Automatic design of multi-objective local search algorithms

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.

Recently, the property of connectedness has been claimed to give a strong motivation on the design of local search techniques for multiobjective combinatorial optimization. Indeed, when connectedness holds, a basic Pareto local search, initialized with at least one non-dominated solution, allows to identify the efficient set exhaustively. However, this becomes quickly infeasible in practice as the number of efficient solutions typically grows exponentially with the instance size. As a consequence, we generally have to deal with a limited-size approximation, ideally a representative sample of efficient solutions. In this paper, we propose the biobjective long and multiple path problems. We show experimentally that, on the first problem, even if the efficient set is connected, a local search may be outperformed by a simple evolutionary algorithm in the sampling of the efficient set. At the opposite, on the second problem, a local search algorithm may successfully approximate a disconnected efficient set. Then, we argue that connectedness is not the single property to study for the design of multiobjective local search algorithms. This work opens new discussions on a proper definition of multiobjective fitness landscapes.KeywordsLocal SearchProblem InstancePareto FrontObjective SpaceLocal Search AlgorithmThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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.

In multiobjective genetic local search (MOGLS) algorithms, the local search is usually applied to all offsprings generated by genetic operations. This paper proposes an idea of selecting only good offsprings as initial solutions for the local search. Simulation results show that the proposed idea significantly improves the search ability of MOGLS algorithms.

In this paper, we present a fast hypervolume-based multi-objective local search algorithm, where the fitness assignment is realized by the approximating computation of hypervolume contribution. In the algorithm, we define an approximate hypervolume contribution indicator as the selection mechanism and apply this indicator to an iterated local search. We carry out a range of experiments on three-objective flow shop problem. Experimental results indicate that our algorithm is highly effective in comparison with the algorithms based on the binary indicators and the exact hypervolume contribution indicator.Keywordsmulti-objective optimizationapproximate hypervolume contributionlocal searchflow shop problem

A Variable Iterated Local Search Algorithm for Energy-Efficient No-idle Flowshop Scheduling Problem

Recently, scalarizing-function based approaches have received a renewed interest in multi-objective optimization. In fact, the simplicity of these functions allows them to be easily adaptable to any resolution method. In this contribution, we propose an iterated multi-objective local search algorithm, called MoLS <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">AugWT</sup> , based on well-known and frequently-used scalarizing-function: the augmented weighted Chebyshev function. A neighborhood structure employing a ranking algorithm based on a weighted addition ratio is introduced in this work. The proposed ranking algorithm is integrated in MoLS <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">AugWT</sup> in order to try to establish an order between the candidate items. It has the goal not only to focus the search on the most promising areas of the search space, thus to improve the quality of the obtained solutions, but also to help the population to converge while diminishing the computational time during the optimization process. To evaluate the performance of the proposed algorithm, MoLS <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">AugWT</sup> is applied to the multi-objective multidimensional knapsack problem (MOMKP). Experimental results have shown the efficiency of MoLS <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">AugWT</sup> compared to the state-of the-art algorithms on nine well-known benchmark instances of MOMKP.

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.

A Muti-Start Multiobjective Local Search algorithm is implemented to solve a bi-objective variant of the Vehicle Routing Problem appearing in industry and environmental enterprises. The problem seeks to design a set of routes for each time on a period and in which the service frequency is a decision variable. The algorithm minimizes total emissions by all vehicles and maximizes service quality measure as the number of times that a customer is visited in order to be served.

It is very important that the sequencing and lot sizing in the flow-line environment are not independent. They should be integrated. In this paper, a multiobjective hybrid evolutionary search algorithm which combines a genetic algorithm and a simulated annealing algorithm is proposed and the performance of the proposed algorithm is compared with the existing genetic algorithm and the simulated annealing algorithm. The algorithms are coded independently and the performance is compared with randomly generated test problems. The objective functions considered for evaluation are the minimisation of makespan, minimisation of overtime and minimisation of holding cost. The scalar fitness function combining all the three objective functions, which minimises total cost, is used. The results are presented in tables and figures. The results show that the proposed hybrid algorithm performs better than the genetic algorithm and the simulated annealing algorithm.

Classification is important task of data mining used to extract knowledge from huge volume of data. By nature, classification is multi-objective problem, as it required optimization of multiple objectives simultaneously like accuracy, sensitivity, squared error, precision etc. Traditionally, evolutionary algorithms were used to solve multi-objective classification problem by considering it as single-objective problem, but this approach gives single solution to problem. Therefore, multi-objective evolutionary algorithms are used to solve classification problem. In this paper, we have used Pareto approach to optimize neural network to solve classification problem. Non-dominated sorting genetic algorithm is used to simultaneously optimize accuracy and mean squared error objectives of neural network along with local search. As slow convergence to optimal solutions is major disadvantage of evolutionary algorithm. To speed up convergence to optimal solutions hybrid technique is adopted by augmenting evolutionary technique with local search algorithm. This proposed approach gives set of Pareto optimal solutions which represent different solutions for given classification problem.

In Search-Based Software Engineering (SBSE), users typically select a set of Multi-Objective Search Algorithms (MOSAs) for their experiments without any justification, or they simply choose an MOSA because of its popularity (e.g., NSGA-II). On the other hand, users know certain characteristics of solutions they are interested in. Such characteristics are typically measured with Quality Indicators (QIs) that are commonly used to evaluate the quality of solutions produced by an MOSA. Consequently, these QIs are often employed to empirically evaluate a set of MOSAs for a particular search problem to find the best MOSA. Thus, to guide SBSE users in choosing an MOSA that represents the solutions measured by a specific QI they are interested in, we present an empirical evaluation with a set of SBSE problems to study the relationships among commonly used QIs and MOSAs in SBSE. Our aim, by studying such relationships, is to identify whether there are certain characteristics of a QI because of which it prefers a certain MOSA. Such preferences are then used to provide insights and suggestions to SBSE users in selecting an MOSA, given that they know which quality aspects of solutions they are looking for.

A unified ant colony optimization algorithm for continuous optimization

Automated algorithm configuration methods have proven to be instrumental in deriving high-performing algorithms and such methods are increasingly often used to configure evolutionary algorithms. One major challenge in devising automatic algorithm configuration techniques is to handle the inherent stochasticity in the configuration problems. This article analyses a post-selection mechanism that can also be used for this task. The central idea of the post-selection mechanism is to generate in a first phase a set of high-quality candidate algorithm configurations and then to select in a second phase from this candidate set the (statistically) best configuration. Our analysis of this mechanism indicates its high potential and suggests that it may be helpful to improve automatic algorithm configuration methods.

This chapter presents a newly defined novel combinatorial optimisation problem, namely, the General Combinatorial Optimisation Problem (GCOP), whose decision variables are a set of elementary algorithm components. The combinations of these algorithm components, i.e. solutions of GCOP, thus represent different search algorithms. The objective of GCOP is to find the optimal combinations of algorithm components for solving optimisation problems. Solving the GCOP is thus equivalent to automatically designing the best search algorithms for optimisation problems. The definition of the GCOP is presented with a new taxonomy which categorises relevant literature on automated algorithm design into three lines of research, namely, automated algorithm configuration, selection and composition. Based on the decision space under consideration, the algorithm design itself is defined as an optimisation problem. Relevant literature is briefly reviewed, motivating a new line of exciting and challenging directions on the emerging research of automated algorithm design.