Set Of Candidate Solutions Research Articles

Optimal Selection and Location of Fixed-Step Capacitor Banks in Distribution Networks Using a Discrete Version of the Vortex Search Algorithm

This paper deals with the problem of the optimal selection of capacitor banks in electrical AC distribution systems for minimizing the costs of energy losses during a year of operation through a discrete version of the vortex search algorithm (DVSA). This algorithm works with a hypersphere with a variable radius defined by an exponential function where a Gaussian distribution is used to generate a set of candidate solutions uniformly distributed around the center of this hypersphere. This center corresponds to the best solution obtained at the iteration t, which is initialized at the center of the solution space at the iterative search beginning. The main advantage of combining the exponential function with the Gaussian distribution is the correct balance between the exploration and exploitation of the solution space, which allows reaching the global optimal solution of the optimization problem with a low standard deviation, i.e., guaranteeing repeatability at each simulation. Two classical distribution networks composed of 33 and 69 nodes were used to validate the proposed DVSA algorithm. They demonstrated that the DVSA improves numerical reports found in specialized literature regarding the optimal selection and location of fixed-step capacitor banks with a low computational burden. All the simulations were carried out in MATLAB software.

Cooperation search algorithm: A novel metaheuristic evolutionary intelligence algorithm for numerical optimization and engineering optimization problems

This paper develops a novel population-based evolutionary method called cooperation search algorithm (CSA) to address the complex global optimization problem. Inspired by the team cooperation behaviors in modern enterprise, the CSA method randomly generates a set of candidate solutions in the problem space, and then three operators are repeatedly executed until the stopping criterion is met: the team communication operator is used to improve the global exploration and determine the promising search area; the reflective learning operator is used to achieve a comprise between exploration and exploitation; the internal competition operator is used to choose solutions with better performances for the next cycle. Firstly, three kinds of mathematical optimization problems (including 24 famous test functions, 25 CEC2005 test problems and 30 CEC2014 test problems) are used to test the convergence speed and search accuracy of the CSA method. Then, several famous engineering optimization problems (like Gear train design, Welded beam design and Speed reducer design) are chosen to testify the engineering practicality of the CSA method. The results in different scenarios demonstrate that as compared with several existing evolutionary algorithms, the CSA method can effectively explore the decision space and produce competitive results in terms of various performance evaluation indicators. Thus, an effective tool is provided for solving the complex global optimization problems.

Multiobjective feature selection for key quality characteristic identification in production processes using a nondominated-sorting-based whale optimization algorithm

Identifying key quality characteristics (QCs) in production processes is essential for product quality control and improvement. This paper proposes a multiobjective wrapper-based feature selection (FS) method for key QC (KQC) identification on unbalanced production data using a novel modified nondominated-sorting-based whale optimization algorithm (MNSWOA) and the ideal point method (IPM). In the proposed approach, the FS problem is defined as maximizing the geometric mean (GM) measure and minimizing the feature (QC) subset size. To solve the defined FS problem, MNSWOA is adopted first to find a set of candidate solutions (feature subsets), and then IPM is adopted to select the final solution. In MNSWOA, a modified fast nondominated sorting approach is proposed to adapt the single objective whale optimization algorithm to the multiobjective scenario. Moreover, a uniform reference solution selection strategy and the mutation operations are embedded in MNSWOA to improve its search performance. Experimental results on four unbalanced production datasets show that the proposed FS method performs effectively and efficiently for KQC identification. Further comparisons show that MNSWOA obtains better search performance than benchmark multiobjective optimization methods, including a modified NSGA-II, SPEA2, MOEA/D, NSPSO and CMDPSO.

Re-sampled inheritance compact optimization

Compact optimization is an alternative paradigm in the field of metaheuristics requiring a modest use of memory to optimize a problem. As opposed to population-based algorithms, which conduct the search by employing a set of candidate solutions, compact algorithms use a probabilistic model to describe how solutions are distributed over the search space. Compared to other Estimation of Distribution Algorithms, peculiar features such as the use of simple probabilistic models, in which variables are treated independently, and the need for a minimal number of solutions to be sampled to perform the search, make these algorithms suitable for those applications plagued by memory limitations. Compact algorithms show good results on different kinds of optimization problems but often prematurely converge and perform poorly on non-separable. In this paper, we attempt to overcome these limitations by combining compact algorithms with a restart mechanism named Re-Sampled Inheritance (RI) whose purpose is to avoid premature convergence while also inheriting parts of the variables from the best solution found so far. To assess the effect of the RI mechanism, we extensively test various existing compact algorithms, with and without RI, and compare the best RI-based compact algorithm against several competing algorithms on several optimization problems at different dimensionalities. We also evaluate the effect of the RI parameters on the overall algorithmic performance. Our numerical results not only show that RI consistently enhances the performances of compact algorithms, but also shed some light on the effectiveness of different compact logics at handling problems at different dimensionalities.

A rule-based automated machine learning approach in the evaluation of recommender engine

PurposeAny business that opts to adopt a recommender engine (RE) for various potential benefits must choose from the candidate solutions, by matching to the task of interest and domain. The purpose of this paper is to choose RE that fits best from a set of candidate solutions using rule-based automated machine learning (ML) approach. The objective is to draw trustworthy conclusion, which results in brand building, and establishing a reliable relation with customers and undeniably to grow the business.Design/methodology/approachAn experimental quantitative research method was conducted in which the ML model was evaluated with diversified performance metrics and five RE algorithms by combining offline evaluation on historical and simulated movie data set, and the online evaluation on business-alike near-real-time data set to uncover the best-fitting RE.FindingsThe rule-based automated evaluation of RE has changed the testing landscape, with the removal of longer duration of manual testing and not being comprehensive. It leads to minimal manual effort with high-quality results and can possibly bring a new revolution in the testing practice to start a service line “Machine Learning Testing as a service” (MLTaaS) and the possibility of integrating with DevOps that can specifically help agile team to ship a fail-safe RE evaluation product targeting SaaS (software as a service) or cloud deployment.Research limitations/implicationsA small data set was considered for A/B phase study and was captured for ten movies from three theaters operating in a single location in India, and simulation phase study was captured for two movies from three theaters operating from the same location in India. The research was limited to Bollywood and Ollywood movies for A/B phase, and Ollywood movies for simulation phase.Practical implicationsThe best-fitting RE facilitates the business to make personalized recommendations, long-term customer loyalty forecasting, predicting the company's future performance, introducing customers to new products/services and shaping customer's future preferences and behaviors.Originality/valueThe proposed rule-based ML approach named “2-stage locking evaluation” is self-learned, automated by design and largely produces time-bound conclusive result and improved decision-making process. It is the first of a kind to examine the business domain and task of interest. In each stage of the evaluation, low-performer REs are excluded which leads to time-optimized and cost-optimized solution. Additionally, the combination of offline and online evaluation methods offer benefits, such as improved quality with self-learning algorithm, faster time to decision-making by significantly reducing manual efforts with end-to-end test coverage, cognitive aiding for early feedback and unattended evaluation and traceability by identifying the missing test metrics coverage.

Multi-Objective Model Predictive Control for Real-Time Operation of a Multi-Reservoir System

This paper presents an extended Model Predictive Control scheme called Multi-objective Model Predictive Control (MOMPC) for real-time operation of a multi-reservoir system. The MOMPC approach incorporates the non-dominated sorting genetic algorithm II (NSGA-II), multi-criteria decision making (MCDM) and the receding horizon principle to solve a multi-objective reservoir operation problem in real time. In this study, a water system is simulated using the De Saint Venant equations and the structure flow equations. For solving multi-objective optimization, NSGA-II is used to find the Pareto-optimal solutions for the conflicting objectives and a control decision is made based on multiple criteria. Application is made to an existing reservoir system in the Sittaung river basin in Myanmar, where the optimal operation is required to compromise the three operational objectives. The control objectives are to minimize the storage deviations in the reservoirs, to minimize flood risks at a downstream vulnerable place and to maximize hydropower generation. After finding a set of candidate solutions, a couple of decision rules are used to access the overall performance of the system. In addition, the effect of the different decision-making methods is discussed. The results show that the MOMPC approach is applicable to support the decision-makers in real-time operation of a multi-reservoir system.

An Improved Artificial Electric Field Algorithm for Multi-Objective Optimization

Real-world problems such as scientific, engineering, mechanical, etc., are multi-objective optimization problems. In order to achieve an optimum solution to such problems, multi-objective optimization algorithms are used. A solution to a multi-objective problem is to explore a set of candidate solutions, each of which satisfies the required objective without any other solution dominating it. In this paper, a population-based metaheuristic algorithm called an artificial electric field algorithm (AEFA) is proposed to deal with multi-objective optimization problems. The proposed algorithm utilizes the concepts of strength Pareto for fitness assignment and the fine-grained elitism selection mechanism to maintain population diversity. Furthermore, the proposed algorithm utilizes the shift-based density estimation approach integrated with strength Pareto for density estimation, and it implements bounded exponential crossover (BEX) and polynomial mutation operator (PMO) to avoid solutions trapping in local optima and enhance convergence. The proposed algorithm is validated using several standard benchmark functions. The proposed algorithm’s performance is compared with existing multi-objective algorithms. The experimental results obtained in this study reveal that the proposed algorithm is highly competitive and maintains the desired balance between exploration and exploitation to speed up convergence towards the Pareto optimal front.

A novel numerical function optimization framework: campaign based optimization framework

This paper proposes a new optimization framework: campaign optimization framework (COF), which is based on the historical results of traditional swarm intelligence algorithms and uses two different campaign rules to get better solutions. Firstly, the candidate solution set is generated by running the swarm optimization algorithm. Secondly, cross campaign rule (CCR) or increment campaign rule (ICR) is used to update the candidate solution set. The campaign rule describes the steps to get better solutions. In CCR, the better solution is obtained by combining the variable bits of two randomly selected solutions. But in ICR, it is generated by every variable bits’ optimal pools. Then, the best candidate solution is optimized by swarm optimization algorithm again. Finally, the proposed framework is tested on two well-known benchmark functions. Through the analysis of the experimental results, the proposed algorithm is compared with traditional swarm optimization algorithm. And two campaign rules are compared in terms of results and optimization time dimensions.

Exact and heuristic approaches for multi-objective garbage accumulation points location in real scenarios

Municipal solid waste management is a major challenge for nowadays urban societies, because it accounts for a large proportion of public budget and, when mishandled, it can lead to environmental and social problems. This work focuses on the problem of locating waste bins in an urban area, which is considered to have a strong influence in the overall efficiency of the reverse logistic chain. This article contributes with an exact multiobjective approach to solve the waste bin location in which the optimization criteria that are considered are: the accessibility to the system (as quality of service measure), the investment cost, and the required frequency of waste removal from the bins (as a proxy of the posterior routing costs). In this approach, different methods to obtain the objectives ideal and nadir values over the Pareto front are proposed and compared. Then, a family of heuristic methods based on the PageRank algorithm is proposed which aims to optimize the accessibility to the system, the amount of collected waste and the installation cost. The experimental evaluation was performed on real-world scenarios of the cities of Montevideo, Uruguay, and Bahía Blanca, Argentina. The obtained results show the competitiveness of the proposed approaches for constructing a set of candidate solutions that considers the different trade-offs between the optimization criteria.

Optimized Path-Planning in Continuous Spaces for Unmanned Aerial Vehicles Using Meta-Heuristics

This work presents a novel path-planning approach for Unmanned Aerial Vehicles (UAVs) in continuous 3D environments. This proposal aims to minimize the path length while avoiding collisions through the suitable adjusting of control points (the points that take the UAV from a start position to a target location). The above is stated as a constrained global optimization problem. This problem considers the overall length of the path as the single objective function. Regarding the problem constraints, they are related to the collision of the obstacles with the 3D shape of a path. The assignment of the path shape is also proposed in this work to streamline the planning process. Due to the optimization problem features (high nonlinearity, multimodality, non-differentiability, and the lack of an initial guess solution), a constraints-handling mechanism is used in meta-heuristics to find suitable optimized paths. Also, an enhanced path-search mechanism is included in these algorithms to deal with complex planning scenarios. The enhanced mechanism incorporates a path computed by a variant of the A-Star method (the Pruned A-Star) in the first set of candidate solutions of the meta-heuristics. The proposed approach is tested through six complex scenarios. Moreover, the performance of three well-known meta-heuristics, Differential Evolution (DE), Particle Swarm Optimization (PSO), and the Genetic Algorithm (GA), is studied to find a potential candidate to solve the path-planning problem. In this way, the paths found by DE show outstanding performance. The paths obtained by the Pruned A-Star technique are adopted as a point of comparison to determine the advantages and drawbacks of the proposal.

New Insights on the Optimality Conditions of the $$\ell _2-\ell _0$$ Minimization Problem

This paper is devoted to the analysis of necessary (not sufficient) optimality conditions for the l0-regularized least-squares minimization problem. Such conditions are the roots of the plethora of algorithms that have been designed to cope with this NP-hard problem. Indeed, as global optimality is, in general, intractable, these algorithms only ensure the convergence to suboptimal points that verify some necessary optimality conditions. The degree of restrictiveness of these conditions is thus directly related to the performance of the algorithms. Within this context, our first goal is to provide a comprehensive review of commonly used necessary optimality conditions as well as known relationships between them. Then, we complete this hierarchy of conditions by proving new inclusion properties between the sets of candidate solutions associated to them. Moreover, we go one step further by providing a quantitative analysis of these sets. Finally, we report the results of a numerical experiment dedicated to the comparison of several algorithms with different optimality guaranties. In particular, this illustrates the fact that the performance of an algorithm is related to the restrictiveness of the optimality condition verified by the point it converges to.

Optimal Remote Estimation of Discrete Random Variables Over the Collision Channel

Consider a system comprising sensors that communicate with a remote estimator by way of a so-called collision channel. Each sensor observes a discrete random variable and must decide whether to transmit it to the remote estimator or to remain silent. The variables are independent across sensors. There is no communication among the sensors, which precludes the use of coordinated transmission policies. The collision channel functions as an ideal link when a single sensor transmits. If there are two or more simultaneous transmissions, then a collision occurs and is detected at the remote estimator. The role of the remote estimator is to form estimates of all the observations at the sensors. Our goal is to design transmission policies that are globally optimal with respect to two criteria: the aggregate probability of error, which is a convex combination of the probabilities of error in estimating the individual observations; and the total probability of error. We show that, for the aggregate probability of error criterion, it suffices to sift through a structured finite set of candidate solutions to find a globally optimal one. In general, the cardinality of this set is exponential on the number of sensors, but we discuss important cases in which it becomes quadratic or even one. For the total probability of error criterion, we prove that the solution in which each sensor transmits when it observes all but a preselected most probable value is globally optimal. So, no search is needed in this case. Our results hold irrespective of the probability mass functions of the observed random variables, regardless the size of their support.

Effective image clustering based on human mental search

Image segmentation is one of the fundamental techniques in image analysis. One group of segmentation techniques is based on clustering principles, where association of image pixels is based on a similarity criterion. Conventional clustering algorithms, such as k-means, can be used for this purpose but have several drawbacks including dependence on initialisation conditions and a higher likelihood of converging to local rather than global optima.In this paper, we propose a clustering-based image segmentation method that is based on the human mental search (HMS) algorithm. HMS is a recent metaheuristic algorithm based on the manner of searching in the space of online auctions. In HMS, each candidate solution is called a bid, and the algorithm comprises three major stages: mental search, which explores the vicinity of a solution using Levy flight to find better solutions; grouping which places a set of candidate solutions into a group using a clustering algorithm; and moving bids toward promising solution areas. In our image clustering application, bids encode the cluster centres and we evaluate three different objective functions.In an extensive set of experiments, we compare the efficacy of our proposed approach with several state-of-the-art metaheuristic algorithms including a genetic algorithm, differential evolution, particle swarm optimisation, artificial bee colony algorithm, and harmony search. We assess the techniques based on a variety of metrics including the objective functions, a cluster validity index, as well as unsupervised and supervised image segmentation criteria. Moreover, we perform some tests in higher dimensions, and conduct a statistical analysis to compare our proposed method to its competitors. The obtained results clearly show that the proposed algorithm represents a highly effective approach to image clustering that outperforms other state-of-the-art techniques.

The Set-Based Hypervolume Newton Method for Bi-Objective Optimization.

In this paper, we propagate the use of a set-based Newton method that enables computing a finite size approximation of the Pareto front (PF) of a given twice continuously differentiable bi-objective optimization problem (BOP). To this end, we first derive analytically the Hessian matrix of the hypervolume indicator, a widely used performance indicator for PF approximation sets. Based on this, we propose the hypervolume Newton method (HNM) for hypervolume maximization of a given set of candidate solutions. We first address unconstrained BOPs and focus further on first attempts for the treatment of inequality constrained problems. The resulting method may even converge quadratically to the optimal solution, however, this property is-as for all Newton methods-of local nature. We hence propose as a next step a hybrid of HNM and an evolutionary strategy in order to obtain a fast and reliable algorithm for the treatment of such problems. The strengths of both HNM and hybrid are tested on several benchmark problems and comparisons of the hybrid to state-of-the-art evolutionary algorithms for hypervolume maximization are presented.

Guiding Evolutionary Multiobjective Optimization With Generic Front Modeling.

In evolutionary multiobjective optimization, the Pareto front (PF) is approximated by using a set of representative candidate solutions with good convergence and diversity. However, most existing multiobjective evolutionary algorithms (MOEAs) have general difficulty in the approximation of PFs with complicated geometries. To address this issue, we propose a generic front modeling method for evolutionary multiobjective optimization, where the shape of the nondominated front is estimated by training a generalized simplex model. On the basis of the estimated front, we further develop an MOEA, where both the mating selection and environmental selection are driven by the approximate nondominated fronts modeled during the optimization process. For performance assessment, the proposed algorithm is compared with several state-of-the-art evolutionary algorithms on a wide range of benchmark problems with various types of PFs and different numbers of objectives. Experimental results demonstrate that the proposed algorithm performs consistently on a variety of multiobjective optimization problems.

SVSA: a Semi-Vortex Search Algorithm for solving optimization problems

The Vortex Search Algorithm (VSA) is a single-based meta-heuristic algorithm inspired by the vortices created by stirred fluids. A VSA search creates nested vortices starting from an initial center (the middle of the boundaries), and the vortices are gradually scaled down. In each iteration, the center of a new vortex is created by searching around the previous center and creating a set of candidate solutions with a Gaussian distribution, selecting best of them and comparing it with previous center, in order to replace it. However, this strategy can become trapped in a local optimum, since the search space may not be explored properly by time passing and according to the structure of the many objective functions. Therefore, in this paper an improved version of the VSA is introduced. Actually, the proposed method is not necessarily limited to creating nested vortices; after employing the VSA, the search space is explored by a uniform distribution in each iteration, then the center of the vortex moves toward the best random solution. In this situation, if the shifted center is better than the previous center, then the center is transferred to the new point; in this way, the VSA runs at the shifted center in the next iteration. Therefore, the proposed method is Semi-VSA (SVSA) and its vortices are animated, not necessarily nested. Experiments on 50 benchmark optimization functions indicate that the SVSA is able to improve the VSA, especially when the VSA has been trapped in a local optimum.

Key quality characteristics selection for imbalanced production data using a two-phase bi-objective feature selection method

The selection of key quality characteristics (KQCs) that are significantly associated with product quality is essential for improving product quality. Production lines generally yield a larger number of regular products than do premium products, which creates an imbalance in production datasets and complicates KQC selection. In this study, a KQC selection method with an excellent ability to predict product quality is proposed based on a two-phase bi-objective feature selection method. The KQC selection model is established as a bi-objective problem of maximizing feature (i.e., quality characteristic) importance and minimizing percentage of selected features, and the geometric mean (G-mean) is selected as the feature importance metric for imbalanced data. To solve this model, a two-phase multi-objective optimization method is proposed; this method yields a set of candidate solutions (KQC sets) using an improved direct multi-search (DMS) strategy and uses the ideal point method (IPM) to select the final KQC sets from the candidate solutions. The experimental results indicate that the proposed method is effective for selecting KQCs for imbalanced production data.

Methods to reduce dimensionality and identify candidate solutions in multi-objective signal timing problems

Adjusting traffic signal timings is a practical way for agencies to manage urban traffic without the need for significant infrastructure investments. Signal timings are generally selected to minimize the total control delay vehicles experience at an intersection, particularly when the intersection is isolated or undersaturated. However, in practice, there are many other potential objectives that might be considered in signal timing design, including: total passenger delay, pedestrian delays, delay inequity among competing movements, total number of stopping maneuvers, among others. These objectives do not tend to share the same relationships with signal timing plans and some of these objectives may be in direct conflict. The research proposes the use of a new multi-objective optimization (MOO) visualization technique—the mosaic plot—to easily quantify and identify significant tradeoffs between competing objectives using the set of Pareto optimal solutions that are normally provided by MOO algorithms. Using this tool, methods are also proposed to identify and remove potentially redundant or unnecessary objectives that do not have any significant tradeoffs with others in an effort to reduce problem dimensionality. Since MOO procedures will still be needed if more than one objective remains and MOO algorithms generally provide a set of candidate solutions instead of a single final solution, two methods are proposed to rank the set of Pareto optimal solutions based on how well they balance between the competing objectives to provide a final recommendation. These methods rely on converting the objectives to dimensionless values based on the optimal value for each specific objectives, which allows for direct comparison between and weighting of each. The proposed methods are demonstrated using a simple numerical example of an undersaturated intersection where all objectives can be analytically obtained. However, they can be readily applied to other signal timing problems where objectives can be obtained using simulation outputs to help identify the signal timing plan that provides the most reasonable tradeoff between competing objectives.

Majority voting for discrete population-based optimization algorithms

Population-based metaheuristic algorithms have been extensively applied to solve discrete optimization problems. Generally speaking, they work with a set of candidate solutions in the population which evolve during generations using variant reproduction and selection operations to find the optimal solution(s). The population is similar to a small society having several individuals which seek a common goal/solution. This study is motivated from the election systems of societies which can be applied in the population-based algorithms. We propose utilizing the majority voting for discrete population-based optimization algorithms which uses the information of all candidate solutions in the current generation to create a new trial candidate solution, called a president candidate solution. During optimization process, after applying the evolutionary operations, all candidate solutions vote collectively to determine the values of the president’s variables. In the proposed method, a majority voting is utilized to choose a value for each variable (gene) of the president candidate solution. This method keeps untouched all other steps of population-based algorithms; therefore, it can be used with any kind of population-based algorithm. As case studies, the discrete differential evolution (DDE) algorithm and the discrete particle swarm optimization (DPSO) are used as the parent algorithms to develop majority voting-based discrete DE (MVDDE) and majority voting-based discrete PSO (MVDPSO). These two algorithms are evaluated on the fifteen discrete benchmark functions with the dimensions of D = 10, 30, 50, 100, 200 and 500. Simulation results confirm that majority voting-based discrete optimization algorithms obtain a promising performance on the majority of the benchmark functions. In addition, we have conducted some tests on large-scale 0–1 knapsack problems with large scales as a real-world application.

Stochastic global optimization algorithms: A systematic formal approach

Up to now, different algorithmic methods have been developed to find ’good’ solutions (near to the optimal solution) for global optimization problems that cannot be solved using analytical methods. In particular, algorithmic methods such as differential evolution, evolutionary algorithms, and hill climbing belong to the class of Stochastic Global Optimization Algorithms (SGoals). In general, an SGoal iteratively applies stochastic operations to a set of candidate solutions (population), following, in some cases, a heuristic/metaheuristic. Although some research works have tried to formalize SGoals using Markov kernels, such formalization is not general and sometimes is blurred. In this paper, we propose a comprehensive, systematic and formal approach for studying SGoals. First, we present concepts of probability theory that are required to perform such formalization and we demonstrate that the swapping, sorting, and permutation functions, among others, can be represented by Markov kernels. Then, we introduce the joint Markov kernel as a way of characterizing the combination of stochastic methods. Next, we define the optimization space, a σ-algebra that contains ϵ-optimal states, and develop Markov kernels for stochastic methods like swapping, sorting and permutation. Finally, we introduce sufficient convergence conditions for SGoals and present some popular SGoals in terms of the developed theory.