Multi‐objective optimization using metaheuristics: non‐standard algorithms

In recent years, the application of metaheuristic techniques to solve multi‐objective optimization problems has become an active research area. Solving this kind of problems involves obtaining a set of Pareto‐optimal solutions in such a way that the corresponding Pareto front fulfils the requirements of convergence to the true Pareto front and uniform diversity. Most of the studies on metaheuristics for multi‐objective optimization are focused on Evolutionary Algorithms, and some of the state‐of‐the‐art techniques belong this class of algorithms. Our goal in this paper is to study open research lines related to metaheuristics but focusing on less explored areas to provide new perspectives to those researchers interested in multi‐objective optimization. In particular, we focus on non‐evolutionary metaheuristics, hybrid multi‐objective metaheuristics, parallel multi‐objective optimization and multi‐objective optimization under uncertainty. We analyze these issues and discuss open research lines.     

Engineering an efficient two‐phase local search algorithm for the co‐rotating twin‐screw extruder configuration problem

The twin‐screw configuration problem arises during polymer extrusion and compounding. It consists in defining the location of a set of pre‐defined screw elements along the screw axis in order to optimize different, typically conflicting objectives. In this paper, we present a simple yet effective stochastic local search (SLS) algorithm for this problem. Our algorithm is based on efficient single‐objective iterative improvement algorithms, which have been developed by studying different neighborhood structures, neighborhood search strategies, and neighborhood restrictions. These algorithms are embedded into a variation of the two‐phase local search framework to tackle various bi‐objective versions of this problem. An experimental comparison with a previously proposed multi‐objective evolutionary algorithm shows that a main advantage of our SLS algorithm is that it converges faster to a high‐quality approximation to the Pareto front.     

Multi‐objective memetic algorithm: comparing artificial neural networks and pattern search filter method approaches

In this work, two methodologies to reduce the computation time of expensive multi‐objective optimization problems are compared. These methodologies consist of the hybridization of a multi‐objective evolutionary algorithm (MOEA) with local search procedures. First, an inverse artificial neural network proposed previously, consisting of mapping the decision variables into the multiple objectives to be optimized in order to generate improved solutions on certain generations of the MOEA, is presented. Second, a new approach based on a pattern search filter method is proposed in order to perform a local search around certain solutions selected previously from the Pareto frontier. The results obtained, by the application of both methodologies to difficult test problems, indicate a good performance of the approaches proposed.     

Multi‐criteria IoT resource discovery: a comparative analysis

The growth of real‐world objects with embedded and globally networked sensors allows to consolidate the Internet of things paradigm and increase the number of applications in the domains of ubiquitous and context‐aware computing. The merging between cloud computing and Internet of things named cloud of things will be the key to handle thousands of sensors and their data. One of the main challenges in the cloud of things is context‐aware sensor search and selection. Typically, sensors require to be searched using two or more conflicting context properties. Most of the existing work uses some kind of multi‐criteria decision analysis to perform the sensor search and selection, but does not show any concern for the quality of the selection presented by these methods. In this paper, we analyse the behaviour of the SAW, TOPSIS and VIKOR multi‐objective decision methods and their quality of selection comparing them with the Pareto‐optimality solutions. The gathered results allow to analyse and compare these algorithms regarding their behaviour, the number of optimal solutions and redundancy. Copyright © 2016 John Wiley & Sons, Ltd.     

Meta‐heuristic multi‐ and many‐objective optimization techniques for solution of machine learning problems

Recently, multi‐ and many‐objective meta‐heuristic algorithms have received considerable attention due to their capability to solve optimization problems that require more than one fitness function. This paper presents a comprehensive study of these techniques applied in the context of machine learning problems. Three different topics are reviewed in this work: (a) feature extraction and selection, (b) hyper‐parameter optimization and model selection in the context of supervised learning, and (c) clustering or unsupervised learning. The survey also highlights future research towards related areas.     

An evolutionary algorithm for the multi‐objective pick‐up and delivery pollution‐routing problem

The design of sustainable logistics solutions poses new challenges for the study of vehicle‐routing problems. The design of efficient systems for transporting products via a heterogeneous fleet of vehicles must consider the minimization of cost, emissions of greenhouse gases, and the ability to serve every customer within an available time slot. This phenomenon gives rise to a multi‐objective problem that considers the emission of greenhouse gases, the total traveling time, and the number of customers served. The proposed model is approached with an ε‐constraint technique that allows small instances to be solved and an evolutionary algorithm is proposed to deal with complex instances. Results for small instances show that all the points that approach the Pareto frontier found by the evolutionary algorithm are nondominated by any solution found by the multi‐objective model. For complex instances, nondominated solutions that serve most of the requests are found with low computational requirements.     

Evolutionary algorithms for the multi‐objective test data generation problem

Automatic test data generation is a very popular domain in the field of search‐based software engineering. Traditionally, the main goal has been to maximize coverage. However, other objectives can be defined, such as the oracle cost, which is the cost of executing the entire test suite and the cost of checking the system behavior. Indeed, in very large software systems, the cost spent to test the system can be an issue, and then it makes sense by considering two conflicting objectives: maximizing the coverage and minimizing the oracle cost. This is what we did in this paper. We mainly compared two approaches to deal with the multi‐objective test data generation problem: a direct multi‐objective approach and a combination of a mono‐objective algorithm together with multi‐objective test case selection optimization. Concretely, in this work, we used four state‐of‐the‐art multi‐objective algorithms and two mono‐objective evolutionary algorithms followed by a multi‐objective test case selection based on Pareto efficiency. The experimental analysis compares these techniques on two different benchmarks. The first one is composed of 800 Java programs created through a program generator. The second benchmark is composed of 13 real programs extracted from the literature. In the direct multi‐objective approach, the results indicate that the oracle cost can be properly optimized; however, the full branch coverage of the system poses a great challenge. Regarding the mono‐objective algorithms, although they need a second phase of test case selection for reducing the oracle cost, they are very effective in maximizing the branch coverage. Copyright © 2011 John Wiley & Sons, Ltd.     

MRMOGA: a new parallel multi‐objective evolutionary algorithm based on the use of multiple resolutions

In this paper, we introduce MRMOGA (Multiple Resolution Multi‐Objective Genetic Algorithm), a new parallel multi‐objective evolutionary algorithm which is based on an injection island approach. This approach is characterized by adopting an encoding of solutions which uses a different resolution for each island. This approach allows us to divide the decision variable space into well‐defined overlapped regions to achieve an efficient use of multiple processors. Also, this approach guarantees that the processors only generate solutions within their assigned region. In order to assess the performance of our proposed approach, we compare it to a parallel version of an algorithm that is representative of the state‐of‐the‐art in the area, using standard test functions and performance measures reported in the specialized literature. Our results indicate that our proposed approach is a viable alternative to solve multi‐objective optimization problems in parallel, particularly when dealing with large search spaces. Copyright © 2006 John Wiley & Sons, Ltd.     

A taxonomical analysis,current methods and objectives on location‐routing problems

Location‐routing is a branch of locational analysis that takes into account distribution aspects. This paper proposes a taxonomy, with two levels, for location‐routing problems. The first level focuses on the structural characteristics of the problems. The second level branches into the different algorithmic approaches and objective perspectives. An introduction to the previously defined problems is presented, categorising the papers in the literature (a total of 149 references) according to the proposed classification. Moreover, an overview of the most significant aspects of the different solution methods and main objectives, with special emphasis on multi‐objective approaches, is provided. Some data providing a better insight into the publication progress are also included. Finally, several promising research directions are identified.     

Instance variant nearest neighbor using particle swarm optimization for function approximation

In this paper, a new approach called ‘instance variant nearest neighbor’ approximates a regression surface of a function using the concept of k nearest neighbor. Instead of fixed k neighbors for the entire dataset, our assumption is that there are optimal k neighbors for each data instance that best approximates the original function by fitting the local regions. This approach can be beneficial to noisy datasets where local regions form data characteristics that are different from the major data clusters. We formulate the problem of finding such k neighbors for each data instance as a combinatorial optimization problem, which is solved by a particle swarm optimization. The particle swarm optimization is extended with a rounding scheme that rounds up or down continuous-valued candidate solutions to integers, a number of k neighbors. We apply our new approach to five real-world regression datasets and compare its prediction performance with other function approximation algorithms, including the standard k nearest neighbor, multi-layer perceptron, and support vector regression. We observed that the instance variant nearest neighbor outperforms these algorithms in several datasets. In addition, our new approach provides consistent outputs with five datasets where other algorithms perform poorly.     

Application of bacteria foraging algorithm for the design optimization of multi‐objective Yagi‐Uda array

The design of antenna array with desirable multiple performance parameters such as directivity, input impedance, beam width, and side‐lobe level using any optimization algorithm is a highly challenging task. Bacteria Foraging Algorithm (BFA), as reported by electrical engineers, is the most robust and efficient algorithm in comparison with other presently available algorithms for global optimization of multi‐objective, multi‐parameter design problems. The objective of this article is to apply this new optimization technique, BFA, in the design of Yagi‐Uda array for multi‐objective design parameters. We optimize length and spacing for 6 and 15 elements array to achieve higher directivity, pertinent input impedance, minimum 3‐dB beam width, and maximum front to back ratio both in the E and H planes of the array. At first, we develop a Method of Moments code in MATLAB environment for the Yagi‐Uda array structure for obtaining the above design parameters and then coupled with the BFA for the evaluation of the optimized design parameters. Detail simulation results are included to confirm the design criteria. © 2010 Wiley Periodicals, Inc. Int J RF and Microwave CAE , 2010.     

Solving scalarized multi‐objective network flow problems using an interior point method

In this paper, we present a primal‐dual interior‐point algorithm to solve a class of multi‐objective network flow problems. More precisely, our algorithm is an extension of the single‐objective primal infeasible dual feasible inexact interior point method for multi‐objective linear network flow problems. Our algorithm is contrasted with standard interior point methods and experimental results on bi‐objective instances are reported. The multi‐objective instances are converted into single objective problems with the aid of an achievement function, which is particularly adequate for interactive decision‐making methods.     

Work stealing with private integer–vector–matrix data structure for multi‐core branch‐and‐bound algorithms

In this paper, the focus is put on multi‐core branch‐and‐bound algorithms for solving large‐scale permutation‐based optimization problems. We investigate five work stealing (WS) strategies with a new data structure called integer–vector–matrix (IVM). In these strategies, each thread has a private IVM allowing the local management of a set of subproblems enumerated using a factorial system. The WS strategies differ in the way the victim thread is selected and the granularity of stolen work units (intervals of factoradics). To assess the efficiency of the private IVM‐based WS approach, the five WS strategies have been extensively experimented on the flowshop scheduling permutation problem and compared with their conventional linked‐list‐based counterparts. The obtained results demonstrate that the IVM‐based WS outperforms the linked‐list‐based one in terms of CPU time, memory usage and number of performed WS operations. Copyright © 2016 John Wiley & Sons, Ltd.     

一种基于个体密度估算的多目标优化演化算法

通过在目标空间中利用目标本身信息估算个体k最近邻距离之和,作为个体的密度信息,根据个体的密度信息对群体中过剩的非劣解进行逐个去除,以便更好地维护解的多样性,由此给出了一种基于个体密度估算的多目标优化演化算法IDEMOEA。用这个算法对几个典型的多目标优化函数进行测试。测试结果表明,算法IDEMOEA求解多目标优化问题是行之有效的。     

A bi‐objective approach to reschedule new jobs in a one machine model

We consider a one machine scheduling model, minimizing a classical objective function—either the total completion time or the maximum tardiness—and with two sets of jobs: one with initial jobs already scheduled and one with new jobs that must be inserted in the schedule. As such rescheduling can create a modification of the schedule of the initial jobs, a disruption objective is considered in addition to the original objective. This additional objective can be formulated in four different ways. Such model has been introduced by Hall and Potts, minimizing either a linear aggregation of the two objectives or the initial objective under a constraint giving an upper limit of the disruption objective. In this paper, the aim is to obtain the set of efficient schedules in regard to the two objectives. Algorithms are provided for the eight possible bi‐objective problems and illustrated by some didactic examples.     

A preference multi-objective optimization based on adaptive rank clone and differential evolution

Evolutionary multi-objective optimization (EMO) algorithms have been used in various real-world applications. However, most of the Pareto domination based multi-objective optimization evolutionary algorithms are not suitable for many-objective optimization. Recently, EMO algorithm incorporated decision maker’s preferences became a new trend for solving many-objective problems and showed a good performance. In this paper, we first use a new selection scheme and an adaptive rank based clone scheme to exploit the dynamic information of the online antibody population. Moreover, a special differential evolution (DE) scheme is combined with directional information by selecting parents for the DE calculation according to the ranks of individuals within a population. So the dominated solutions can learn the information of the non-dominated ones by using directional information. The proposed method has been extensively compared with two-archive algorithm, light beam search non-dominated sorting genetic algorithm II and preference rank immune memory clone selection algorithm over several benchmark multi-objective optimization problems with from two to ten objectives. The experimental results indicate that the proposed algorithm achieves competitive results.     

Multi‐objective optimal motion control of a laboratory helicopter based on parallel simple cell mapping method

This paper presents a study of multi‐objective optimal design of nonlinear control systems and has validated the control design with a twin rotor model helicopter. The gains of the porportional integral differential (PID) control are designed in the framework of multi‐objective opitmization. Eight design paramaters are optimized to minimize six time‐domain objective objective functions. The study of multi‐objective optimal design of feedback control with such a number of design paramaters and objective functions is rare in the literature. The Pareto optimal solutions are obtained by the proposed parallel simple cell mapping method consisting of a robust Pareto set recovery algorithm and a rolling subdivision technique. The proposed parallel simple cell mapping algorithm has two features: the number of cells in the invariant set grows linearly with the rolling subdivisions, and the Pareto set is insensitive to the inital set of seed cells. The current control design is compared with the classical LQE control for linear systems, and is also experimentally validated. The current design provides improved control performance as compares with the LQR control, and is applicable to complex nonlinear systems.     

一种求解高维优化问题的多目标遗传算法及其收敛性分析

单纯Pareto遗传算法很难解决目标数目很多的高维多目标优化问题，在多个指标之间引入偏好信息，提出的多目标遗传算法使进化群体按协调模型进行偏好排序，改变了传统的基于Pareto优于关系来比较个体的优劣。另外讨论了算法在满足一定条件下具有全局收敛性，典型算例的数学解析和实验验证了其具有较好的收敛性和收敛速度．     

Consensus of linear multi‐agent systems with stochastic noises and binary‐valued communications

This article studies consensus problems of discrete‐time linear multi‐agent systems with stochastic noises and binary‐valued communications. Different from quantized consensus of first‐order systems with binary‐valued observations, the quantized consensus of linear multi‐agent systems requires that each agent observes its neighbors' states dynamically. Unlike the existing quantized consensus of linear multi‐agent systems, the information that each agent in this article gets from its neighbors is only binary‐valued. To estimate its neighbors' states dynamically by using the binary‐valued observations, we construct a two‐step estimation algorithm. Based on the estimates, a stochastic approximation‐based distributed control is proposed. The estimation and control are analyzed together in the closed‐loop system, since they are strongly coupled. Finally, it is proved that the estimates can converge to the true states in mean square sense and the states can achieve consensus at the same time by properly selecting the coefficient in the estimation algorithm. Moreover, the convergence rate of the estimation and the consensus speed are both given by O(1/t). The theoretical results are illustrated by simulations.     

Robust control under worst‐case uncertainty for unknown nonlinear systems using modified reinforcement learning

Reinforcement learning (RL) is an effective method for the design of robust controllers of unknown nonlinear systems. Normal RLs for robust control, such as actor‐critic (AC) algorithms, depend on the estimation accuracy. Uncertainty in the worst case requires a large state‐action space, this causes overestimation and computational problems. In this article, the RL method is modified with the k‐nearest neighbor and the double Q‐learning algorithm. The modified RL does not need the neural estimator as AC and can stabilize the unknown nonlinear system under the worst‐case uncertainty. The convergence property of the proposed RL method is analyzed. The simulations and the experimental results show that our modified RLs are much more robust compared with the classic controllers, such as the proportional‐integral‐derivative, the sliding mode, and the optimal linear quadratic regulator controllers.