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Abstract The hybridization of population-based meta-heuristics and Local Search strategies is an effective algorithmic proposal for solving complex continuous optimization problems. Such hybridization becomes much more effective when the local search heuristics are applied in the most promising areas of the solution space. This paper presents a hybrid method based on Clustering Search (CS) to solve continuous optimization problems. The CS divides the search space in clusters, which are composed of solutions generated by a population meta-heuristic, called Variable Mesh Optimization. Each cluster is explored further with local search procedures. Computational results considering a benchmark of multimodal continuous functions are presented.
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... These methods lacked the use of efficient hybrid metaheuristic methods (except the hybrid GRASP-ILS method of Haddadene et al., 2016). In fact, Salas et al. (2015) and Masmoudi et al. (2016) suggest that the hybridization of population-based metaheuristics with advanced local search mechanism (i.e., single solution-based metaheuristics) is effective to solve such complex variants of the VRP. We, therefore, propose three hybrid populationbased metaheuristics based on ABC algorithm. ...
In the context of home healthcare services, patients may need to be visited multiple times by different healthcare specialists who may use a fleet of heterogeneous vehicles. In addition, some of these visits may need to be synchronized with each other for performing a treatment at the same time. We call this problem the Heterogeneous Fleet Vehicle Routing Problem with Synchronized visits (HF-VRPS). It consists of planning a set of routes for a set of light duty vehicles running on alternative fuels. We propose three population-based hybrid Artificial Bee Colony metaheuristic algorithms for the HF-VRPS. These algorithms are tested on newly generated instances and on a set of homogeneous VRPS instances from the literature. Besides producing quality solutions, our experimental results illustrate the trade-offs between important factors, such as CO2 emissions and driver wage. The computational results also demonstrate the advantages of adopting a heterogeneous fleet rather than a homogeneous one for the use in home healthcare services.
... Also, new clusters may be introduced or existing ones removed. Costa Salas et al. (2015) utilized the CS for continuous optimization by combining variable mesh optimization (VMO) ( Puris et al., 2012) and a couple of LS procedures. Since CS is a generic framework, Nagano et al. (2014) successfully applied it to a combinatorial optimization problem i.e. a flow shop scheduling problem. ...
The initial population of an evolutionary algorithm is an important factor which affects the convergence rate and ultimately its ability to find high quality solutions or satisfactory solutions for that matter. If composed of good individuals it may bias the search towards promising regions of the search space right from the beginning. Although, if no knowledge about the problem at hand is available, the initial population is most often generated completely random, thus no such behavior can be expected. This paper proposes a method for initializing the population that attempts to identify i.e. to get close to promising parts of the search space and to generate (relatively) good solutions in their proximity. The method is based on clustering and a simple Cauchy mutation. The results obtained on a broad set of standard benchmark functions suggest that the proposed method succeeds in the aforementioned which is most noticeable as an increase in convergence rate compared to the usual initialization approach and a method from the literature. Also, insight into the usefulness of advanced initialization methods in higher-dimensional search spaces is provided, at least to some degree, by the results obtained on higher-dimensional problem instances—the proposed method is beneficial in such spaces as well. Moreover, results on several very high-dimensional problem instances suggest that the proposed method is able to provide a good starting position for the search.
This paper introduces a hybrid algorithm of Nelder-Mead and scatter search algorithms called SSNM. Numerical results for some known test problems with varying dimensions from 2 to 100 variables prove its great performance for a bounded or constrained problem. This paper also has a considerable contribution to the joint economic lot sizing (JELS) problem literature. This problem is considered for a two-stage supply chain with price-sensitive demand for geometric, geometric-then-equal size and optimal shipment policies. Solution procedures are also developed which use the SSNM algorithm in their steps. These models and solution procedures are novel in the JELS literature.
Malaysia has seen tremendous growth in the standard of living and household per capita income. The demand for a more systematic and efficient planning has become increasingly more important, one of the keys to achieving a high standard in healthcare. In this paper, a Maximal Covering Location Problem (MCLP) is used to study the healthcare facilities of one of the districts in Malaysia. We address the limited capacity of the facilities and the problem is formulated as Capacitated MCLP (CMCLP). We propose a new solution approach based on genetic algorithm to examine the percentage of coverage of the existing facilities within the allowable distance specified/targeted by Malaysian government. The algorithm was shown to generate good results when compared to results obtained using CPLEX version 12.2 on a medium size problem consisting of 179 nodes network. The algorithm was extended to solve larger network consisting of 809 nodes where CPLEX failed to produce non-trivial solutions. We show that the proposed solution approach produces significant results in determining good locations for the facility such that the population coverage is maximized.
The problem of transporting patients or elderly people has been widely studied in literature and is usually modeled as a dial-a-ride problem (DARP). In this paper we analyze the corresponding problem arising in the daily operation of the Austrian Red Cross. This nongovernmental organization is the largest organization performing patient transportation in Austria. The aim is to design vehicle routes to serve partially dynamic transportation requests using a fixed vehicle fleet. Each request requires transportation from a patient's home location to a hospital (outbound request) or back home from the hospital (inbound request). Some of these requests are known in advance. Some requests are dynamic in the sense that they appear during the day without any prior information. Finally, some inbound requests are stochastic. More precisely, with a certain probability each outbound request causes a corresponding inbound request on the same day. Some stochastic information about these return transports is available from historical data. The purpose of this study is to investigate, whether using this information in designing the routes has a significant positive effect on the solution quality. The problem is modeled as a dynamic stochastic dial-a-ride problem with expected return transports. We propose four different modifications of metaheuristic solution approaches for this problem. In detail, we test dynamic versions of variable neighborhood search (VNS) and stochastic VNS (S-VNS) as well as modified versions of the multiple plan approach (MPA) and the multiple scenario approach (MSA). Tests are performed using 12 sets of test instances based on a real road network. Various demand scenarios are generated based on the available real data. Results show that using the stochastic information on return transports leads to average improvements of around 15%. Moreover, improvements of up to 41% can be achieved for some test instances.
A challenge in hybrid evolutionary algorithms is to employ efficient strategies to cover all the search space, applying local search only in actually promis-ing search areas. The inspiration in nature has been pursued to design flexible, co-herent and efficient computational models. In this chapter, the Clustering Search (*CS) is proposed as a generic way of combining search metaheuristics with cluster-ing to detect promising search areas before applying local search procedures. The clustering process aims to gather similar information about the search space into groups, maintaining a representative solution associated to this information. Two applications are examined for combinatorial and continuous optimization problems, presenting how to develop hybrid evolutionary algorithms based on *CS.
Production planning and scheduling seeks to efficiently allocate resources while fulfilling customer requirements and market demand, often by trading-off conflicting objectives. The decisions involved are typically operational (short-term) and tactical (medium-term) planning problems, such as work force levels, production lot sizes and the sequencing of production runs. Lot sizing seeks to determine the optimal timing and level of production. The early developments in this field have their roots in the Economic Order Quantity model developed by Harris (1913), extended some decades later by Wagner-Whitin (1958). Since then, researchers have developed successive generations of models combining capacitated and dynamic approaches, with a blurring of the boundaries between lot sizing and other research fields (Drexl and Kimms, 1997; Karimi et al., 2003). Most of the lot sizing literature is focused on discrete manufacturing. Currently, with changes in the philosophy of production planning and control, along with lean manufacturing processes and the shift from make-to-stock to make-to-order, there is a debate about whether or not lot sizing as a trade-off between setups and stocks is still an issue. Nonetheless, a high number of production processes are characterized by strong fluctuations of seasonal demand (with not enough capacity in some periods to process all the orders), by significant setup times and costs and by the economical advantage of holding stock rather than maintaining a capacity surplus. This is the case in process industries, where just-in-time systems cannot be implemented (Pochet, 2001). As a result, process industries are a promising research area which is, in fact, addressed by the most recent papers on lot sizing and its extensions (Suerie, 2005; Quadt and Kuhn, 2008).
This paper proposes a class of surrogate constraint heuristics for obtaining approximate, near optimal solutions to integer programming problems. These heuristics are based on a simple framework that illuminates the character of several earlier heuristic proposals and provides a variety of new alternatives. The paper also proposes additional heuristics that can be used either to supplement the surrogate constraint procedures or to provide independent solution strategies. Preliminary computational results are reported for applying one of these alternatives to a class of nonlinear generalized set covering problems involving approximately 100 constraints and 300–500 integer variables. The solutions obtained by the tested procedure had objective function values twice as good as values obtained by standard approaches (e.g., reducing the best objective function values of other methods from 85 to 40 on the average. Total solution time for the tested procedure ranged from ten to twenty seconds on the CDC 6600.
A challenge in hybrid evolutionary algorithms is to define efficient strategies to cover all search space, applying local
search only in actually promising search areas. This paper proposes a way of detecting promising search areas based on clustering.
In this approach, an iterative clustering works simultaneously to an evolutionary algorithm accounting the activity (selections
or updatings) in search areas and identifying which of them deserves a special interest. The search strategy becomes more
aggressive in such detected areas by applying local search. A first application to unconstrained numerical optimization is
developed, showing the competitiveness of the method.
KeywordsHybrid evolutionary algorithms-unconstrained numerical optimization
Ant Colony Optimization (ACO) is a metaheuristic that is inspired by the pheromone trail laying and following behavior of
some ant species. Artificial ants in ACO are stochastic solution construction procedures that build candidate solutions for
the problem instance under concern by exploiting (artificial) pheromone information that is adapted based on the ants’ search
experience and possibly available heuristic information. Since the proposal of the Ant System, the first ACO algorithm, many
significant research results have been obtained. These contributions focused on the development of high-performing algorithmic
variants, the development of a generic algorithmic framework for ACO algorithms, successful applications of ACO algorithms
to a wide range of computationally hard problems, and the theoretical understanding of properties of ACO algorithms. This
chapter reviews these developments and gives an overview of recent research trends in ACO.
Population-based meta-heuristics are algorithms that can obtain very good results for complex continuous optimization problems
in a reduced amount of time. These search algorithms use a population of solutions to maintain an acceptable diversity level
during the process, thus their correct distribution is crucial for the search. This paper introduces a new population meta-heuristic
called “variable mesh optimization” (VMO), in which the set of nodes (potential solutions) are distributed as a mesh. This
mesh is variable, because it evolves to maintain a controlled diversity (avoiding solutions too close to each other) and to
guide it to the best solutions (by a mechanism of resampling from current nodes to its best neighbour). This proposal is compared
with basic population-based meta-heuristics using a benchmark of multimodal continuous functions, showing that VMO is a competitive
This editorial note presents the motivations, objectives, and structure of the special issue on scalability of evolutionary
algorithms and other metaheuristics for large-scale continuous optimization problems. In addition, it provides the link to
an associated Website where complementary material to the special issue is available.
KeywordsLarge-scale continuous optimization problems–Evolutionary algorithms–Metaheuristics
There is a deep and useful connection between statistical mechanics (the behavior of systems with many degrees of freedom in thermal equilibrium at a finite temperature) and multivariate or combinatorial optimization (finding the minimum of a given function depending on many parameters). A detailed analogy with annealing in solids provides a framework for optimization of the properties of very large and complex systems. This connection to statistical mechanics exposes new information and provides an unfamiliar perspective on traditional optimization problems and methods.
The interest about hybrid optimization methods has grown for the last few years. Indeed, more and more papers about cooperation between heuristics and exact techniques are published. In this paper, we propose to extend an existing taxonomy for hybrid methods involving heuristic approaches in order to consider cooperative schemes between exact methods and metaheuristics. First, we propose some natural approaches for the different schemes of cooperation encountered, and we analyse, for each model, some examples taken from the literature. Then we recall and complement the proposed grammar and provide an annotated bibliography.
There is a deep and useful connection between statistical mechanics (the behavior of systems with many degrees of freedom
in thermal equilibrium at a finite temperature) and multivariate or combinatorial optimization (finding the minimum of a given
function depending on many parameters). A detailed analogy with annealing in solids provides a framework for optimization
of the properties of very large and complex systems. This connection to statistical mechanics exposes new information and
provides an unfamiliar perspective on traditional optimization problems and methods.
Vehicle routing problem with time windows (VRPTVV) is a well-known combinatorial problem. Many researches have presented meta-heuristics are effective approaches for VRPTW. This paper proposes a hybrid approach, which consists of ant colony optimization (ACO) and Tabu search, to solve the problem. To improve the performance of ACO, a neighborhood search is introduced. Furthermore, when ACO is close to the convergence Tabu search is used to maintain the diversity of ACO and explore new solutions. Computational experiments are reported for a set of the Solomon's 56 VRPTW and the approach is compared with some meta-heuristic published in literature. Results show that considering the tradeoff of quality and computation time, the hybrid algorithm is a competitive approach for VRPTVV.
The Point-Feature Cartographic Label Placement (PFCLP) problem consists of placing text labels to point features on a map avoiding overlaps to improve map visualization. This paper presents a Clustering Search (CS) metaheuristic as a new alternative to solve the PFCLP problem. Computational experiments were performed over sets of instances with up to 13,206 points. These instances are the same used in several recent and important researches about the PFCLP problem. The results enhance the potential of CS by finding optimal solutions (proven in previous works) and improving the best-known solutions for instances whose optimal solutions are unknown so far.
This paper examines the m machine no-wait flow shop problem with setup times of a job separated from its processing time. The performance measure considered is the makespan. The hybrid metaheuristic Evolutionary Cluster Search (ECS_NSL) proposed in Nagano et al. (2012) is extended to solve the scheduling problem. The ECS_NSL performance is evaluated and the results are compared with the best method reported in the literature. Experimental tests show superiority of the ECS_NSL regarding the solution quality.
The continuous casting batch machine scheduling with flexible jobs is proposed based on its character. The original problem is firstly preprocessed based on rule, and then the optimization model with minimizing setup costs is proposed. To improve the efficiency of local search, the Particle Swarm Optimization (PSO) is introduced, and then the PSO and heuristic strategy are embedded into the Iterated Local Search (ILS) to solve the problem. The solution space is divided into many subspaces based on the charge information, and then the subspaces are integrated after local search. The maximum number of iteration is introduced as stopping condition. Then, the proposed algorithm and ILS are compared, and the changing of learning factors, number of generation, and the maximum number of iteration are also tested respectively. Finally, the simulation results show that the proposed algorithm can solve the problem efficiently.
This paper addresses the m-machine no-wait flow shop problem where the set-up time of a job is separated from its processing time. The performance measure considered is the total flowtime. A new hybrid metaheuristic Genetic Algorithm–Cluster Search is proposed to solve the scheduling problem. The performance of the proposed method is evaluated and the results are compared with the best method reported in the literature. Experimental tests show superiority of the new method for the test problems set, regarding the solution quality.
In this paper we are looking at routing and scheduling problems arising in the context of home health care services. Many small companies are working in this sector in Germany and planning is still done manually, resulting in long planning times and relatively inflexible solutions.First, we consider the home health care problem (HHCP) which seeks for a weekly optimal plan. However, in practice a master schedule is generated which is modified to incorporate operational changes. We take this approach into account by looking at the master schedule problem (MSP) and at the operational planning problem (OPP).The problems are solved using different metaheuristics combined with methods from constraint programming. This allows a very flexible treatment of realistic constraints.
The comparison of two treatments generally falls into one of the following two categories: (a) we may have a number of replications for each of the two treatments, which are unpaired, or (b) we may have a number of paired comparisons leading to a series of differences, some of which may be positive and some negative. The appropriate methods for testing the significance of the differences of the means in these two cases are described in most of the textbooks on statistical methods.
Two general convergence proofs for random search algorithms. The authors review the literature and show how the results extend those available for specific variants of the conceptual algorithm studied. An examination is made of the convergence results to examine convergence rates and to actually design implementable methods. A report is presented on some computational experience.
The key idea underlying iterated local search is to focus the search not on the full space of all candidate solutions but on the solutions that are returned by some underlying algorithm, typically a local search heuristic. The resulting search behavior can be characterized as iteratively building a chain of solutions of this embedded algorithm. The result is also a conceptually simple metaheuristic that nevertheless has led to state-of-the-art algorithms for many computationally hard problems. In fact, very good performance is often already obtained by rather straightforward implementations of the metaheuristic. In addition, the modular architecture of iterated local search makes it very suitable for an algorithm engineering approach where, progressively, the algorithms' performance can be further optimized. Our purpose here is to give an accessible description of the underlying principles of iterated local search and a discussion of the main aspects that need to be taken into account for a successful application of it. In addition, we review the most important applications of this method and discuss its relationship to other metaheuristics.
This paper presents two hybrid differential evolution algorithms for optimizing engineering design problems. One hybrid algorithm enhances a basic differential evolution algorithm with a local search operator, i.e., random walk with direction exploitation, to strengthen the exploitation ability, while the other adding a second metaheuristic, i.e., harmony search, to cooperate with the differential evolution algorithm so as to produce the desirable synergetic effect. For comparison, the differential evolution algorithm that the two hybrids are based on is also implemented. All algorithms incorporate a generalized method to handle discrete variables and Deb's parameterless penalty method for handling constraints. Fourteen engineering design problems selected from different engineering fields are used for testing. The test results show that: (i) both hybrid algorithms overall outperform the differential evolution algorithms; (ii) among the two hybrid algorithms, the cooperative hybrid overall outperforms the other hybrid with local search; and (iii) the performance of proposed hybrid algorithms can be further improved with some effort of tuning the relevant parameters.
This paper presents a hybrid evolution strategy (ES) for solving the open vehicle routing problem (OVRP), which is a well-known combinatorial optimization problem that addresses the service of a set of customers using a homogeneous fleet of non-depot returning capacitated vehicles. The objective is to minimize the fleet size and the distance traveled. The proposed solution method manipulates a population of μ individuals using a (μ+λ)-ES; at each generation, a new intermediate population of λ offspring is produced via mutation, using arcs extracted from parent individuals. The selection and combination of arcs is dictated by a vector of strategy parameters. A multi-parent recombination operator enables the self-adaptation of the mutation rates based on the frequency of appearance of each arc and the diversity of the population. Finally, each new offspring is further improved via a memory-based trajectory local search algorithm, while an elitist scheme guides the selection of survivors. Experimental results on well-known benchmark data sets demonstrate the competitiveness of the proposed population-based hybrid metaheuristic algorithm.
The capacitated centered clustering problem (CCCP) consists in partitioning a set of n points into p disjoint clusters with a known capacity. Each cluster is specified by a centroid. The objective is to minimize the total dissimilarity within each cluster, such that a given capacity limit of the cluster is not exceeded. This paper presents a solution procedure for the CCCP, using the hybrid metaheuristic clustering search (CS), whose main idea is to identify promising areas of the search space by generating solutions through a metaheuristic and clustering them into groups that are then further explored with local search heuristics. Computational results in test problems of the literature show that the CS found a significant number of new best-known solutions in reasonable computational times.
In this paper we introduce a methodology for optimizing the expected cost of routing a single vehicle which has a probability of breaking down or failing to complete some of its tasks. More specifically, a calculus is devised for finding the optimal order in which each site should be visited.
This work presents a new approach to the Berth Allocation Problem (BAP) for ships in ports. Due to the increasing demand for ships carrying containers, the BAP can be considered as a major optimization problem in marine terminals. In this paper, the BAP is considered as dynamic and modeled in discrete case and we propose a new alternative to solve it. The proposed alternative is based on applying the Clustering Search (CS) method using the Simulated Annealing (SA) for solutions generation. The CS is an iterative method which divides the search space in clusters and it is composed of a metaheuristic for solutions generation, a grouping process and a local search heuristic. The computational results are compared against recent methods found in the literature.
The Capacitated Centered Clustering Problem (CCCP) consists of defining a set of p groups with minimum dissimilarity on a network with n points. Demand values are associated with each point and each group has a demand capacity. The problem is well known to be NP-hard and has many practical applications. In this paper, the hybrid method Clustering Search (CS) is implemented to solve the CCCP. This method identifies promising regions of the search space by generating solutions with a metaheuristic, such as Genetic Algorithm, and clustering them into clusters that are then explored further with local search heuristics. Computational results considering instances available in the literature are presented to demonstrate the efficacy of CS.
Research in metaheuristics for combinatorial optimization problems has lately experienced a noteworthy shift towards the hybridization of metaheuristics with other techniques for optimization. At the same time, the focus of research has changed from being rather algorithm-oriented to being more problem-oriented. Nowadays the focus is on solving the problem at hand in the best way possible, rather than promoting a certain metaheuristic. This has led to an enormously fruitful cross-fertilization of different areas of optimization. This cross-fertilization is documented by a multitude of powerful hybrid algorithms that were obtained by combining components from several different optimization techniques. Hereby, hybridization is not restricted to the combination of different metaheuristics but includes, for example, the combination of exact algorithms and metaheuristics. In this work we provide a survey of some of the most important lines of hybridization. The literature review is accompanied by the presentation of illustrative examples.
The purpose of this paper is to propose and compare several optimization methods for elective surgery planning when operating room (OR) capacity is shared by elective and emergency surgery. The planning problem is considered as a stochastic optimization problem in order to minimize expected overtime costs and patients' related costs. An "almost" exact method combining Monte Carlo simulation and mixed integer programming is presented, and its convergence properties are investigated. Several heuristic and meta-heuristic methods are then proposed. Numerical experimentations are conducted to compare the performance of different optimization methods.
A method is described for the minimization of a function of n variables, which depends on the comparison of function values at the (n + 1) vertices of a general simplex, followed by the replacement of the vertex with the highest value by another point. The
simplex adapts itself to the local landscape, and contracts on to the final minimum. The method is shown to be effective and
computationally compact. A procedure is given for the estimation of the Hessian matrix in the neighbourhood of the minimum,
needed in statistical estimation problems.
Traditional approaches for SCM usually focus on process operations and neglect the financial side of the problem. In this work we present a novel approach for holistically optimizing the combined effects of operations and finances in SCM. To achieve such integration between different business areas, it is derived an integrated model for SCM, which incorporates process operations as well as budgetary constraints. The novelty of this formulation lies not only in the insertion of financial aspects within a SC planning formulation, but also in the choice of a financial performance indicator, i.e. the change in equity, as the objective to be optimized in the integrated model. The main advantages of this mathematical formulation are highlighted through a case study, in which the results obtained by the integrated model are compared with those computed by the traditional sequential strategy, in which the operations are firstly computed and the finances are fitted afterwards. The obtained results show the importance of devising broader modeling systems for SCM leading to increased overall earnings and providing further insights on the interactions between operations and finances.
eberhart @ engr.iupui.edu A concept for the optimization of nonlinear functions using particle swarm methodology is introduced. The evolution of several paradigms is outlined, and an implementation of one of the paradigms is discussed. Benchmark testing of the paradigm is described, and applications, including nonlinear function optimization and neural network training, are proposed. The relationships between particle swarm optimization and both artificial life and genetic algorithms are described, 1
Computer viruses are the first and only form of artificial life to have had a measurable impact on society. Currently, they are a relatively manageable nuisance. However, two alarming trends are likely to make computer viruses a much greater threat. First, the rate at which new viruses are being written is high, and accelerating. Second, the trend towards increasing interconnectivity and interoperability among computers will enable computer viruses and worms to spread much more rapidly than they do today. To address these problems, we have designed an immune system for computers and computer networks that takes much of its inspiration from nature. Like the vertebrate immune system, our system develops antibodies to previously unencountered computer viruses or worms and remembers them so as to recognize and respond to them more quickly in the future. We are careful to minimize the risk of an auto-immune response, in which the immune system mistakenly identifies legitimate software as being undesirable. We also employ nature's technique of fighting self-replication with self-replication which our theoretical studies have shown to be highly effective. Many components of the proposed immune system are already being used to automate computer virus analysis in our laboratory, and we anticipate that this technology will gradually be incorporated into IBM's commercial anti-virus product during the next year or two.