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The $k\text {-means}$ clustering problem concerns finding a partition of the data points into $k$ clusters such that the total within-cluster squared distance is minimized. This optimization objective is non-convex, and not everywhere differentiable. In general, there exist spurious local solutions other than the global optimum. Moreover, the simplest and most popular algorithm for $k\text {-means}$ , namely Lloyd’s algorithm, generally converges to such spurious local solutions both in theory and in practice. In this paper, we investigate the structures of these spurious local solutions under a probabilistic generative model with $k$ ground truth clusters. As soon as $k=3$ , spurious local minima provably exist, even for well-separated clusters. One such local minimum puts two centers at one true cluster, and the third center in the middle of the other two true clusters. We prove that this is essentially the only type of spurious local minima under a separation condition. In particular, any local minimum solution only involves a configuration that puts multiple centers at a true cluster, and one center in the middle of multiple true clusters. Our results pertain to the $k\text {-means}$ formulation for mixtures of Gaussians or bounded distributions, and hold in the over- and under-parametrization regimes where the number of centers in $k\text {-means}$ may not equal to the number of true clusters. Our theoretical results corroborate existing empirical observations and provide justification for popular heuristics for $k\text {-means}$ clustering. [ABSTRACT FROM AUTHOR]

When solving constrained optimization problems (COPs) by evolutionary algorithms, the search algorithm plays a crucial role. In general, we expect that the search algorithm has the capability to balance not only diversity and convergence but also constraints and objective function during the evolution. For this purpose, this paper proposes a composite differential evolution (DE) for constrained optimization, which includes three different trial vector generation strategies with distinct advantages. In order to strike a balance between diversity and convergence, one of these three trial vector generation strategies is able to increase diversity, and the other two exhibit the property of convergence. In addition, to accomplish the tradeoff between constraints and objective function, one of the two trial vector generation strategies for convergence is guided by the individual with the least degree of constraint violation in the population, and the other is guided by the individual with the best objective function value in the population. After producing offspring by the proposed composite DE, the feasibility rule and the $\boldsymbol {\varepsilon }$ constrained method are combined elaborately for selection in this paper. Moreover, a restart scheme is proposed to help the population jump out of a local optimum in the infeasible region for some extremely complicated COPs. By assembling the above techniques together, a constrained composite DE is proposed. The experiments on two sets of benchmark test functions with various features, i.e., 24 test functions from IEEE CEC2006 and 18 test functions with 10 dimensions and 30 dimensions from IEEE CEC2010, have demonstrated that the proposed method shows better or at least competitive performance against other state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Pareto dominance-based multiobjective optimization has been successfully applied to constrained evolutionary optimization during the last two decades. However, as another famous multiobjective optimization framework, decomposition-based multiobjective optimization has not received sufficient attention from constrained evolutionary optimization. In this paper, we make use of decomposition-based multiobjective optimization to solve constrained optimization problems (COPs). In our method, first of all, a COP is transformed into a biobjective optimization problem (BOP). Afterward, the transformed BOP is decomposed into a number of scalar optimization subproblems. After generating an offspring for each subproblem by differential evolution, the weighted sum method is utilized for selection. In addition, to make decomposition-based multiobjective optimization suit the characteristics of constrained evolutionary optimization, weight vectors are elaborately adjusted. Moreover, for some extremely complicated COPs, a restart strategy is introduced to help the population jump out of a local optimum in the infeasible region. Extensive experiments on three sets of benchmark test functions, namely, 24 test functions from IEEE CEC2006, 36 test functions from IEEE CEC2010, and 56 test functions from IEEE CEC2017, have demonstrated that the proposed method shows better or at least competitive performance against other state-of-the-art methods. [ABSTRACT FROM AUTHOR]

In order to obtain a good optimization method for the electrical transformer design with optimal selection of parameters, performance evaluation of three evolutionary algorithms (EAs), namely, genetic algorithm (GA), differential evolution algorithm, and nondominated sorting GA (NSGA-II), is carried out. The aim of this paper is to optimize parameters of transformer design (core thicknesses, primary-turn number, secondary-turn number, primary conductor area, and secondary conductor area) for minimization of total power losses (no-load losses and load losses) in three-phase transformer topology while maintaining high efficiency and low cost. The method used for this optimization scheme combines the finite-element method (FEM) and EAs to provide an accurate selection of parameters together with the optimized magnetic flux density and decreased loss. Experimental results show that NSGA-II+FEM model successfully provides a global feasible solution by minimizing total loss and related cost while improving the efficiency of three-phase transformer, rendering it suitable for application in the design environment of industrial transformers. [ABSTRACT FROM AUTHOR]

Band selection refers to finding the most representative channels from hyperspectral images. Usually, certain objective functions are designed and combined via regularization terms. A possible drawback of these methods is that they can only generate one solution in a single run with a given band number. To overcome this problem, multiobjective (MO)-based methods, which were able to simultaneously obtain a series of subsets with different band numbers, were investigated for band selection. However, because the range of band selection problem is discrete, recently proposed weighted Tchebycheff (WT)-based MO methods may suffer weakly Pareto optimal problem. In this case, the solutions for each band number will be nonunique and no optimal solution exists. Decision makers have to manually select a unique solution for each band number. In this paper, we provide a theoretical analysis about the weakly Pareto optimal problem in band selection, and quantitatively give the boundary conditions. Moreover, we further summarize the suggestions which will help users avoid the weakly Pareto optimal problem. According to these criteria, we develop a new adaptive-penalty-based boundary intersection (APBI) framework to improve the MO algorithm in hyperspectral band selection. APBI mainly includes two advantages: 1) avoiding weakly Pareto optimum and 2) reducing the sensibility of the penalty factor. The theoretical analysis is further validated by contrast experiments. The results demonstrate that the weakly Pareto optimal solutions really exist in WT methods, while APBI can overcome this problem. [ABSTRACT FROM AUTHOR]

Power converters systems aimed at renewable energy applications have become a common option for sustainable electricity and distributed generation, since their performance has improved, and prices have steadily been reduced in the last years. However, there are still several drawbacks that hinder their widespread installation, such as the simultaneous minimization of cost and volume, efficiency maximization, size reduction, etc. Quite often, accomplishing these goals requires dealing with complicated optimization problems, which are difficult to solve by classical methods. Metaheuristic techniques provide a viable alternative to solve complex intricate optimization problems, such as those encountered in the development of power electronics converters. This paper presents a comprehensive coverage of metaheuristic methodologies applied in the area of power converters. The review includes a classification of the methodologies and main objective functions in each paper surveyed. An aim for this paper is to highlight the importance of the optimization tools, and the many benefits they provide to tackle the challenges encountered in the design, operation, and control of power converters. [ABSTRACT FROM AUTHOR]

This paper addresses the integrated volt-var control for distribution network operation via multiobjective optimization. This paper seeks to explore the problem of energy savings and peak demand relief through the voltage reduction procedure. Currently, due to the emergence of the distribution smart grids, these procedures are gaining renewed interest and attention. The proposal presented here is for the operation phase, with a strategy based on an hourly load forecast for the next day/week, taking into account the active power intake reduction, and the voltage deviation. Therefore, the result is a set of nondominated optimal solutions, and then one may decide when, where, and how to apply them to meet different goals. The obtained solutions, for two typical distribution networks, describe relevant economic and technical benefits. [ABSTRACT FROM AUTHOR]

In this paper, hybridization of invasive weed optimization (IWO) and space transformation search (STS) are presented to solve, by applying multiple populations for multiple objectives individually, multiobjective optimization. This whole process is addressed as hybrid cooperative multiobjective optimization IWO (HCMOIWO). We carried out an application to solve system of nonlinear equations. In HCMOIWO, M single objectives are optimized simultaneously using the hybrid IWO with STS and all the nondominated solutions that are extracted from the group of parent weeds and offspring are stored in an archive, A . This archive is used not only to store nondominated solutions, but also to exchange information among subpopulations to explore the new search areas along the Pareto front. To exploit the nondominated solutions, a local search technique is adopted in HCMOIWO. The performance of HCMOIWO is evaluated with different sets of benchmark problems having different characteristics. Empirical results reveal the supremacy of HCMOIWO over state-of-the-art algorithms reported in recent literature. [ABSTRACT FROM AUTHOR]

In the classical non-adaptive group testing setup, pools of items are tested together, and the main goal of a recovery algorithm is to identify the complete defective set given the outcomes of different group tests. In contrast, the main goal of a non-defective subset recovery algorithm is to identify a subset of non-defective items given the test outcomes. In this paper, we present a suite of computationally efficient and analytically tractable non-defective subset recovery algorithms. By analyzing the probability of error of the algorithms, we obtain bounds on the number of tests required for non-defective subset recovery with arbitrarily small probability of error. Our analysis accounts for the impact of both the additive noise (false positives) and dilution noise (false negatives). By comparing with information theoretic lower bounds, we show that the upper bounds on the number of tests are orderwise tight up to a \log ^2K factor, where $K$ is the number of defective items. We also provide simulation results that compare the relative performance of the different algorithms and reveal insights into their practical utility. The proposed algorithms significantly outperform the straightforward approaches of testing items one-by-one, and of first identifying the defective set and then choosing the non-defective items from the complement set, in terms of the number of measurements required to ensure a given success rate. [ABSTRACT FROM PUBLISHER]

In this paper we present a multi-objective optimization approach to subarrayed linear antenna arrays design. We define this problem as a bi-objective one. We consider two objective functions for directivity maximization and sidelobe level minimization. Memetic algorithms (MAs) are hybrid algorithms that combine the benefits of a global search Evolutionary Algorithm (EA) with a local search method. In this paper, we introduce a new memetic multi-objective evolutionary algorithm namely the memetic generalized differential evolution (MGDE3). This algorithm is a memetic extension of the popular generalized differential evolution (GDE3) algorithm. Another popular MOEA is the nondominated sorting genetic algorithm-II (NSGA-II). MGDE3, GDE3 and NSGA-II are applied to the synthesis of uniform and nonuniform subarrayed linear arrays, providing an extensive set of solutions for each design case. Depending on the desired array characteristics, the designer can select the most suitable solution. The results of the proposed method are compared with those reported in the literature, indicating the advantages and applicability of the multi-objective approach. [ABSTRACT FROM PUBLISHER]

Seismic inversion problems often involve nonlinear relationships between data and model and usually have many local minima. Linearized inversion methods have been widely used to solve such problems. However, these kinds of methods often strongly depend on the initial model and are easily trapped in a local minimum. Global optimization methods, on the other hand, do not require a very good initial model and can approach a global minimum. However, global optimization methods are exhaustive search techniques that can be very time consuming. When the model dimension or the search space becomes large, these methods can be very slow to converge. In this paper, we propose a new global optimization algorithm by incorporating a new multimutation scheme into a differential evolution algorithm. Because mutation operation with the new multimutation scheme can generate better mutant vectors, the new global optimization algorithm has a very good ability of exploring the search space and can converge very fast. We apply the proposed algorithm to both synthetic and field data to test its performance. The results have clearly indicated that the new global optimization algorithm provides faster convergence and yields better results compared with the conventional global optimization methods in seismic inversion. [ABSTRACT FROM AUTHOR]

A ring topology is a common solution of network-on-chip (NoC) in industry, but is frequently criticized to have poor scalability. In this paper, we present a novel type of multi-ring NoC called isolated multi-ring (IMR), which can even support chip multi-processors (CMPs) with 1,024 cores. In IMR, any pair of cores are connected via at least one isolated ring, so that each packet can reach the destination without transferring from one ring to another. Therefore, IMR no longer needs expensive routers as mesh, which not only enhances the network performance but also reduces hardware overheads. We utilize simulated evolution to design optimized IMR topologies. We compare these IMR topologies against nine representative NoCs (e.g., traditional mesh, multi mesh, low-cost mesh, Express-virtual-channels mesh (EVC), torus ring, and hierarchical ring). We observe from experiments that IMR significantly outperforms its competitors in both saturation throughput and latency across all scenarios considered. For example, in a 16 $\times$ 16 CMP, IMR improves the saturation throughput of a state-of-the-art mesh (EVC) by 265.29 percent on average, and reduces the average packet latency on SPLASH-2 application traces by 71.58 percent, while consuming 5.08 percent less area and 9.76 percent less power. In a 32 $\times$ 32 CMP, IMR averagely improves the saturation throughput of EVC by 191.58 percent, and averagely reduces the packet latency on SPLASH-2 application traces by 23.09 percent, while consuming 2.86 percent less area and 10.81 percent less power. [ABSTRACT FROM PUBLISHER]

Pulse width-modulated dc–dc converters are widely used in the renewable power systems. In practice, their reliability is of major concern. To identify the converter system, the Walsh–Hadamard transformation and recursive least square (RLS) methods are used in some previous works. However, the accuracy of the identified parameters is degraded under measurement noise. In this paper, a new approach for the full parameter estimation of a dc–dc buck converter is proposed. The new approach is realized using the biogeography-based optimization. Unlike the traditional RLS method, the proposed method is based on a state-space model with full-state observation. Therefore, the performance of parameter estimation under different measurement noise levels is improved. Both simulation and experimental results are presented to validate the effectiveness of the new estimation scheme. [ABSTRACT FROM PUBLISHER]

The development of efficient parallel algorithms based on mixed mode programming represents one of the most popular lines of research in current bioinformatics. By exploiting hardware resources at inter-node/intra-node level, we can address grand computational challenges which involve the optimization of multiple objective functions simultaneously. In this sense, the inference of evolutionary trees represents one of the most difficult NP-hard problems in the field. Tackling such a problem requires efficient parallel designs to take advantage of the characteristics of modern multicore clusters. In this paper, we aim to solve the phylogenetic inference problem by applying MPI/OpenMP schemes to two multiobjective metaheuristics: fast non-dominated sorting genetic algorithm and multiobjective firefly algorithm. In order to assess the performance achieved by these proposals under different system and problem sizes, we have conducted experiments on six real nucleotide data sets according to a statistical methodology. Our parallel and multiobjective metrics point out the relevance of combining hybrid programming and novel bioinspired designs with regard to other parallel and biological approaches from the literature. [ABSTRACT FROM PUBLISHER]

The populations of industrialized countries will decline over the coming decades. To ensure that we have efficient access networks in the coming age of depopulation, it is important to consider the reorganization of central offices over time. The cost for operating and maintaining central offices can be reduced by efficiently closing central offices. However, dynamic facility location models that have been developed largely focused on the problem of optimally expanding a network over time to meet increasing demand. The practical relevance of the dynamic models is limited because the complexity and the required amount of data are much greater than with static models. This paper proposes a dynamic access network reorganization model for the depopulation age. Although the proposed model is a dynamic model, it is simple because it assumes that the only option will be to close central offices. The model first searches for a set of optimal solutions for each planning period as a capacitated facility location problem. Then, it selects the optimal combination of optimal solutions that can minimize the total number of open offices with the limitation of network reorganization. The validity of the proposed model was evaluated with computer simulations. It was confirmed that although the proposed model is a dynamic model it is simple and practical. [ABSTRACT FROM PUBLISHER]

A way to reduce the cost of regression testing consists of selecting or prioritizing subsets of test cases from a test suite according to some criteria. Besides greedy algorithms, cost cognizant additional greedy algorithms, multi-objective optimization algorithms, and multi-objective genetic algorithms (MOGAs), have also been proposed to tackle this problem. However, previous studies have shown that there is no clear winner between greedy and MOGAs, and that their combination does not necessarily produce better results. In this paper we show that the optimality of MOGAs can be significantly improved by diversifying the solutions (sub-sets of the test suite) generated during the search process. Specifically, we introduce a new MOGA, coined as DIversity based Genetic Algorithm (DIV-GA), based on the mechanisms of orthogonal design and orthogonal evolution that increase diversity by injecting new orthogonal individuals during the search process. Results of an empirical study conducted on eleven programs show that DIV-GA outperforms both greedy algorithms and the traditional MOGAs from the optimality point of view. Moreover, the solutions (sub-sets of the test suite) provided by DIV-GA are able to detect more faults than the other algorithms, while keeping the same test execution cost. [ABSTRACT FROM PUBLISHER]

Distribution system reconfiguration (DSR) is a multi-objective, nonlinear problem. This paper introduces a new, fast, nondominated sorting genetic algorithm (FNSGA) for the purpose of solving the DSR problem in normal operation by satisfying all objectives simultaneously with a relatively small number of generations and relatively short computation time. The objectives of the problem are to minimize real power losses and improve the voltage profile and load balancing index with minimum switching operations. Instead of generating several ranks from the nondominated set of solutions, this algorithm deals with only one rank; then the most suitable solution is chosen according to the operator's wishes. If there is no preference and all objectives have the same degree of importance, the best solution is determined by simply considering the sum of the normalized objective values. Also, a guided mutation operation is applied instead of a random one to speed up convergence. Radial system topology is satisfied using graph theory by formulating the branch-bus incidence matrix (BBIM) and checking the rank of each topology. To test the algorithm, it was applied to two widely studied test systems and a real one. The results show the efficiency of this algorithm as compared to other methods in terms of achieving all the goals simultaneously with reasonable population and generation sizes and without using a mutation rate, which is usually problem-dependent. [ABSTRACT FROM PUBLISHER]

In order to optimize hydro power plants generator scheduling according to 24-h system demand, a parallel self-adaptive differential evolution algorithm has been applied. The proposed algorithm presents a novel approach to considering the multi-population and utilization of the preselection step for the improvements of the algorithm's global search capabilities. A preselection step with the best, middle, and worst populations' individuals establishes the new trial vectors. This algorithm has been verified on two different models. The first one consists of eight power plants with real parameters, and the second one consists of four power plants, mostly used as a test model in scientific papers. The main goal of the optimization process is to satisfy system demand for 24 h with a decreased usage of water quantity per electrical energy unit. The initial and final states of the reservoirs must also be satisfied. [ABSTRACT FROM PUBLISHER]

This paper aims to design new strategies to extend traditional multiobjective optimization algorithms to efficiently obtain Pareto-optimal solutions in presence of noise on the objective surfaces. The first strategy, referred to as adaptive selection of sample size, is employed to balance the tradeoff between quality measure of fitness and run-time complexity. The second strategy is concerned with determining statistical expectation, instead of conventional averaging, of fitness samples as the measure of fitness of the trial solutions. The third strategy attempts to extend Goldberg's method to compare slightly worse trial solutions with its competitor by a more statistically viable comparator to examine possible placement of the former solution in the Pareto optimal front. The traditional differential evolution for multiobjective optimization algorithm has been modified by extending its selection step with the proposed strategies. Experiments undertaken to study the performance of the extended algorithm reveal that the extended algorithm outperforms its competitors with respect to three performance metrics, when examined on a test suite of 23 standard benchmarks with additive noise of three statistical distributions. The extended algorithm has been applied on the well known box-pushing problem, where the forces and torques required to shift the box by two robots are evaluated to jointly satisfy the conflicting objectives on task-execution time and energy consumption in presence of noise on range estimates from the sidewalls of the workspace. The application justifies the importance of the proposed noise-handling strategies in practical systems. [ABSTRACT FROM AUTHOR]

Smart-grid development calls for effective solutions, such as electric vehicles (EVs), to meet the energy and environmental challenges. To facilitate large-scale EV applications, optimal locating and sizing of charging stations in smart grids have become essential. This paper proposes a multiobjective EV charging station planning method which can ensure charging service while reducing power losses and voltage deviations of distribution systems. A battery capacity-constrained EV flow capturing location model is proposed to maximize the EV traffic flow that can be charged given a candidate construction plan of EV charging stations. The data-envelopment analysis method is employed to obtain the final optimal solution. Subsequently, the well-established cross-entropy method is utilized to solve the planning problem. The simulation results have demonstrated the effectiveness of the proposed method based on a case study consisting of a 33-node distribution system and a 25-node traffic network system. [ABSTRACT FROM AUTHOR]

Some recent studies have posed the problem of data clustering as a multiobjective optimization problem, where several cluster validity indices are simultaneously optimized to obtain tradeoff clustering solutions. A number of cluster validity index measures are available in the literature. However, none of the measures can perform equally well in all kinds of datasets. Depending on the dataset properties and its inherent clustering structure, different cluster validity measures perform differently. Therefore, it is important to find the best set of validity indices that should be optimized simultaneously to obtain good clustering results. In this paper, a novel interactive genetic algorithm-based multiobjective approach is proposed that simultaneously finds the clustering solution as well as evolves the set of validity measures that are to be optimized simultaneously. The proposed method interactively takes the input from the human decision maker (DM) during execution and adaptively learns from that input to obtain the final set of validity measures along with the final clustering result. The algorithm is applied for clustering real-life benchmark gene expression datasets and its performance is compared with that of several other existing clustering algorithms to demonstrate its effectiveness. The results indicate that the proposed method outperforms the other existing algorithms for all the datasets considered here. [ABSTRACT FROM PUBLISHER]