Complex Multi-objective Problems Research Articles

Multi-objective sparrow search algorithm: A novel algorithm for solving complex multi-objective optimisation problems

This study proposes a multi-objective sparrow search algorithm (MOSSA) based on a 2k crowding-distance entropy and the optimal strategy of the positions to solve complex multi-objective optimisation problems (MOPs) using the excellent performance of the sparrow search algorithm (SSA). A fast non-dominated sorting approach is incorporated to permit SSA to solve MOPs. To maintain the evenness and spread of the Pareto solution set obtained in each run, a 2k crowding-distance entropy is proposed to measure the diversity of the solution set. Modified formulas for updating positions and additional adaptive parameters can improve the global search ability of MOSSA. The position archive of the population is introduced to realise the optimal strategy of the positions. This strategy ensures that the positions of the population in each generation are optimal, which significantly improves the performance of MOSSA. MOSSA is compared with three well-known algorithms using a set of complex unconstrained test problems and a complex constrained engineering optimisation problem. This study explores the effect of the 2k crowding-distance entropy and crowding distance on maintaining diversity. The impact of the k in 2k crowding-distance entropy on the performance of MOSSA is analysed. The experimental results demonstrate that MOSSA exhibits competitive performance in solving complex MOPs.

Response surface methodology for design of gas turbine combustor

• Automated design space exploration with CFD quantifies combustor performance. • SST - kω turbulence model with partially premixed FGM combustion model used. • Removing blow-off design points improves response surface prediction accuracy by 57.2% • Pareto fronts from multi objective optimization used for trade-off decisions. • Six sigma DOE analysis quantifies uncertainty in combustor performance. Gas turbine combustor design is a complex multi-objective problem. In the present study, parametric design space study and optimization of a gas turbine combustor using computational fluid dynamics (CFD) simulations is presented. Baseline case validation, automated workflow setup for geometry modification, meshing, boundary condition specification, CFD solution and output parameter calculations are discussed. Response surface methodology is used to study combustor performance based on combustion efficiency, pattern factor, total pressure drop, Carbon monoxide (CO) and Nitrogen oxides (NOx) with variations in three design variables: swirl number, secondary hole diameter and dilution hole diameter. We use central composite design for design of experiments (DOE) and genetic aggregation for response surface generation. Design space refinement is carried out to identify the blow-off region and limit the search space for optimal designs to swirl number greater than 0.9. Exclusion of blow-off design points while generating the response surface resulted not only in 57.2% average reduction of root mean square error in the response surface predictions but also smoother trends away from the blow-off region. A candidate optimal design point with swirl number = 1.0, secondary hole diameter = 12.24 mm and dilution hole diameter = 15.26 mm is chosen using multi objective genetic algorithm on the response surface. Finally, uncertainty quantification with six sigma DOE analysis quantifies the confidence intervals for performance parameters based on the variations in geometric design variables. This preliminary design methodology can be used to improve existing combustors and guide the design of novel combustor concepts.

The Combination of Internet of Things Technology Based on Probability Model Network and Mass Education

With the continuous development of the Internet of things, educational informatization has become a hot spot in the application of education. Internet of things technology, combined with various subject fields of education, can better achieve subject teaching objectives and teaching assistance. In the multimode teaching optimization model, weight distribution is a complex multiobjective decision-making problem. In this paper, a Bayesian network based on probability model is proposed, which is combined with the large entropy criterion to determine the comprehensive weight. The combination of Bayesian network and Bayesian statistics can make full use of the information of domain knowledge and sample data. Bayesian network uses arc to represent the dependence between variables and probability distribution table to represent the strength of dependence. It organically combines prior information with sample knowledge to promote the integration of prior knowledge and data, which is particularly effective when sample data is sparse or difficult to obtain. Bayesian network is used to associate objective attributes and influencing factors to self-study the target weight. By grasping the characteristics of information technology and the nature of university citizenship curriculum, this paper further analyzes the internal relationship between them, promotes the deep integration of the two, and improves the effectiveness of university citizenship curriculum teaching. By grasping the characteristics of information technology and the nature of the school civics curriculum, we promote a deeper integration of the two. It is my education that is more advanced.

A dual-operator strategy for a multiobjective evolutionary algorithm based on decomposition

Evolutionary Algorithms (EAs) are a kind of population based on optimization method by adopting survival of the fittest rules. The performance of EAs can be greatly improved by appropriate genetic operators, so how to select an appropriate genetic operator is a key issue. In order to solve this problem, some genetic operators are mixed to use with a certain probability to improve their spatial search capabilities. However, it is difficult to solve most complex multi-objective problems (MOPs) based on a certain probability value. In this paper, under the concept of co-evolution and Duty Ratio, we built a genetic operator based on Differential Evolution (DE) and Simulated Binary Crossover (SBX), and the adjustment of Duty Ratio parameter is learned based on the historical used times of DE and SBX. Under the framework of Multi-objective Evolutionary Algorithm Based on Decomposition (MOEA/D), we propose our dual-operator strategy (DOS) based on learning strategy, namely MOEA/D-DOS. We compared MOEA/D-DOS with other six versions of multi-objective EAs, and the final result showed that MOEA/D-DOS has achieved the better results.

Optimality and duality for complex multi-objective programming

<p style='text-indent:20px;'>We consider a complex multi-objective programming problem (CMP). In order to establish the optimality conditions of problem (CMP), we introduce several properties of optimal efficient solutions and scalarization techniques. Furthermore, a certain parametric dual model is discussed, and their duality theorems are proved.</p>

A multi-objective cross-entropy optimization algorithm and its application in high-speed train lateral control

In this paper a novel improved multi-objective cross-entropy optimization (MOCEO+) algorithm is proposed. We seek to provide a low-cost, fast and effective solution for complex multi-objective problems. Firstly, a population size segmentation mechanism is adopted to reduce the computational cost. This also helps to increase the exploration ability of the algorithm to the optimal Pareto front and the convergence rate is accelerated as well. Then, an individual selection mechanism based on hyper volume (HV) sorting strategy is proposed to retain the elite individuals in the evolution process. Finally, a recombination mechanism is provided to increase diversity of the population individuals and to avoid local optimum. The test results of 2-, 3-, 5-objective WFG test functions indicate that MOCEO+ offers better performance and faster convergence compared with six optimization algorithms. In order to verify feasibility and effectiveness of the MOCEO+ in engineering practice, it is applied to the parameter optimization of the repetitive learning controller for the high-speed train lateral suspension system. The simulation demonstrates that the suspension system optimized by MOCEO+ has better lateral stability compared with three other algorithms. Particularly, the lateral vibration is significantly decreased in the sensitive frequency range [1,2] Hz of human body.

An improved multi-objective gravitational search algorithm

Multi-objective search algorithm is a common optimization tool to deal with complex multi-objective problems, such as Multiple Objectives Particle Swarm Optimization (MOPSO) and Non dominated Sorting Genetic Algorithm-II (NSGA-II). Gravitational Search Algorithm (GSA) is a new heuristic evolutionary algorithm, which is based on the Newtonian gravity and the laws of motion to search optimal solutions. Some of agents have bigger mass, so other smaller mass agents are affected easily to fall into local optimization. In order to improve the search ability of the algorithm, this paper proposes an Improved Multi-Objective Gravitational Search Algorithm (IMOGSA). The proposed method uses the fast non-dominated sorting strategy and crowding distance of NSGA-II, and uses Sine Cosine Algorithm (SCA). Using strategy of NSGA-II is to reduce the complexity of the algorithm, in addition, using SCA is to improve the convergence and distribution of IMOGSA by improving the weight of acceleration. Finally, the proposed method has been compared with other well-known heuristic search methods by using some benchmark functions.

Overview of multiobjective particle swarm optimization algorithm

In the real world, the development model of optimization problems tends to be diversified and large scale. Therefore, optimization technologies are facing severe challenges in terms of nonlinearity, multi-dimensionality, intelligence, and dynamic programming. Multiobjective optimization problems have multiple conflicting objective functions, so the unique optimal solution is impossible to obtain when optimizing, and multiple objective values must be considered to obtain a compromise optimal solution set. When traditional optimization methods treat complex multiobjective problems, such as those with nonlinearity and high dimensionality, good optimization results are difficult to ensure or even infeasible. The evolutionary algorithm is a method that simulates the natural evolution process and is optimized via group search technology. It has the characteristics of strong robustness and high search efficiency. Inspired by the foraging behavior of bird flocks in nature, the particle swarm optimization algorithm has a simple implementation, fast convergence, and unique updating mechanism. With its outstanding performance in the single-objective optimization process, particle swarm optimization has been successfully extended to multiobjective optimization, and many breakthrough research achievements have been made in combinatorial optimization and numerical optimization. Consequently, the multiobjective particle swarm algorithm has far-reaching research value in theoretical research and engineering practice. As a meta-heuristic optimization algorithm, particle swarm optimization is widely used to solve multiobjective optimization problems. This paper summarized the advanced strategies of the multiobjective particle swarm optimization algorithm. First, the basic theories of multiobjective optimization and particle swarm optimization were reviewed. Second, the difficult problems involving multiobjective optimization were analyzed. Third, the achievements in recent years were summarized from five aspects: optimal particle selection strategies, diversity maintenance mechanisms, convergence improvement measures, coordination methods between diversity and convergence, and improvement schemes of iterative formulas, parametric and topological structure. Finally, the problems to be solved and the future research direction of the multiobjective particle swarm optimization algorithm were presented.

Multi-objective steady-state optimization for a complex bioprocess in glycerol metabolism

This paper addresses the multi-objective steady-state optimization of a complex nonlinear system in glycerol metabolism. In the bioconversion system, we consider some mechanisms including the regulation for dha regulon, enzyme-catalytic kinetics, the inhibition of intracellular 3-hydroxypropionaldehyde (3-HPA), and so on. Firstly, we propose several new multi-objective steady-state optimization problems. These problems can simultaneously optimize any two of the following objectives: (1) minimization of the intracellular 3-HPA concentration; (2) maximization of the production rate of extracellular 1,3-propanediol (1,3-PDO); (3) maximization of the conversion rate of extracellular glycerol to extracellular 1,3-PDO; (4) maximization of the conversion rate of extracellular glycerol. Then a hybrid optimization method is proposed to solve the presented complex multi-objective problems. This optimization method couples a deterministic interior point approach and a stochastic genetic algorithm in the framework of normal-boundary intersection (NBI) method. After solving the proposed multi-objective problems of the addressed bioconversion system, we finally obtain their approximate Pareto optimal sets. The analysis for the attained optimization results is given. And a comparative study is also presented.

Energy and SLA-driven MapReduce Job Scheduling Framework for Cloud-based Cyber-Physical Systems

Energy consumption minimization of cloud data centers (DCs) has attracted much attention from the research community in the recent years; particularly due to the increasing dependence of emerging Cyber-Physical Systems on them. An effective way to improve the energy efficiency of DCs is by using efficient job scheduling strategies. However, the most challenging issue in selection of efficient job scheduling strategy is to ensure service-level agreement (SLA) bindings of the scheduled tasks. Hence, an energy-aware and SLA-driven job scheduling framework based on MapReduce is presented in this article. The primary aim of the proposed framework is to explore task-to-slot/container mapping problem as a special case of energy-aware scheduling in deadline-constrained scenario. Thus, this problem can be viewed as a complex multi-objective problem comprised of different constraints. To address this problem efficiently, it is segregated into three major subproblems (SPs), namely, deadline segregation, map and reduce phase energy-aware scheduling. These SPs are individually formulated using Integer Linear Programming. To solve these SPs effectively, heuristics based on Greedy strategy along with classical Hungarian algorithm for serial and serial-parallel systems are used. Moreover, the proposed scheme also explores the potential of splitting Map/Reduce phase(s) into multiple stages to achieve higher energy reductions. This is achieved by leveraging the concepts of classical Greedy approach and priority queues. The proposed scheme has been validated using real-time data traces acquired from OpenCloud. Moreover, the performance of the proposed scheme is compared with the existing schemes using different evaluation metrics, namely, number of stages, total energy consumption, total makespan, and SLA violated. The results obtained prove the efficacy of the proposed scheme in comparison to the other schemes under different workload scenarios.

Sustainable supply chain management for perishable products in emerging markets: An integrated location-inventory-routing model

The demand for perishable products in emerging markets has been increasing. However, the perishability of products brings tremendous challenges for firms to build a sustainable supply chain. In this paper, we propose an integrated model of location-inventory-routing for perishable products, considering the factors of carbon emissions and product freshness. First, the economic cost, carbon emission levels, and freshness of the perishable products are analyzed. Second, with the goals of achieving the lowest economic cost and carbon emissions and the highest product freshness, a multi-objective planning model is developed, and constraints are established based on the actual location-inventory-routing situation. Third, the YALMIP toolbox is used to solve the model, and the optimal solution to this complex multi-objective problem is obtained. Finally, the effectiveness and feasibility of the proposed method are verified by the case study, as well as the sensitivity vehicle speed to the results. It is found that the integrated model proposed in this paper is able to significantly improve the efficiency of perishable goods supply chain management from the perspective of global optimization, and vehicle speed is able to significantly affect economic costs and carbon emissions.

An AI-Powered System for Residential Demand Response

Recent studies show that energy consumption of buildings has dramatically increased over the last decade, accounting for more than 35% of global energy use. However, with proper operation, significant energy savings can be achieved. Demand response is envisioned as a key enabler of this operation enhancement, as it may contribute to the reduction of demand peaks and maximization of renewable energy exploitation while mitigating potential problems with grid stability. In this article, a system based on artificial intelligence that solves the complex multi-objective problem to bring demand response programs to the residential sector is proposed. Through the application of novel machine learning-based algorithms, a unique control loop is developed to help dwellers determine how and when to use their appliances. The feasibility and validity of the proposed system has been demonstrated in a real-world neighbourhood where a notable reduction and shift of electricity demand peaks has been achieved. Concretely, in accordance with extreme changes in the energy prices, the users have demonstrated the ability to shift their demand to periods with lower prices as well as reducing power consumption during periods with higher prices, thus fully translating the demand peak in time.

A Web Server for Designing Molecular Switches Composed of Two Interacting RNAs.

The programmability of RNA–RNA interactions through intermolecular base-pairing has been successfully exploited to design a variety of RNA devices that artificially regulate gene expression. An in silico design for interacting structured RNA sequences that satisfies multiple design criteria becomes a complex multi-objective problem. Although multi-objective optimization is a powerful technique that explores a vast solution space without empirical weights between design objectives, to date, no web service for multi-objective design of RNA switches that utilizes RNA–RNA interaction has been proposed. We developed a web server, which is based on a multi-objective design algorithm called MODENA, to design two interacting RNAs that form a complex in silico. By predicting the secondary structures with RactIP during the design process, we can design RNAs that form a joint secondary structure with an external pseudoknot. The energy barrier upon the complex formation is modeled by an interaction seed that is optimized in the design algorithm. We benchmarked the RNA switch design approaches (MODENA+RactIP and MODENA+RNAcofold) for the target structures based on natural RNA-RNA interactions. As a result, MODENA+RactIP showed high design performance for the benchmark datasets.

MOGBO: A new Multiobjective Gradient-Based Optimizer for real-world structural optimization problems

To handle the multiobjective optimization problems of truss-bar design, this paper introduces a new metaheuristic multiobjective optimization algorithm. The proposed algorithm is based on a recently reported single objective version of the gradient-based optimizer (GBO) inspired by the gradients of Newton’s equations. The proposed algorithm is called as multiobjective gradient-based optimizer (MOGBO), in which two operators, such as local escaping operator and gradient search rule, and few vector sets are utilized in the search phase and the elitist non-dominated sorting mechanism is used for agent sorting to find Pareto optimal solutions. The proposed MOGBO is a posteriori method, and the traditional crowding distance mechanism is employed to confirm the coverage of the best solutions for the objectives of the given problem. The performance of the proposed MOGBO algorithm is verified and validated on different test cases, including 15 unconstraint benchmark test suites and eight constraint multiobjective truss bar design problems. To prove the superiority of the MOGBO algorithm, the performance is compared with state-of-the-art algorithms, such as multiobjective ant lion optimization (MOALO), multiobjective water cycle algorithm (MOWCA), multiobjective colliding bodies optimization (MOCBO), and non-dominated sorting gray wolf optimizer (NSGWO) in terms of metrics, such as hyper-volume, coverage, inverted generational distance, pure diversity, Spacing, Spread, coverage Pareto front, diversity maintenance, generational distance, and runtime. The solutions obtained by the proposed MOGBO algorithm is highly accurate and requires less runtime than the other selected algorithms. The obtained results also show the efficiency of the MOGBO in solving most of all the complex multiobjective problems. This research will be further backed up with external guidance for the future research at https://premkumarmanoharan.wixsite.com/mysite.

Improving the Performance of Multiobjective Genetic Algorithms: An Elitism-Based Approach

Today, many complex multiobjective problems are dealt with using genetic algorithms (GAs). They apply the evolution mechanism of a natural population to a “numerical” population of solutions to optimize a fitness function. GA implementations must find a compromise between the breath of the search (to avoid being trapped into local minima) and its depth (to prevent a rough approximation of the optimal solution). Most algorithms use “elitism”, which allows preserving some of the current best solutions in the successive generations. If the initial population is randomly selected, as in many GA packages, the elite may concentrate in a limited part of the Pareto frontier preventing its complete spanning. A full view of the frontier is possible if one, first, solves the single-objective problems that correspond to the extremes of the Pareto boundary, and then uses such solutions as elite members of the initial population. The paper compares this approach with more conventional initializations by using some classical tests with a variable number of objectives and known analytical solutions. Then we show the results of the proposed algorithm in the optimization of a real-world system, contrasting its performances with those of standard packages.

A quantum class topper optimization algorithm to solve combined emission economic dispatch problem

A combined emission and economic dispatch problem is referred as a complex multi-objective problem related to power system. In this article, an hybridized version of class topper optimization known as quantum class topper optimization is proposed to solve this problem. In quantum class topper optimization, quantum mechanism is used to enhance the searching ability of the proposed algorithm. The exploration, exploitation and convergence behavior of quantum class topper optimization is validated using benchmark functions. Later, four test cases on combined emission and economic dispatch are used to test the effectiveness of quantum class topper optimization. These four tests prove that the proposed optimization algorithm is effective to solve this real time optimization problem.

Leader recommend operators selection strategy for a multiobjective evolutionary algorithm based on decomposition

The decomposition-based multi-objective evolutionary algorithm (MOEA/D) shows strong performance in solving complex multi-objective problems (MOPs), wherein evolutionary operators have great influence on the search ability. Appropriate operators can greatly improve the performance of MOEA/D. However, one omnipotent operator usually cannot handle all different MOPs very well. According to the characteristics of the problems, the operators that adapt to the problems are also different. This paper proposes an adaptive operator selection strategy called Leader Recommend Operator Selection (LROS). We construct an operator pool consisting of Simulated Binary Crossover (SBX) and three operators of Differential Evolution (DE). Meanwhile, we divide the entire evolutionary process into several stages, and each stage is divided into Part 1 and Part 2. In Part 1 of each stage, we use a subset of individuals to test the performance of each operator in the operator pool and choose the best performance. In Part 2, we adopt the best performing operator selected in Part 1 to generate offspring, meanwhile we verify the actual quality of these offspring to decide in the next stage whether to continue using this operator to generate offspring or to choose a more suitable operator. Experimental results demonstrate the effectiveness of LROS.

Study on the two-sides matching between multiple rovers and multiple orbiters in Mars relay communications

In Mars relay communications, if multiple rovers and multiple orbiters are visible with each other at the same time in certain contact, there are not only issues concerned with the multiple rovers' access to single orbiter, but also the issues concerned with the optimal access orbiter selection for each rover, which is a complex multi-objective decision-making problem relating to the resource allocation optimizations in deep-space networks. In this paper, the two-sides matching between multiple rovers and multiple orbiters in Mars relay communications is proposed based on the access preferences, taking the two-sides combined fitness of preferences and the single-side evaluation equilibrium as the optimization objectives, which utilizes the parallel capsule operations architecture encapsulated with several one-to-many two-sides matching algorithms to obtain stable multiple access matching results. Simulation results show that, our method performs better than the CCSDS Proximity-1 protocols, and could achieve the effective utilization of deep space communication network resources.

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.

DEaf-MOPS/D: An Improved Differential Evolution Algorithm for Solving Complex Multi-objective Portfolio Selection Problems Based on Decomposition

DEaf-MOPS/D: An Improved Differential Evolution Algorithm for Solving Complex Multi-objective Portfolio Selection Problems Based on Decomposition