Showing papers on "Multi-objective optimization published in 2016"
TL;DR: The results of DA and BDA prove that the proposed algorithms are able to improve the initial random population for a given problem, converge towards the global optimum, and provide very competitive results compared to other well-known algorithms in the literature.
Abstract: A novel swarm intelligence optimization technique is proposed called dragonfly algorithm (DA). The main inspiration of the DA algorithm originates from the static and dynamic swarming behaviours of dragonflies in nature. Two essential phases of optimization, exploration and exploitation, are designed by modelling the social interaction of dragonflies in navigating, searching for foods, and avoiding enemies when swarming dynamically or statistically. The paper also considers the proposal of binary and multi-objective versions of DA called binary DA (BDA) and multi-objective DA (MODA), respectively. The proposed algorithms are benchmarked by several mathematical test functions and one real case study qualitatively and quantitatively. The results of DA and BDA prove that the proposed algorithms are able to improve the initial random population for a given problem, converge towards the global optimum, and provide very competitive results compared to other well-known algorithms in the literature. The results of MODA also show that this algorithm tends to find very accurate approximations of Pareto optimal solutions with high uniform distribution for multi-objective problems. The set of designs obtained for the submarine propeller design problem demonstrate the merits of MODA in solving challenging real problems with unknown true Pareto optimal front as well. Note that the source codes of the DA, BDA, and MODA algorithms are publicly available at http://www.alimirjalili.com/DA.html.
1,897 citations
TL;DR: In the proposed algorithm, a scalarization approach, termed angle-penalized distance, is adopted to balance convergence and diversity of the solutions in the high-dimensional objective space, and reference vectors are effective and cost-efficient for preference articulation, which is particularly desirable for many-objective optimization.
Abstract: In evolutionary multiobjective optimization, maintaining a good balance between convergence and diversity is particularly crucial to the performance of the evolutionary algorithms (EAs). In addition, it becomes increasingly important to incorporate user preferences because it will be less likely to achieve a representative subset of the Pareto-optimal solutions using a limited population size as the number of objectives increases. This paper proposes a reference vector-guided EA for many-objective optimization. The reference vectors can be used not only to decompose the original multiobjective optimization problem into a number of single-objective subproblems, but also to elucidate user preferences to target a preferred subset of the whole Pareto front (PF). In the proposed algorithm, a scalarization approach, termed angle-penalized distance, is adopted to balance convergence and diversity of the solutions in the high-dimensional objective space. An adaptation strategy is proposed to dynamically adjust the distribution of the reference vectors according to the scales of the objective functions. Our experimental results on a variety of benchmark test problems show that the proposed algorithm is highly competitive in comparison with five state-of-the-art EAs for many-objective optimization. In addition, we show that reference vectors are effective and cost-efficient for preference articulation, which is particularly desirable for many-objective optimization. Furthermore, a reference vector regeneration strategy is proposed for handling irregular PFs. Finally, the proposed algorithm is extended for solving constrained many-objective optimization problems.
1,020 citations
TL;DR: A novel multi-objective algorithm called Multi-Objective Grey Wolf Optimizer (MOGWO) is proposed in order to optimize problems with multiple objectives for the first time.
Abstract: Due to the novelty of the Grey Wolf Optimizer (GWO), there is no study in the literature to design a multi-objective version of this algorithm. This paper proposes a Multi-Objective Grey Wolf Optimizer (MOGWO) in order to optimize problems with multiple objectives for the first time. A fixed-sized external archive is integrated to the GWO for saving and retrieving the Pareto optimal solutions. This archive is then employed to define the social hierarchy and simulate the hunting behavior of grey wolves in multi-objective search spaces. The proposed method is tested on 10 multi-objective benchmark problems and compared with two well-known meta-heuristics: Multi-Objective Evolutionary Algorithm Based on Decomposition (MOEA/D) and Multi-Objective Particle Swarm Optimization (MOPSO). The qualitative and quantitative results show that the proposed algorithm is able to provide very competitive results and outperforms other algorithms. Note that the source codes of MOGWO are publicly available at http://www.alimirjalili.com/GWO.html. A novel multi-objective algorithm called Multi-objective Grey Wolf Optimizer is proposed.MOGWO is benchmarked on 10 challenging multi-objective test problems.The quantitative results show the superior convergence and coverage of MOGWO.The coverage ability of MOGWO is confirmed by the qualitative results as well.
967 citations
20 Jul 2016
TL;DR: TPOT as mentioned in this paper is an open source Tree-based Pipeline Optimization Tool (TPOT) in Python that can design machine learning pipelines that provide a significant improvement over a basic machine learning analysis while requiring little to no input nor prior knowledge from the user.
Abstract: As the field of data science continues to grow, there will be an ever-increasing demand for tools that make machine learning accessible to non-experts. In this paper, we introduce the concept of tree-based pipeline optimization for automating one of the most tedious parts of machine learning--pipeline design. We implement an open source Tree-based Pipeline Optimization Tool (TPOT) in Python and demonstrate its effectiveness on a series of simulated and real-world benchmark data sets. In particular, we show that TPOT can design machine learning pipelines that provide a significant improvement over a basic machine learning analysis while requiring little to no input nor prior knowledge from the user. We also address the tendency for TPOT to design overly complex pipelines by integrating Pareto optimization, which produces compact pipelines without sacrificing classification accuracy. As such, this work represents an important step toward fully automating machine learning pipeline design.
357 citations
TL;DR: The idea is implemented to enhance two well-performing decomposition-based algorithms, i.e., MOEA, based on decomposition and ensemble fitness ranking, and they are also very competitive against other existing algorithms for solving many-objective optimization problems.
Abstract: The decomposition-based multiobjective evolutionary algorithms (MOEAs) generally make use of aggregation functions to decompose a multiobjective optimization problem into multiple single-objective optimization problems. However, due to the nature of contour lines for the adopted aggregation functions, they usually fail to preserve the diversity in high-dimensional objective space even by using diverse weight vectors. To address this problem, we propose to maintain the desired diversity of solutions in their evolutionary process explicitly by exploiting the perpendicular distance from the solution to the weight vector in the objective space, which achieves better balance between convergence and diversity in many-objective optimization. The idea is implemented to enhance two well-performing decomposition-based algorithms, i.e., MOEA, based on decomposition and ensemble fitness ranking. The two enhanced algorithms are compared to several state-of-the-art algorithms and a series of comparative experiments are conducted on a number of test problems from two well-known test suites. The experimental results show that the two proposed algorithms are generally more effective than their predecessors in balancing convergence and diversity, and they are also very competitive against other existing algorithms for solving many-objective optimization problems.
327 citations
TL;DR: In this paper, a multi-objective particle swarm optimization (MOPSO) algorithm is coupled with EnergyPlus building energy simulation software to find a set of non-dominated solutions to enhance the building energy performance.
326 citations
TL;DR: An evolutionary multi-objective optimization (EMO)-based algorithm is proposed to solve this workflow scheduling problem on an infrastructure as a service (IaaS) platform and can achieve significantly better solutions than existing state-of-the-art QoS optimization scheduling algorithms in most cases.
Abstract: Cloud computing provides promising platforms for executing large applications with enormous computational resources to offer on demand. In a Cloud model, users are charged based on their usage of resources and the required quality of service (QoS) specifications. Although there are many existing workflow scheduling algorithms in traditional distributed or heterogeneous computing environments, they have difficulties in being directly applied to the Cloud environments since Cloud differs from traditional heterogeneous environments by its service-based resource managing method and pay-per-use pricing strategies. In this paper, we highlight such difficulties, and model the workflow scheduling problem which optimizes both makespan and cost as a Multi-objective Optimization Problem (MOP) for the Cloud environments. We propose an evolutionary multi-objective optimization (EMO)-based algorithm to solve this workflow scheduling problem on an infrastructure as a service (IaaS) platform. Novel schemes for problem-specific encoding and population initialization, fitness evaluation and genetic operators are proposed in this algorithm. Extensive experiments on real world workflows and randomly generated workflows show that the schedules produced by our evolutionary algorithm present more stability on most of the workflows with the instance-based IaaS computing and pricing models. The results also show that our algorithm can achieve significantly better solutions than existing state-of-the-art QoS optimization scheduling algorithms in most cases. The conducted experiments are based on the on-demand instance types of Amazon EC2; however, the proposed algorithm are easy to be extended to the resources and pricing models of other IaaS services.
321 citations
TL;DR: COCO as discussed by the authors is an open source platform for comparing continuous optimizers in a black-box setting, which aims at automatizing the tedious and repetitive task of benchmarking numerical optimization algorithms to the greatest possible extent.
Abstract: We introduce COCO, an open source platform for Comparing Continuous Optimizers in a black-box setting. COCO aims at automatizing the tedious and repetitive task of benchmarking numerical optimization algorithms to the greatest possible extent. The platform and the underlying methodology allow to benchmark in the same framework deterministic and stochastic solvers for both single and multiobjective optimization. We present the rationales behind the (decade-long) development of the platform as a general proposition for guidelines towards better benchmarking. We detail underlying fundamental concepts of COCO such as the definition of a problem as a function instance, the underlying idea of instances, the use of target values, and runtime defined by the number of function calls as the central performance measure. Finally, we give a quick overview of the basic code structure and the currently available test suites.
300 citations
TL;DR: Numerical results not only demonstrate the close-to-optimal performance of the proposed suboptimal schemes but unveil an interesting tradeoff among the considered conflicting system design objectives as well.
Abstract: In this paper, we study resource allocation for multiuser multiple-input–single-output secondary communication systems with multiple system design objectives. We consider cognitive radio (CR) networks where the secondary receivers are able to harvest energy from the radio frequency when they are idle. The secondary system provides simultaneous wireless power and secure information transfer to the secondary receivers. We propose a multiobjective optimization framework for the design of a Pareto-optimal resource allocation algorithm based on the weighted Tchebycheff approach. In particular, the algorithm design incorporates three important system design objectives: total transmit power minimization, energy harvesting efficiency maximization, and interference-power-leakage-to-transmit-power ratio minimization. The proposed framework takes into account a quality-of-service (QoS) requirement regarding communication secrecy in the secondary system and the imperfection of the channel state information (CSI) of potential eavesdroppers (idle secondary receivers and primary receivers) at the secondary transmitter. The proposed framework includes total harvested power maximization and interference power leakage minimization as special cases. The adopted multiobjective optimization problem is nonconvex and is recast as a convex optimization problem via semidefinite programming (SDP) relaxation. It is shown that the global optimal solution of the original problem can be constructed by exploiting both the primal and the dual optimal solutions of the SDP-relaxed problem. Moreover, two suboptimal resource allocation schemes for the case when the solution of the dual problem is unavailable for constructing the optimal solution are proposed. Numerical results not only demonstrate the close-to-optimal performance of the proposed suboptimal schemes but unveil an interesting tradeoff among the considered conflicting system design objectives as well.
251 citations
TL;DR: A bi-criterion evolution (BCE) framework of the PC and NPC, which attempts to make use of their strengths and compensates for each other's weaknesses, making it applicable for any non-Pareto-based algorithm.
Abstract: It is known that Pareto dominance has its own weaknesses as the selection criterion in evolutionary multiobjective optimization. Algorithms based on Pareto criterion (PC) can suffer from problems such as slow convergence to the optimal front and inferior performance on problems with many objectives. Non-Pareto criterion (NPC), such as decomposition-based criterion and indicator-based criterion, has already shown promising results in this regard, but its high selection pressure may lead to the algorithm to prefer some specific areas of the problem’s Pareto front, especially when the front is highly irregular. In this paper, we propose a bi-criterion evolution (BCE) framework of the PC and NPC, which attempts to make use of their strengths and compensates for each other’s weaknesses. The proposed framework consists of two parts: PC evolution and NPC evolution. The two parts work collaboratively, with an abundant exchange of information to facilitate each other’s evolution. Specifically, the NPC evolution leads the PC evolution forward and the PC evolution compensates the possible diversity loss of the NPC evolution. The proposed framework keeps the freedom on the implementation of the NPC evolution part, thus making it applicable for any non-Pareto-based algorithm. In the PC evolution, two operations, population maintenance and individual exploration, are presented. The former is to maintain a set of representative nondominated individuals and the latter is to explore some promising areas that are undeveloped (or not well-developed) in the NPC evolution. Experimental results have shown the effectiveness of the proposed framework. The BCE works well on seven groups of 42 test problems with various characteristics, including those in which Pareto-based algorithms or non-Pareto-based algorithms struggle.
231 citations
TL;DR: Performance of seven commonly-used multi-objective evolutionary optimization algorithms in solving the design problem of a nearly zero energy building (nZEB) where more than 1.610 solutions would be possible is compared.
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TL;DR: This paper implements an open source Tree-based Pipeline Optimization Tool (TPOT) in Python and shows that TPOT can design machine learning pipelines that provide a significant improvement over a basic machine learning analysis while requiring little to no input nor prior knowledge from the user.
Abstract: As the field of data science continues to grow, there will be an ever-increasing demand for tools that make machine learning accessible to non-experts. In this paper, we introduce the concept of tree-based pipeline optimization for automating one of the most tedious parts of machine learning---pipeline design. We implement an open source Tree-based Pipeline Optimization Tool (TPOT) in Python and demonstrate its effectiveness on a series of simulated and real-world benchmark data sets. In particular, we show that TPOT can design machine learning pipelines that provide a significant improvement over a basic machine learning analysis while requiring little to no input nor prior knowledge from the user. We also address the tendency for TPOT to design overly complex pipelines by integrating Pareto optimization, which produces compact pipelines without sacrificing classification accuracy. As such, this work represents an important step toward fully automating machine learning pipeline design.
TL;DR: This paper develops a mixed integer linear multi-objective optimization model and develops a constructive heuristic for fast trade-off analysis between makespan and energy consumption, which can serve as a visual aid for production and sales planners to consider energy consumption explicitly in making quick decisions while negotiating with customers on due dates.
TL;DR: This paper analyzes a family of frequently used scalarizing methods, the Lp methods, and shows that the p value is crucial to balance the selective pressure toward the Pareto optimal and the algorithm robustness to Pare to optimal front (PF) geometries.
Abstract: Decomposition-based algorithms have become increasingly popular for evolutionary multiobjective optimization. However, the effect of scalarizing methods used in these algorithms is still far from being well understood. This paper analyzes a family of frequently used scalarizing methods, the ${L} _{ {p}}$ methods, and shows that the ${p}$ value is crucial to balance the selective pressure toward the Pareto optimal and the algorithm robustness to Pareto optimal front (PF) geometries. It demonstrates that an ${L} _{ {p}}$ method that can maximize the search ability of a decomposition-based algorithm exists and guarantees that, given some weight, any solution along the PF can be found. Moreover, a simple yet effective method called Pareto adaptive scalarizing (PaS) approximation is proposed to approximate the optimal ${p}$ value. In order to demonstrate the effectiveness of PaS, we incorporate PaS into a state-of-the-art decomposition-based algorithm, i.e., multiobjective evolutionary algorithm based on decomposition (MOEA/D), and compare the resultant MOEA/D-PaS with some other MOEA/D variants on a set of problems with different PF geometries and up to seven conflicting objectives. Experimental results demonstrate that the PaS is effective.
TL;DR: This approach exploits the transfer learning technique as a tool to generate an effective initial population pool via reusing past experience to speed up the evolutionary process, and at the same time any population-based multiobjective algorithms can benefit from this integration without any extensive modifications.
Abstract: One of the major distinguishing features of the dynamic multiobjective optimization problems (DMOPs) is the optimization objectives will change over time, thus tracking the varying Pareto-optimal front becomes a challenge. One of the promising solutions is reusing the "experiences" to construct a prediction model via statistical machine learning approaches. However most of the existing methods ignore the non-independent and identically distributed nature of data used to construct the prediction model. In this paper, we propose an algorithmic framework, called Tr-DMOEA, which integrates transfer learning and population-based evolutionary algorithm for solving the DMOPs. This approach takes the transfer learning method as a tool to help reuse the past experience for speeding up the evolutionary process, and at the same time, any population based multiobjective algorithms can benefit from this integration without any extensive modifications. To verify this, we incorporate the proposed approach into the development of three well-known algorithms, nondominated sorting genetic algorithm II (NSGA-II), multiobjective particle swarm optimization (MOPSO), and the regularity model-based multiobjective estimation of distribution algorithm (RM-MEDA), and then employ twelve benchmark functions to test these algorithms as well as compare with some chosen state-of-the-art designs. The experimental results confirm the effectiveness of the proposed method through exploiting machine learning technology.
TL;DR: It is demonstrated that the replacement neighborhood size is critical for population diversity and convergence, and an approach for adjusting this size dynamically is developed.
Abstract: Multiobjective evolutionary algorithms based on decomposition (MOEA/D) decompose a multiobjective optimization problem into a set of simple optimization subproblems and solve them in a collaborative manner. A replacement scheme, which assigns a new solution to a subproblem, plays a key role in balancing diversity and convergence in MOEA/D. This paper proposes a global replacement scheme which assigns a new solution to its most suitable subproblems. We demonstrate that the replacement neighborhood size is critical for population diversity and convergence, and develop an approach for adjusting this size dynamically. A steady-state algorithm and a generational one with this approach have been designed and experimentally studied. The experimental results on a number of test problems have shown that the proposed algorithms have some advantages.
TL;DR: An adaptive method aiming at spatial-temporal efficiency in a heterogeneous cloud environment based on an optimized Kernel-based Extreme Learning Machine algorithm is presented for faster forecast of job execution duration and space occupation and achieves 26.6% improvement over the original scheme.
Abstract: A heterogeneous cloud system, for example, a Hadoop 2.6.0 platform, provides distributed but cohesive services with rich features on large-scale management, reliability, and error tolerance. As big data processing is concerned, newly built cloud clusters meet the challenges of performance optimization focusing on faster task execution and more efficient usage of computing resources. Presently proposed approaches concentrate on temporal improvement, that is, shortening MapReduce time, but seldom focus on storage occupation; however, unbalanced cloud storage strategies could exhaust those nodes with heavy MapReduce cycles and further challenge the security and stability of the entire cluster. In this paper, an adaptive method is presented aiming at spatial-temporal efficiency in a heterogeneous cloud environment. A prediction model based on an optimized Kernel-based Extreme Learning Machine algorithm is proposed for faster forecast of job execution duration and space occupation, which consequently facilitates the process of task scheduling through a multi-objective algorithm called time and space optimized NSGA-II TS-NSGA-II. Experiment results have shown that compared with the original load-balancing scheme, our approach can save approximate 47-55i¾źs averagely on each task execution. Simultaneously, 1.254i¾ź of differences on hard disk occupation were made among all scheduled reducers, which achieves 26.6% improvement over the original scheme. Copyright © 2016 John Wiley & Sons, Ltd.
TL;DR: In the proposed algorithm, a two-phase strategy (TP) is employed to divide the whole optimization procedure into two phases and a new niche scheme is introduced into the improved MOEA/D to guide the selection of mating parents to avoid producing duplicate solutions.
Abstract: The multiobjective evolutionary algorithm based on decomposition (MOEA/D) has been shown to be very efficient in solving multiobjective optimization problems (MOPs). In practice, the Pareto-optimal front (POF) of many MOPs has complex characteristics. For example, the POF may have a long tail and sharp peak and disconnected regions, which significantly degrades the performance of MOEA/D. This paper proposes an improved MOEA/D for handling such kind of complex problems. In the proposed algorithm, a two-phase strategy (TP) is employed to divide the whole optimization procedure into two phases. Based on the crowdedness of solutions found in the first phase, the algorithm decides whether or not to delicate computational resources to handle unsolved subproblems in the second phase. Besides, a new niche scheme is introduced into the improved MOEA/D to guide the selection of mating parents to avoid producing duplicate solutions, which is very helpful for maintaining the population diversity when the POF of the MOP being optimized is discontinuous. The performance of the proposed algorithm is investigated on some existing benchmark and newly designed MOPs with complex POF shapes in comparison with several MOEA/D variants and other approaches. The experimental results show that the proposed algorithm produces promising performance on these complex problems.
TL;DR: Numerical computations show that the energy-saving module of the extended NEH-Insertion Procedure in MONEH and MMOIG significantly helps to improve the discovered front and the proposed algorithms perform more effectively than other tested high-performing meta-heurisitics in searching for non-dominated solutions.
TL;DR: A new dynamic MOEA using Kalman filter (KF) predictions in decision space is proposed to solve the aforementioned problems and is capable of significantly improving the dynamic optimization performance.
Abstract: Evolutionary algorithms are effective in solving static multiobjective optimization problems resulting in the emergence of a number of state-of-the-art multiobjective evolutionary algorithms (MOEAs). Nevertheless, the interest in applying them to solve dynamic multiobjective optimization problems has only been tepid. Benchmark problems, appropriate performance metrics, as well as efficient algorithms are required to further the research in this field. One or more objectives may change with time in dynamic optimization problems. The optimization algorithm must be able to track the moving optima efficiently. A prediction model can learn the patterns from past experience and predict future changes. In this paper, a new dynamic MOEA using Kalman filter (KF) predictions in decision space is proposed to solve the aforementioned problems. The predictions help to guide the search toward the changed optima, thereby accelerating convergence. A scoring scheme is devised to hybridize the KF prediction with a random reinitialization method. Experimental results and performance comparisons with other state-of-the-art algorithms demonstrate that the proposed algorithm is capable of significantly improving the dynamic optimization performance.
TL;DR: In this paper, a simulation-based model predictive control (MPC) procedure, consisting of the multi-objective optimization of operating cost for space conditioning and thermal comfort, is proposed.
01 Jan 2016
TL;DR: This chapter describes the general knowledge of the teacher-student relationships and the fundamentals and performance of TLBO algorithm, an interesting algorithm which is inspired by the teaching and learning behaviour.
Abstract: This chapter introduces teaching-learning-based optimization (TLBO) algorithm and its elitist and non-dominated sorting multiobjective versions. Two examples of unconstrained and constrained benchmark functions and an example of a multiobjective constrained problem are presented to demonstrate the procedural steps of the algorithm.
TL;DR: In this paper, a stochastic multi-objective ORPD (SMO-ORPD) problem is studied in a wind integrated power system considering the loads and wind power generation uncertainties.
TL;DR: In this paper, the performance of the ORC (organic Rankine cycle) powered by geothermal water, in three different configurations, including the simple ORC, PTORC (parallel two-stage ORC) and STORC (series two stage ORC), using zeotropic working fluids is investigated from the viewpoints of the energy and exergy.
TL;DR: Stochastic ranking-based multi-indicator Algorithm (SRA), adopts the stochastic ranking technique to balance the search biases of different indicators for many-objective optimization problems.
Abstract: Traditional multiobjective evolutionary algorithms face a great challenge when dealing with many objectives. This is due to a high proportion of nondominated solutions in the population and low selection pressure toward the Pareto front. In order to tackle this issue, a series of indicator-based algorithms have been proposed to guide the search process toward the Pareto front. However, a single indicator might be biased and lead the population to converge to a subregion of the Pareto front. In this paper, a multi-indicator-based algorithm is proposed for many-objective optimization problems. The proposed algorithm, namely stochastic ranking-based multi-indicator Algorithm (SRA), adopts the stochastic ranking technique to balance the search biases of different indicators. Empirical studies on a large number (39 in total) of problem instances from two well-defined benchmark sets with 5, 10, and 15 objectives demonstrate that SRA performs well in terms of inverted generational distance and hypervolume metrics when compared with state-of-the-art algorithms. Empirical studies also reveal that, in the case a problem requires the algorithm to have strong convergence ability, the performance of SRA can be further improved by incorporating a direction-based archive to store well-converged solutions and maintain diversity.
TL;DR: An evolutionary algorithm is presented to optimize the design of a trauma system, which is a typical offline data-driven multiobjective optimization problem, where the objectives and constraints can be evaluated using incidents only.
Abstract: Most existing work on evolutionary optimization assumes that there are analytic functions for evaluating the objectives and constraints. In the real world, however, the objective or constraint values of many optimization problems can be evaluated solely based on data and solving such optimization problems is often known as data-driven optimization. In this paper, we divide data-driven optimization problems into two categories, i.e., offline and online data-driven optimization, and discuss the main challenges involved therein. An evolutionary algorithm is then presented to optimize the design of a trauma system, which is a typical offline data-driven multiobjective optimization problem, where the objectives and constraints can be evaluated using incidents only. As each single function evaluation involves a large amount of patient data, we develop a multifidelity surrogate-management strategy to reduce the computation time of the evolutionary optimization. The main idea is to adaptively tune the approximation fidelity by clustering the original data into different numbers of clusters and a regression model is constructed to estimate the required minimum fidelity. Experimental results show that the proposed algorithm is able to save up to 90% of computation time without much sacrifice of the solution quality.
TL;DR: Two evolutionary algorithms, NSGA-II and NRGA, are applied to combine the improvement of makespan and stability simultaneously simultaneously to address the stable scheduling of multi-objective problem in flexible job shop scheduling with random machine breakdown.
24 Jul 2016
TL;DR: The experimental results suggest that existing multi-objective optimization algorithms fail to find all the Pareto sets while the proposed algorithm is able to find almost all the Fermi sets without deteriorating the distribution of solutions in the objective space.
Abstract: In real world applications, there are many multi-objective optimization problems. Most existing multi-objective optimization algorithms focus on improving the diversity, spread and convergence of the solutions in the objective space. Few works study the distribution of solutions in the decision space. In practical applications, some multi-objective problems have different Pareto sets with the same objective values and these problems are defined as multimodal multi-objective optimization problems. It is of great significance to provide all the Pareto sets for the decision maker. This paper describes the concept of multimodal multi-objective optimization problems in detail. Novel test functions are also designed to judge the performance of different algorithms. Moreover, some existing multi-objective algorithms are tested and compared. Finally, a decision space based niching multi-objective evolutionary algorithm is proposed to solve these problems. The experimental results suggest that existing multi-objective optimization algorithms fail to find all the Pareto sets while the proposed algorithm is able to find almost all the Pareto sets without deteriorating the distribution of solutions in the objective space.
TL;DR: In this article, the authors investigated the power efficient resource allocation algorithm design for secure multiuser wireless communication systems employing a full-duplex (FD) base station (BS) for serving multiple half-dulex (HD) downlink (DL) and uplink (UL) users simultaneously.
Abstract: In this paper, we investigate the power efficient resource allocation algorithm design for secure multiuser wireless communication systems employing a full-duplex (FD) base station (BS) for serving multiple half-duplex (HD) downlink (DL) and uplink (UL) users simultaneously. We propose a multi-objective optimization framework to study two conflicting yet desirable design objectives, i.e., total DL transmit power minimization and total UL transmit power minimization. To this end, the weighed Tchebycheff method is adopted to formulate the resource allocation algorithm design as a multi-objective optimization problem (MOOP). The considered MOOP takes into account the quality-of-service requirements of all legitimate users for guaranteeing secure DL and UL transmission in the presence of potential eavesdroppers. Thereby, secure UL transmission is enabled by the FD BS and would not be possible with an HD BS. The imperfectness of the channel state information of the eavesdropping channels and the inter-user interference channels is incorporated for robust resource allocation algorithm design. Although the considered MOOP is non-convex, we solve it optimally by semidefinite programming relaxation. Simulation results not only unveil the trade-off between the total DL transmit power and the total UL transmit power, but also confirm the robustness of the proposed algorithm against potential eavesdroppers.
TL;DR: In this article, a three-objective distribution planner is presented to tackle the tactical optimization of fresh food distribution networks considering operating cost, carbon footprint and delivery time goals, and the most effective distribution network is studied best balancing the economic, environmental and delivery times objective functions.