Multi-objective Metaheuristics Research Articles

Multi-objective meta-heuristic optimization in intelligent control: A survey on the controller tuning problem

Multi-objective optimization has been adopted in many engineering problems where a set of requirements must be met to generate successful applications. Among them, there are the tuning problems from control engineering, which are focused on the correct setting of the controller parameters to properly govern complex dynamic systems to satisfy desired behaviors such as high accuracy, efficient energy consumption, low cost, among others. These requirements are stated in a multi-objective optimization problem to find the most suitable controller parameters. Nevertheless, these parameters are tough to find because of the conflicting control performance requirements (i.e., a requirement cannot be met without harming the others). Hence, the use of techniques from computational intelligence and soft computing is necessary to solve multi-objective problems and handle the trade-offs among control performance objectives. Meta-heuristics have shown to obtain outstanding results when solving complex multi-objective problems at a reasonable computational cost. In this survey, the literature related to the use of multi-objective meta-heuristics in intelligent control focused on the controller tuning problem is reviewed and discussed.

Multi-objective modified heat transfer search for truss optimization

In this article, a modified version of heat transfer search (HTS) is proposed for multi-objective structural optimization. Contrary to the basic HTS optimizer which activates only one of the three phases of HTS at a time, multi-objective HTS simultaneously exploits the effect of all phases. The proposed modified optimizer is based on the principle of thermodynamics with design solutions being thought of molecules that interact with other molecules of the system itself, and simultaneously with the surrounding molecules through the three modes of heat transfer, namely conduction, convection, and radiation phases. To examine the effectiveness and feasibility of the proposed modification, five truss optimization benchmark problems are used for the performance test. Truss mass minimization and nodal displacement maximization are taken as objectives, while design variables are discrete. The new method along with several recent multi-objective meta-heuristics including ant system, ant colony system, symbiotic organism search, and HTS is used to solve the test problems and compared for the hypervolume and spacing-to-extent indicators. The results reveal that the improved version of HTS is superior to its previous version and the other optimizers. The statistical examination of this study has been performed by conducting Friedman’s rank. Results show the dominance of the proposed optimizer performance in comparison with the others.

A perturbation adaptive pursuit strategy based hyper-heuristic for multi-objective optimization problems

Abstract For multi-objective optimization problems, obtaining a uniformly distributed approximation set is among the most important issues. During the past decades, various diversity mechanisms have been proposed to address this challenge. However, the existing diversity mechanisms tend to be problem-specific, and may not generalize well over different problem domains. Inspired by the idea of utilizing multiple low-level heuristics to achieve better diversity performance in multi-discipline problem solving, we focus on efficient algorithm design based on the methodology of selection hyper-heuristics. This study proposes a novel selection hyper-heuristic operating over multiple diversity mechanisms. The unique feature of the proposed approach lies in its ability to intelligently learn, select, and combine different diversity mechanisms with the purpose of taking advantages of them to obtain well-distributed approximation sets. Moreover, this work develops a new learning mechanism, the perturbation adaptive pursuit strategy, which is incorporated into the proposed hyper-heuristic to improve the decision-making process of selecting suitable diversity mechanisms for the problem at hand. The performance of the proposed hyper-heuristic is tested on 2-objective ZDT, 3-objective DTLZ, and 5-objective WFG test suites. Additionally, experiments are also conducted to investigate the ability of the novel hyper-heuristic to integrate existing multi-objective meta-heuristics on MaOP test suite from 3- to 10-objectives. Experimental results demonstrate the effectiveness of the proposed selection hyper-heuristic for cross-domain capacity, particularly in producing well distributed approximation set with respect to Spacing metric and Hypervolume metric.

A hybrid intelligent algorithm for a fuzzy multi-objective job shop scheduling problem with reentrant workflows and parallel machines

This paper presents a multi-objective mathematical model for a flexible job shop scheduling problem (FJSSP) with fuzzy processing times, which is solved by a hybrid intelligent algorithm (HIA). This problem contains a combination of a classical job shop problem with parallel machines (JSPM) to provide flexibility in the production route. Despite the previous studies, the number of parallel machines is not pre-specified in this paper. This constraint with other ones (e.g., sequence-dependent setup times, reentrant workflows, and fuzzy variables) makes the given problem more complex. To solve such a multi-objective JSPM, Pareto-based optimization algorithms based on multi-objective meta-heuristics and multi-criteria decision making (MCDM) methods are utilized. Then, different comparison metrics (e.g., quality, mean ideal distance, and rate of achievement simultaneously) are used. Also, this paper includes two major phases to provide a new model of the FJSSP and introduce a new proposed HIA for solving the presented model, respectively. This algorithm is a hybrid genetic algorithm with the SAW/TOPSIS method, namely HGASAW/HGATOPSIS. The comparative results indicate that HGASAW and HGATOPSIS outperform the non-dominated sorting genetic algorithm (NSGA-II) to tackle the fuzzy multi-objective JSPM.

A Hybrid Leader Selection Strategy for Many-Objective Particle Swarm Optimization

Many existing Multi-objective Particle Swarm Optimizers (MOPSOs) may encounter difficulties for a set of good approximated solutions when solving problems with more than three objectives. One possible reason is that the diluted selection pressure causes MOPSOs to fail to generate a set of good approximated Pareto solutions. In this paper, a new approach called the Hybrid Global Leader Selection Strategy (HGLSS) is proposed to deal with many-objective problems more effectively. HGLSS provides two global leader selection mechanisms: one for exploration and one for exploitation. Each particle (solution) can choose one of these two leader selection schemes to identify its global best leader. An external archive is adopted for maintaining the diversity of the found solutions and it contains the final solution reported at the end of the run. The update of the external archive is based on both Pareto dominance and density estimation. The performance of the proposed approach is compared with respect to nine state-of-the-art multi-objective metaheuristics in solving several benchmark problems. Our results indicate that the proposed algorithm generally outperforms the others in terms of Modified Inverted Generational Distance (IGD <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">+</sup> ) indicator.

An energy-aware scheduling algorithm for budget-constrained scientific workflows based on multi-objective reinforcement learning

Since scientific workflow scheduling becomes a major energy contributor in clouds, much attention has been paid to reduce the energy consumed by workflows. This paper considers a multi-objective workflow scheduling problem with the budget constraint. Most existing works of budget-constrained workflow scheduling cannot always satisfy the budget constraint and guarantee the feasibility of solutions. Instead, they discuss the success rate in the experiments. Only a few works can always figure out feasible solutions. These methods work, but they are too complicated. In workflow scheduling, it has been a trend to consider more than one objective. However, the weight selection is usually ignored in these works. The inappropriate weights will reduce the quality of solutions. In this paper, we propose an energy-aware multi-objective reinforcement learning (EnMORL) algorithm. We design a much simpler method to ensure the feasibility of solutions. This method is based on the remaining cheapest budget. Reinforcement learning based on the Chebyshev scalarization function is a new framework, which is effective in solving the weight selection problem. Therefore, we design EnMORL based on it. Our goal is to minimize the makespan and energy consumption of the workflow. Finally, we compare EnMORL with two state-of-the-art multi-objective meta-heuristics in the case of four different workflows. The results show that our proposed EnMORL outperforms these existing methods.

Ensemble of multi-objective metaheuristics for multiprocessor scheduling in heterogeneous distributed systems: a novel success-proportionate learning-based system

Multi-objective multiprocessor scheduling problem in heterogeneous distributed systems is a remarkable NP-hard problem in parallel processing environments. This study proposes a novel ensemble system comprising six population-based metaheuristics for solving multi-objective multiprocessor scheduling problem. The novelty of this study is mainly related to proposed cooperation strategy. In proposed strategy, solutions and metaheuristics are selected based on dominance-rank and success-rate values respectively. All metaheuristics work on a common population of solutions and during the running time performance of metaheuristics is evaluated and used as success rates of the metaheuristics. Choosing the next metaheuristic based on success rate values leads to the fact that better metaheuristics are used frequently while the poor ones are employed rarely. The advantage of using different metaheuristics is that each metaheuristic covers inabilities of others to discover more promising regions of solution space. Likewise to keep extracted non-dominated solutions, local archives and a common global archive are used. The performance of proposed system is evaluated using well-known benchmarks reported in state-of-the-art literature. The evaluations are done over Gaussian elimination, fast Fourier transformation and internal rate of return (IRR) task graphs. Evaluation outcomes prove the robustness of the proposed system and exhibits that ensemble system outperforms its competitors. As instance, the proposed system finds 52, 19 and 43 as the values of three objectives namely makespan, average flow time and reliability for graph presented in Fig. 2 which are better than results obtained by MFA and NSGAII. Also the results show that ensemble system works better than all individual metaheuristics in which it reaches 475, 523 and 381 as values of three objectives for IRR graph.

A bi-objective model for a scheduling problem of unrelated parallel batch processing machines with fuzzy parameters by two fuzzy multi-objective meta-heuristics

This paper considers a bi-objective model for a scheduling problem of unrelated parallel batch processing machines to minimize the makespan and maximum tardiness, simultaneously. Each job has a specific size and the data corresponding to its ready time, due date and processing time-dependent machine are uncertain and determined by trapezoidal fuzzy numbers. Each machine has a specific capacity, in which the number of jobs assigned to each batch on the machine does not violate the machine capacity. The batch processing time, the batch ready time and the batch due date are presented by the longest processing time, the longest ready time and the shortest due date of the jobs that belong to the batch, respectively. To determine the longest and shortest time, the method suggested by Jimenez et al.cite{c18} is used for ranking the fuzzy numbers. A bi-objective fuzzy mixed-integer linear programming model is proposed and solved by two exact methods (i.e., two-phase fuzzy and $epsilon$-constraint) for small-sized problems to obtain a set of Pareto solutions. Because the problem belongs to the class NP-hard, two meta-heuristics, namely fuzzy non-dominated sorting genetic algorithm (FNSGA-II) and fuzzy multi-objective discrete teaching–learning-based optimization (FMODTLBO), are proposed. Then, the comparison of results is illustrated to show their performances. Furthermore, a new representation of the solutions is a matrix with two rows and $N$ columns (i.e., jobs) used to assign the jobs to the batches that processed on the machines.

Self-adaptive MRPBIL-DE for 6D robot multiobjective trajectory planning

This work presents self-adaptive multiobjective real-code population-based incremental learning hybridised with differential evolution (MRPBIL-DE) for solving a 6D robot trajectory planning multiobjective optimisation problem. The objective functions are assigned to minimise travelling time and minimise maximum jerk taking place during motion while the constraints are velocity, acceleration and jerk constraints. A five order polynomial function is used to represent a motion equation while the motion path is divided into two sub-paths; from initial to intermediate positions and from intermediate to final positions. The optimiser is used to find a set of design variables including joint positions, velocities and accelerations at intermediate positions, moving time from the initial to intermediate positions, and that from the intermediate to final positions. Several multiobjective meta-heuristics (MOMHs) along with the proposed algorithm are used to solve the trajectory optimisation problem of robot manipulators while their performances are investigated. The results indicated that the proposed algorithm is effective and efficient for multiobjective robot trajectory planning optimisation problem. The results obtained from such a method are set as the baseline for further study of robot trajectory planning optimisation.

A Two-Stage Green Supply Chain Network with a Carbon Emission Price by a Multi-objective Interior Search Algorithm

This paper presented a new two-stage green supply chain network, in which includes two innovations. Firstly, it presents a new multi-objective model for a two-stage green supply chain problem that considers the amount of shortage in the network, reworking, and carbon-trading cost produced in the green supply chain. Secondly, because of the complexity of this model, it uses a new multi-objective interior search algorithm (MOISA) to solve the presented model. The obtained results of the proposed algorithm were compared with the results of other multi-objective meta-heuristics, namely MOPSO, SPEA2, and NSGA-II. The outcomes demonstrate that the proposed MOISA gives better Pareto solutions and indicates the superiority of the proposed algorithm in most cases. This paper presented a new two-stage green supply chain network, in which includes two innovations. Firstly, it presents a new multi-objective model for a two-stage green supply chain problem that considers the amount of shortage in the network, reworking, and carbon-trading cost produced in the green supply chain. Secondly, because of the complexity of this model, it uses a new multi-objective interior search algorithm (MOISA) to solve the presented model. The obtained results of the proposed algorithm were compared with the results of other multi-objective meta-heuristics, namely MOPSO, SPEA2, and NSGA-II. The outcomes demonstrate that the proposed MOISA gives better Pareto solutions and indicates the superiority of the proposed algorithm in most cases.

A parallel MOEA with criterion-based selection applied to the Knapsack Problem

In this paper, we propose a parallel multiobjective evolutionary algorithm called Parallel Criterion-based Partitioning MOEA (PCPMOEA), with an application to the Multiobjective Knapsack Problem (MOKP). The suggested search strategy is based on a periodic partitioning of potentially efficient solutions, which are distributed to multiple multiobjective evolutionary algorithms (MOEAs). Each MOEA is dedicated to a sole objective, in which it combines both criterion-based and dominance-based approaches. The suggested algorithm addresses two main sub-objectives: minimizing the distance between the current non-dominated solutions and the ideal point, and ensuring the spread of the potentially efficient solutions. Experimental results are included, where we assess the performance of the suggested algorithm against the above mentioned sub-objectives, compared with state-of-the-art results using well-known multi-objective metaheuristics.

A bi-objective multi-period facility location problem for household e-waste collection

This paper addresses the multi-period facility location problem during the market expansion stage, where the decision maker plans to add a certain number of new facilities in each period to gradually increase the accessibility of the infrastructural collection network. In order to consider the trade-off between cost efficiency and service coverage, we propose a multi-period bi-objective 0–1 integer programming formulation for the problem. We develop three metaheuristics to solve the problem. The first metaheuristic is based on the NSGA II framework with the traditional operators for the single-period location problem. The second metaheuristic is based on the local search strategy, where five new neighbourhood structures are designed. The last metaheuristic integrates the former two algorithms. The proposed modelling framework is justified by a case study of the system infrastructure design in Vancouver for E-waste collection. To demonstrate the computational performance of the proposed modelling framework, sixty random instances of different sizes (200 or 500 demand points), with different demand distributions (Uniform, Normal and Gamma distributions) are generated. We compare the proposed modelling framework with two popular multi-objective metaheuristics, MOEA/D and NNIA. Computational results show that the proposed metaheuristic based on local search is the most efficient for searching Pareto solutions of the problem.

Bio-inspired optimization for the molecular docking problem: State of the art, recent results and perspectives

Molecular docking is a Bioinformatics method based on predicting the position and orientation of a small molecule or ligand when it is bound to a target macromolecule. This method can be modeled as an optimization problem where one or more objectives can be defined, typically around an energy scoring function. This paper reviews developments in the field of single- and multi-objective meta-heuristics for efficiently addressing molecular docking optimization problems. We comprehensively analyze both problem formulations and applied techniques from Evolutionary Computation and Swarm Intelligence, jointly referred to as Bio-inspired Optimization. Our prospective analysis is supported by an experimental study dealing with a molecular docking problem driven by three conflicting objectives, which is tackled by using different multi-objective heuristics. We conclude that genetic algorithms are the most widely used techniques by far, with a noted increasing prevalence of particle swarm optimization in the last years, being these last techniques particularly adequate when dealing with multi-objective formulations of molecular docking problems. We end this experimental survey by outlining future research paths that should be under target in this vibrant area.

Two-Stage Multi-Objective Meta-Heuristics for Environmental and Cost-Optimal Energy Refurbishment at District Level

Energy efficiency and environmental performance optimization at the district level are following an upward trend mostly triggered by minimizing the Global Warming Potential (GWP) to 20% by 2020 and 40% by 2030 settled by the European Union (EU) compared with 1990 levels. This paper advances over the state of the art by proposing two novel multi-objective algorithms, named Non-dominated Sorting Genetic Algorithm (NSGA-II) and Multi-Objective Harmony Search (MOHS), aimed at achieving cost-effective energy refurbishment scenarios and allowing at district level the decision-making procedure. This challenge is not trivial since the optimisation process must provide feasible solutions for a simultaneous environmental and economic assessment at district scale taking into consideration highly demanding real-based constraints regarding district and buildings’ specific requirements. Consequently, in this paper, a two-stage optimization methodology is proposed in order to reduce the energy demand and fossil fuel consumption with an affordable investment cost at building level and minimize the total payback time while minimizing the GWP at district level. Aimed at demonstrating the effectiveness of the proposed two-stage multi-objective approaches, this work presents simulation results at two real district case studies in Donostia-San Sebastian (Spain) for which up to a 30% of reduction of GWP at district level is obtained for a Payback Time (PT) of 2–3 years.

A Learning Automata-Based Multiobjective Hyper-Heuristic

Metaheuristics, being tailored to each particular domain by experts, have been successfully applied to many computationally hard optimization problems. However, once implemented, their application to a new problem domain or a slight change in the problem description would often require additional expert intervention. There is a growing number of studies on reusable cross-domain search methodologies, such as selection hyper-heuristics, which are applicable to problem instances from various domains, requiring minimal expert intervention or even none. This paper introduces a new learning automata-based selection hyper-heuristic controlling a set of multiobjective metaheuristics. The approach operates above three well-known multiobjective evolutionary algorithms and mixes them, exploiting the strengths of each algorithm. The performance and behavior of two variants of the proposed selection hyper-heuristic, each utilizing a different initialization scheme are investigated across a range of unconstrained multiobjective mathematical benchmark functions from two different sets and the real-world problem of vehicle crashworthiness. The empirical results illustrate the effectiveness of our approach for cross-domain search, regardless of the initialization scheme, on those problems when compared to each individual multiobjective algorithm. Moreover, both variants perform significantly better than some previously proposed selection hyper-heuristics for multiobjective optimization, thus significantly enhancing the opportunities for improved multiobjective optimization.

Automated design of aircraft fuselage stiffeners using multiobjective evolutionary optimisation

This paper proposes an optimisation process for the design of aircraft fuselage stiffeners using evolutionary optimisation. A new design problem is developed to find a layout for fuselage stiffeners (rings and stringers) such that the structural mass, compliance, and the first-mode natural frequency can be optimised, subject to structural constraints. The stiffeners are modelled as beam elements. Three multiobjective meta-heuristics are employed to solve the problem, and a comparative study of the results of these optimisers is carried out. It is found that the proposed layout synthesis problem for aircraft fuselage stiffeners leads to a set of efficient structural solutions, which can be used at the decision-making stage. It is an automated design strategy with high potential for further investigation.

Automated design of aircraft fuselage stiffeners using multiobjective evolutionary optimisation

This paper proposes an optimisation process for the design of aircraft fuselage stiffeners using evolutionary optimisation. A new design problem is developed to find a layout for fuselage stiffeners (rings and stringers) such that the structural mass, compliance, and the first-mode natural frequency can be optimised, subject to structural constraints. The stiffeners are modelled as beam elements. Three multiobjective meta-heuristics are employed to solve the problem, and a comparative study of the results of these optimisers is carried out. It is found that the proposed layout synthesis problem for aircraft fuselage stiffeners leads to a set of efficient structural solutions, which can be used at the decision-making stage. It is an automated design strategy with high potential for further investigation.

Multi-Objective Optimization for Edge Device Placement and Reliable Broadcasting in 5G NFV-Based Small Cell Networks

This paper investigates the problem of locating edge devices in ultra-dense 5G network function virtualization-based small cell networks for the provisioning of reliable broadcasting services. The problem is formulated as a capacitated reliable facility location problem (CRFLP) with failure probability. The solution aims at placing the VNFs of broadcast transmissions optimally on selected edge devices in order to ensure high reliability and minimize the cost of providing broadcast services as well as the probability of loss of service requests. The CRFLP is a non-linear NP-hard problem and it is evaluated by using a multi-objective evolutionary algorithm. Two multi-objective metaheuristics are compared: the multi-objective particle swarm optimization and the nondominated sorting genetic algorithm. Results demonstrate that the proposed solution achieves high levels of reliability as well as low latency.

ND-Tree-Based Update: A Fast Algorithm for the Dynamic Nondominance Problem

In this paper, we propose a new method called ND-Tree-based update (ND-Tree) for the dynamic nondominance problem, i.e., the problem of online update of a Pareto archive composed of mutually nondominated points. It uses a new ND-Tree data structure in which each node represents a subset of points contained in a hyperrectangle defined by its local approximate ideal and nadir points. By building subsets containing points located close in the objective space and using basic properties of the local ideal and nadir points we can efficiently avoid searching many branches in the tree. ND-Tree may be used in multiobjective evolutionary algorithms and other multiobjective metaheuristics to update an archive of potentially nondominated points. We prove that the proposed algorithm has sublinear time complexity under mild assumptions. We experimentally compare ND-Tree to the simple list, Quad-tree, and M-Front methods using artificial and realistic benchmarks with up to ten objectives and show that with this new method substantial reduction of the number of point comparisons and computational time can be obtained. Furthermore, we apply the method to the nondominated sorting problem showing that it is highly competitive to some recently proposed algorithms dedicated to this problem.

Multiobjective adaptive symbiotic organisms search for truss optimization problems

This paper presents a multiobjective adaptive symbiotic organisms search (MOASOS) and its two-archive technique for solving truss optimization problems. The SOS algorithm considers the symbiotic relationship among various species, such as mutualism, commensalism, and parasitism, to live in nature. The heuristic characteristics of the mutualism phase permits the search to jump into not visited sections (named an exploration) and allows a local search of visited sections (named an exploitation) of the search region. As search progresses, a good balance between an exploration and exploitation has a greater impact on the solutions. Thus, adaptive control is now incorporated to propose MOASOS. In addition, two-archive approach is applied in MOASOS to maintain population diversity which is a major issue in multiobjective meta-heuristics.For the design problems, minimization of the truss’ mass and maximization of nodal displacement are objectives whereas elemental stress and discrete cross-sectional areas are assumed to be behaviour and side constraints respectively. The usefulness of these methods to solve complex problems is validated by five truss problems (i.e. 10-bar truss, 25-bar truss, 60-bar truss, 72-bar truss, and 942-bar truss) with discrete design variables. The results of the proposed algorithms have demonstrated that adaptive control is able to provide a better and competitive solutions when compared against the previous studies.