Multi-objective Local Search Algorithm Research Articles

Scheduling an Agile Multipayload Earth-Observing Satellite

A highly integrated Earth-observing satellite can possess several maneuverable payloads to perform different missions simultaneously, which brings some challenges to the method of task scheduling. This paper addresses the selection and scheduling problem of an agile satellite with several independently maneuverable optical payloads. Some differences compared to the traditional scheduling problem of agile satellites are presented and considered in a constrained optimization model. A two-stage method is proposed to accomplish the scheduling of the satellite and payloads in different stages. Clusters are generated from preprocessed tasks by a clique partition algorithm, and their centers are used to calculate the pointing direction of the satellite in the first stage. A multiobjective local search algorithm is introduced to schedule tasks in each selected cluster in the second stage. Considering the time-dependent property of the transition time, the problem of determining the start observation time is transformed into linear programming in a proposed insertion operator that guarantees the feasibility of generated solutions. Two types of instances are created and tested to demonstrate the effectiveness of the proposed method, and some analyses are conducted based on the experimental results.

Comparing Multi-Objective Local Search Algorithms for the Beam Angle Selection Problem

In intensity-modulated radiation therapy, treatment planners aim to irradiate the tumour according to a medical prescription while sparing surrounding organs at risk as much as possible. Although this problem is inherently a multi-objective optimisation (MO) problem, most of the models in the literature are single-objective ones. For this reason, a large number of single-objective algorithms have been proposed in the literature to solve such single-objective models rather than multi-objective ones. Further, a difficulty that one has to face when solving the MO version of the problem is that the algorithms take too long before converging to a set of (approximately) non-dominated points. In this paper, we propose and compare three different strategies, namely random PLS (rPLS), judgement-function-guided PLS (jPLS) and neighbour-first PLS (nPLS), to accelerate a previously proposed Pareto local search (PLS) algorithm to solve the beam angle selection problem in IMRT. A distinctive feature of these strategies when compared to the PLS algorithms in the literature is that they do not evaluate their entire neighbourhood before performing the dominance analysis. The rPLS algorithm randomly chooses the next non-dominated solution in the archive and it is used as a baseline for the other implemented algorithms. The jPLS algorithm first chooses the non-dominated solution in the archive that has the best objective function value. Finally, the nPLS algorithm first chooses the solutions that are within the neighbourhood of the current solution. All these strategies prevent us from evaluating a large set of BACs, without any major impairment in the obtained solutions’ quality. We apply our algorithms to a prostate case and compare the obtained results to those obtained by the PLS from the literature. The results show that algorithms proposed in this paper reach a similar performance than PLS and require fewer function evaluations.

Research on hot rolling scheduling problem based on Two-phase Pareto algorithm.

Under the background of excess capacity and energy saving in iron and steel enterprises, the hot rolling batch scheduling problem based on energy saving is a multi-objective and multi constraint optimization problem. In this paper, a hybrid multi-objective prize-collecting vehicle routing problem (Hybrid Price Collect Vehicle Routing Problem, HPCVRP) model is established to ensure minimum energy consumption, meet process rules, and maximize resource utilization. A two-phase Pareto search algorithm (2PPLS) is designed to solve this model. The improved MOEA/D with a penalty based boundary intersection distance (PBI) algorithm (MOEA/D-PBI) is introduced to decompose the HPCVRP in the first phase. In the second phase, the multi-objective ant colony system (MOACS) and Pareto local search (PLS) algorithm is used to generate approximate Pareto-optimal solutions. The final solution is then selected according to the actual demand and preference. In the simulation experiment, the 2PPLS is compared with five other algorithms, which shows the superiority of 2PPLS. Finally, the experiment was carried out on actual slab data from a steel plant in Shanghai. The results show that the model and algorithm can effectively reduce the energy consumption in the process of hot rolling batch scheduling.

Analysis of multiobjective evolutionary algorithms on the biobjective traveling salesman problem (1,2)

Multiobjective evolutionary algorithms have been successfully used to deal with multiobjective combinatorial optimization problems for more than two decades. However, we know little about the performance of multiobjective evolutionary algorithms on multiobjective combinatorial optimization problems in theory so far, especially on NP-hard ones from real-world, since Pareto curves are often of exponential size, meanwhile, evolutionary algorithms rely heavily on the use of randomness and are hard to understand from a theoretical point of view. In this paper, we theoretically investigate the performance of two simple multiobjective evolutionary algorithms with different population diversity mechanisms on the biobjective traveling salesman problem (1,2). It is found that one of them can efficiently find a $\frac {3}{2}$ -approximation Pareto curve for the problem, the best result so far. At the same time, these two multiobjective evolutionary algorithms are proved to be superior to a multiobjective local search algorithm, and the multiobjective local search algorithm is also proven to outperform these two multiobjective evolutionary algorithms as well. Finally, the population diversity is proved to be helpful in reducing the expected runtime of multiobjective evolutionary algorithm.

Multi-Objective Optimization for the Vehicle Routing Problem With Outsourcing and Profit Balancing

An importer in Hong Kong employs vehicles, all from external transport companies, to deliver products to its customers geographically scattered in different locations. The delivery plan needs to simultaneously minimize the total traveling cost and balance the profits among all transport companies. This transportation practice engenders a new variant of vehicle routing problems, called the vehicle routing problem with outsourcing and profit balancing (VRPOPB). The profits are balanced by maximizing the minimum unit profit of all transport companies, which can effectively avoid the occurrence of distorted solutions. We develop two multi-objective local search (MOLS) algorithms for the problem, where the second one enhances the first one by incorporating several additional techniques. To evaluate our algorithms, we conduct extensive experiments on 57 generated instances and a real case obtained from a food importer in Hong Kong. The computational results clearly demonstrate that our enhanced MOLS algorithm is able to achieve satisfactory solutions.

Foreword

Automated algorithm selection and configuration are key enabling approaches for improving the state of the art in solving a broad range of important problems, by exploiting performance complementarity between multiple algorithms for the same problem (selection) and by realising the latent performance potential in parameterised algorithms (configuration). Compared to traditional, manual approaches, these techniques are not only more efficient and rely less on human expertise, but also provide a more principled basis for algorithm selection and configuration, enable fairer comparisons between algorithms, and facilitate new insights into which algorithmic techniques and components work best and under which circumstances.Work on automated algorithm selection, configuration, and related areas spans multiple, weakly connected communities, including artificial intelligence, evolutionary computation, mathematical optimisation and operations research. This special issue follows a Dagstuhl seminar on the same topic, held in October 2016, and is intended as a further step toward creating synergy between those communities.For this special issue, we selected, from a substantial number of submissions, seven papers that jointly cover a broad range of topics and approaches, including various methods for algorithm selection and configuration, search landscape analysis, software engineering aspects, as well as applications to prominent discrete and continuous, single- and multiobjective optimisation problems.The survey paper by Kerschke et al. provides an overview of research in automated algorithm selection, ranging from early and seminal works to recent and promising application areas. Unlike earlier surveys, it covers applications to discrete and continuous problems; it also situates algorithm selection in the context of a wide spectrum of conceptually related approaches, such as algorithm configuration, scheduling, and portfolio selection, and discusses open challenges.Alyaha and Rowe present a study of landscape characteristics for three NP-hard combinatorial optimisation problems: number partitioning and two variants of knapsack problems. A comparative analysis of landscapes induced by different neighbourhood operators, penalty functions, and problem parameters led to improved problem understanding and to a heuristic for selecting the most appropriate local search operator.The paper by Saalem et al. introduces an approach for assessing the effectiveness of exploratory landscape features with respect to their impact on the performance of algorithm selection methods. A model-based framework for continuous black-box problem comparison using Gaussian process (GP) regression is presented, leading to a flexible surrogate model for problem landscapes. The GP substantially facilitates problem comparison while efficiently measuring model quality.Kerschke et al. present an automated algorithm selection method for single-objective continuous black-box optimisation problems, based on sophisticated exploratory landscape analysis and machine learning techniques. The efficiency of the selector is illustrated on the Black-Box Optimisation Benchmark (BBOB), by improving the performance over the single best solver from a representative set of solvers by a factor of two on average.In the paper by Wessing et al., an improved initialisation procedure for a well-known automated configuration procedure, irace, is shown to outperform classical uniform sampling of algorithm configurations. Techniques from the design and analysis of computer experiments are applied, that is, several Latin hypercube sampling methods that are able to handle categorical and numerical parameters that may be conditional (nested) on the value of other (branching) parameters.Blot et al. investigate the automatic configuration of multiobjective local search algorithms for permutation problems—specifically, for the bi-objective permutation flowshop and travelling salesman problems. They consider two performance metrics as configuration objectives and study several approaches for automated configuration according to these two objectives, presenting clear evidence that multiobjective algorithms are best configured using a multiobjective configurator.Finally, Swan et al. introduce a new approach to the automation of the design of metaheuristics, the so-called Automated Open-Closed Principle (AOCP), which addresses the problem of state dependencies between configurable components in flexible algorithm frameworks. AOCP extends current approaches to automated algorithm configuration by offering a principled software engineering approach to ensure the automated assembly of algorithms from an extensible palette of components.By now, automated algorithm selection and configuration are mature research areas, as witnessed not only by the sophistication of the methods and the success of their many applications, but also by a large and fast-growing body of literature. Still, we see much room for further work, spanning the gamut from theoretical to empirical studies, from new methodology to applications. We hope that this special issue will inspire interest and future work in these dynamic and exciting research areas.

Automatic Configuration of Multi-Objective Local Search Algorithms for Permutation Problems.

Automatic algorithm configuration (AAC) is becoming a key ingredient in the design of high-performance solvers for challenging optimisation problems. However, most existing work on AAC deals with configuration procedures that optimise a single performance metric of a given, single-objective algorithm. Of course, these configurators can also be used to optimise the performance of multi-objective algorithms, as measured by a single performance indicator. In this work, we demonstrate that better results can be obtained by using a native, multi-objective algorithm configuration procedure. Specifically, we compare three AAC approaches: one considering only the hypervolume indicator, a second optimising the weighted sum of hypervolume and spread, and a third that simultaneously optimises these complementary indicators, using a genuinely multi-objective approach. We assess these approaches by applying them to a highly-parametric local search framework for two widely studied multi-objective optimisation problems, the bi-objective permutation flowshop and travelling salesman problems. Our results show that multi-objective algorithms are indeed best configured using a multi-objective configurator.

A multi-population algorithm for multi-objective knapsack problem

Local search algorithms constitute a growing area of interest to approximate the Pareto sets of multi-objective combinatorial problem instances. In this study, we focus on the multi-objective knapsack problem and its optimization thanks to a multi-population based cooperative framework. The proposed approach, Wϵ-CMOLS, uses a multi-objective local search algorithm based on quality indicator (IBMOLS), initially presented by Basseur and Burke in 2007, and integrates it into a cooperative model. The idea is to optimize the overall quality of a Pareto set approximation by evolving several sub-populations in parallel, each population executing a different configuration of IBMOLS. The algorithm uses a weighted version of the epsilon quality indicator by means of different weight vectors. The populations cooperate through sharing a non-dominated archive, which stores the best compromises found during the optimization process, and which is used to re-initialize regularly each sub-population. Wϵ-CMOLS is compared with state-of-the-art algorithms such as IBEA, NSGA-II and SPEA2. Experiments highlight that the use of a cooperative model as well as a weighted indicator to guide the search toward different directions, can lead to interesting results for the multi-objective knapsack problem.

Survey and unification of local search techniques in metaheuristics for multi-objective combinatorial optimisation

Metaheuristics are algorithms that have proven their efficiency on multi-objective combinatorial optimisation problems. They often use local search techniques, either at their core or as intensification mechanisms, to obtain a well-converged and diversified final result. This paper surveys the use of local search techniques in multi-objective metaheuristics and proposes a general structure to describe and unify their underlying components. This structure can instantiate most of the multi-objective local search techniques and algorithms in literature.

RETRACTED ARTICLE: Research on semi supervised K-means clustering algorithm in data mining

K-means clustering has become an important tool for the analysis of gene expression data, which can also look for the expression of cluster with the same fluctuation from two directions of genes and conditions. But the K-means clustering is a multi-objective local search algorithm, which is easy to fall into local optimum when dealing with complex data of the gene. In order to improve the global search capability of the algorithm, this paper presents a semi supervised K clustering algorithm. Firstly, the K—means clustering algorithm is used to deal with gene data. Then the improved semi supervised K mean clustering is used for the greedy iteration to find the K mean clustering, so as to achieve better results. Through the simulation experiment, the results prove the global semi supervised K clustering algorithm has better optimization ability and better cluster effect compared with MDO algorithm.

Conception of a dominance-based multi-objective local search in the context of classification rule mining in large and imbalanced data sets

Classification on medical data raises several problems such as class imbalance, double meaning of missing data, volumetry or need of highly interpretable results. In this paper a new algorithm is proposed: MOCA-I (Multi-Objective Classification Algorithm for Imbalanced data), a multi-objective local search algorithm that is conceived to deal with these issues all together. It is based on a new modelization as a Pittsburgh multi-objective partial classification rule mining problem, which is described in the first part of this paper. An existing dominance-based multi-objective local search (DMLS) is modified to deal with this modelization. After experimentally tuning the parameters of MOCA-I and determining which version of DMLS algorithm is the most effective, the obtained MOCA-I version is compared to several state-of-the-art classification algorithms. This comparison is realized on 10 small and middle-sized data sets of literature and 2 real data sets; MOCA-I obtains the best results on the 10 data sets and is statistically better than other approaches on the real data sets.

Multiobjective Vehicle Routing Problems With Simultaneous Delivery and Pickup and Time Windows: Formulation, Instances, and Algorithms

This paper investigates a practical variant of the vehicle routing problem (VRP), called VRP with simultaneous delivery and pickup and time windows (VRPSDPTW), in the logistics industry. VRPSDPTW is an important logistics problem in closed-loop supply chain network optimization. VRPSDPTW exhibits multiobjective properties in real-world applications. In this paper, a general multiobjective VRPSDPTW (MO-VRPSDPTW) with five objectives is first defined, and then a set of MO-VRPSDPTW instances based on data from the real-world are introduced. These instances represent more realistic multiobjective nature and more challenging MO-VRPSDPTW cases. Finally, two algorithms, multiobjective local search (MOLS) and multiobjective memetic algorithm (MOMA), are designed, implemented and compared for solving MO-VRPSDPTW. The simulation results on the proposed real-world instances and traditional instances show that MOLS outperforms MOMA in most of instances. However, the superiority of MOLS over MOMA in real-world instances is not so obvious as in traditional instances.

Solving bi-objective flow shop problem with hybrid path relinking algorithm

This paper presents and investigates different ways to integrate path relinking techniques into the hypervolume-based multi-objective local search algorithm (HBMOLS). We aim to evaluate the effectiveness of different path relinking strategies, these strategies focus on two main steps: the ways of path generation and the mechanisms of solutions selection. We propose different methods to establish the path relinking algorithms in a multi-objective context. Computational results on a bi-objective flow shop problem (FSP) and a statistical comparison are reported in the paper. In comparison with two versions of HBMOLS, the algorithms selecting a set of solutions located in the middle of the generated path are efficient. The behavior of these algorithms sheds light on ways to further improvements.

On the structure of multiobjective combinatorial search space: MNK-landscapes with correlated objectives

The structure of the search space explains the behavior of multiobjective search algorithms, and helps to design well-performing approaches. In this work, we analyze the properties of multiobjective combinatorial search spaces, and we pay a particular attention to the correlation between the objective functions. To do so, we extend the multiobjective NK-landscapes in order to take the objective correlation into account. We study the co-influence of the problem dimension, the degree of non-linearity, the number of objectives, and the objective correlation on the structure of the Pareto optimal set, in terms of cardinality and number of supported solutions, as well as on the number of Pareto local optima. This work concludes with guidelines for the design of multiobjective local search algorithms, based on the main fitness landscape features.

A novel multi-objective particle swarm optimization algorithm for no-wait flow shop scheduling problems

The current paper presents a novel multi-objective particle swarm optimization (MOPSO) algorithm for solving no-wait flow shop scheduling problems with makespan and maximum tardiness criteria. First, in the algorithm, particles are represented as job permutations and updated directly in the discrete domain. Second, the concept of Pareto dominance is applied to compare different solutions of multi-objective optimization, and a set is employed to hold and to update the obtained non-dominated solutions, where a randomly selected non-dominated solution is assigned as the global best particle to maintain the diversity of the searching direction and to speed up the convergence process to the Pareto front. Third, a new multi-objective heuristic, named the PWQ (Pan—Wang—Qian) heuristic, is proposed to produce a population of initial particles with relatively good performances. Fourth, a simple but effective multi-objective local search algorithm is developed to embed in the MOPSO algorithm for stressing the balance between global exploration and local exploitation. In addition, two speed-up methods are devised to evaluate a job permutation and its insert neighbourhood respectively. Computational simulation results based on the well-known benchmarks and statistical performance comparisons are provided. It is shown that the proposed algorithm is superior to a recently published multi-objective hybrid differential evolution (MHDE) algorithm in terms of searching quality, diversity level, robustness, and efficiency.

Medical image reconstruction using a multi-objective genetic local search algorithm

Image reconstruction from projections is a key problem in medical image analysis. In this paper, we cast image reconstruction from projections as a multi-objective problem. It is essential to choose some proper objective functions of the problem. We choose the square error, smoothness of the reconstructed image, and the maximum entropy as our objective functions of the problem. Then we introduce a hybrid algorithm comprising of multi-objective genetic and local search algorithms to reconstruct the image. Our algorithm has remarkable global performance. Our experiments show that we can get different results when we give different weights to different objective functions. We can also control the noise by giving different weights on different objective function. At the same time, we can adjust the parameter to let it have good local performance. Though the computation demands of the hybrid algorithm tends to be larger because of the random search of the GA, it is really a common feature of the global optimization method. Our results show that the hybrid algorithm is a more effective than the conventional method. We think our method is very promising for the medical imaging field.