorithms according to the problem to be solved. One more advantage of the hybrid algorithms is that no prior process of control parameter tuning is needed. [ABSTRACT FROM AUTHOR]

In practical applications, there may exist a disparity between real values and optimal results due to uncertainties. This kind of disparity may cause violations of some probabilistic constraints in a reliability based design optimization (RBDO) problem. It is important to ensure that the probabilistic constraints at the optimum in a RBDO problem are insensitive to the variations of design variables. In this paper, we propose a novel concept and procedure for reliability based robust design in the context of random uncertainty and epistemic uncertainty. The epistemic uncertainty of design variables is first described by an info gap model, and then the reliability-based robust design optimization (RBRDO) is formulated. To reduce the computational burden in solving RBRDO problems, a sequential algorithm using shifting factors is developed. The algorithm consists of a sequence of cycles and each cycle contains a deterministic optimization followed by an inverse robustness and reliability evaluation. The optimal result based on the proposed model satisfies certain reliability requirement and has the feasible robustness to the epistemic uncertainty of design variables. Two examples are presented to demonstrate the feasibility and efficiency of the proposed method. [ABSTRACT FROM AUTHOR]