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2023 IEEE Symposium Series on Computational Intelligence, SSCI 2023

作者： Gong, Cheng Nan, Yang Pang, Lie Meng Ishibuchi, Hisao Zhang, Qingfu Southern University of Science and Technology Guangdong Provincial Key Laboratory of Brain-inspired Intelligent Computation Department of Computer Science and Engineering Shenzhen518055 China City University of Hong Kong Department of Computer Science Kowloon Tong Hong Kong The City University of Hong Kong Shenzhen Research Institute Shenzhen China

ISBN: (纸本)9781665430654

Population initialization is a crucial and essential step in evolutionary multi-objective optimization (EMO) algorithms. The quality of the generated initial population can significantly affect the performance of an EMO algorithm. However, few studies have focused on designing a generalized initialization method to improve the performance of EMO algorithms in solving multi-objective combinatorial optimization (MOCO) problems. Most of the existing advanced initialization methods involve complex techniques tailored to the specific characteristics of the problems to be solved. In this paper, we propose a general and effective framework of population initialization for EMO algorithms, aiming to improve their performances in solving various MOCO problems. Our approach involves the inclusion of a few specific heuristic solutions, including extreme solutions and a center solution, into the initial population. This inclusion serves to guide the evolution of the population throughout the optimization process. Our experimental results show that initial populations with a few heuristic solutions significantly improve the performance of EMO algorithms. Algorithm behavior analysis and further study are also provided, allowing for a comprehensive understanding of the effectiveness and applicability of our proposed method. © 2023 IEEE.

关键词： Evolutionary multi-objective optimization algorithms multi-objective combinatorial optimization Population initialization

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Deep reinforcement learning for multi-objective combinatorial optimization: A case study on multi-objective traveling salesman problem

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SWARM AND EVOLUTIONARY COMPUTATION 2023年 83卷

作者： Li, Shicheng Wang, Feng He, Qi Wang, Xujie Wuhan Univ Sch Comp Sci Wuhan 430072 Peoples R China

multi-objective combinatorial optimization problems (MOCOPs) widely exist in real applications, and most of them are computationally difficult or NP-hard. How to solve MOCOPs efficiently has been a challenging issue. The heuristic algorithms have achieved good results on MOCOPs, while they require careful hand-crafted heuristics and iterative computing for the solutions. Recently, deep reinforcement learning (DRL) has been employed to solve combinatorial optimization problems, and many DRL-based algorithms have been proposed with promising results. However, it is difficult for these existing algorithms to obtain diverse solutions efficiently for MOCOPs. In this paper, we propose an algorithm named MOMDAM to solve MOCOPs. In MOMDAM, the attention model (AM) is used and can simply modify the encoder to facilitate the construction of solutions with any weight vector, as well as the multiple decoders (MD) are employed to obtain diverse policies to further improve the diversity and convergence of the solutions. Experimental results on the bi -objective traveling salesman problem show that, MOMDAM significantly outperforms some state-of-the-art algorithms in terms of solution quality and running time.

关键词： multi-objective combinatorial optimization Attention model multiple decoders Traveling salesman problem

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multi-objective unconstrained combinatorial optimization: a polynomial bound on the number of extreme supported solutions

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JOURNAL OF GLOBAL optimization 2019年第3期74卷 495-522页

作者： Schulze, Britta Klamroth, Kathrin Stiglmayr, Michael Univ Wuppertal Gaussstr 20 D-42119 Wuppertal Germany

The multi-objective unconstrained combinatorial optimization problem (MUCO) can be considered as an archetype of a discrete linear multi-objective optimization problem. It can be interpreted as a specific relaxation of any multi-objective combinatorial optimization problem with linear sum objective function. While its single criteria analogon is analytically solvable, MUCO shares the computational complexity issues of most multi-objective combinatorial optimization problems: intractability and NP-hardness of the epsilon-constraint scalarizations. In this article interrelations between the supported points of a MUCO problem, arrangements of hyperplanes and a weight space decomposition, and zonotopes are presented. Based on these interrelations and a result by Zaslavsky on the number of faces in an arrangement of hyperplanes, a polynomial bound on the number of extreme supported solutions can be derived, leading to an exact polynomial time algorithm to find all extreme supported solutions. It is shown how this algorithm can be incorporated into a solution approach for multi-objective knapsack problems.

关键词： multi-objective combinatorial optimization multi-objective unconstrained optimization Weight space decomposition Arrangement of hyperplanes Zonotopes Knapsack problem

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combinatorial optimization of stochastic multi-objective problems: An application to the flow-shop scheduling problem

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4th International Conference on Evolutionary multi-Criterion optimization (EMO 2007)

作者： Liefooghe, Arnaud Basseur, Matthieu Jourdan, Laetitia Talbi, El-Ghazali INRIA Futurs LIFL CNRS Bat M3Cite Sci F-59655 Villeneuve Dascq France

ISBN: (纸本)9783540709275

The importance of multi-objective optimization is globably established nowadays. Furthermore, a great part of real-world problems are subject to uncertainties due to, e.g., noisy or approximated fitness function(s), varying parameters or dynamic environments. Moreover, although evolutionary algorithms are commonly used to solve multi-objective problems on the one hand and to solve stochastic problems on the other hand, very few approaches combine simultaneously these two aspects. Thus, flow-shop scheduling problems are generally studied in a single-objective deterministic way whereas they are, by nature, multi-objective and are subjected to a wide range of uncertainties. However, these two features have never been investigated at the same time. In this paper, we present and adopt a proactive stochastic approach where processing times are represented by random variables. Then, we propose several multi-objective methods that are able to handle any type of probability distribution. Finally, we experiment these methods on a stochastic bi-objective flow-shop problem.

关键词： multi-objective combinatorial optimization stochasticity evolutionnary algorithms flow-shop stochastic processing times

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multi-objective optimization for sensor placement: An integrated combinatorial approach with reduced order model and Gaussian process

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MEASUREMENT 2022年 187卷 110370-110370页

作者： Xu, Zhaoyi Guo, Yanjie Saleh, Joseph Homer Georgia Inst Technol Sch Aerosp Engn Atlanta GA 30332 USA

We develop a novel sensor placement method that maximizes monitoring performance while minimizing deployment cost. Our method integrates a reduced order model and multi-objective combinatorial optimization. We first decompose the spatio-temporal state field to be monitored by proper orthogonal decomposition (POD), and we use the Gaussian Process to model the uncertainty in each POD mode. Next, we develop a lazy greedy (LG)-SMALL ELEMENT OF-constraint optimization to derive the Pareto-optimal sensor configurations. We further design a branch and bound algorithm to calculate the global optimum and validate the correctness of select configurations on the LG-derived Pareto frontier. We evaluate and benchmark our algorithm in computational experiments based on the temperature dataset of the Berkeley Intel Lab. The computational results demonstrate that our algorithm places sensors at locations of large magnitude in the POD modes, and that our method achieves better state estimation accuracy and smaller reconstruction errors compared with alternative methods.

关键词： Sensor placement multi-objective combinatorial optimization Proper orthogonal decomposition Lazy greedy algorithm Branch and bound

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Approximation schemes for bi-objective combinatorial optimization and their application to the TSP with profits

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COMPUTERS & OPERATIONS RESEARCH 2013年第10期40卷 2418-2428页

作者： Filippi, Carlo Stevanato, Elisa Univ Brescia Dept Econ & Management Brescia Italy

We describe two approximation schemes for bi-objective combinatorial optimization problems with nonnegative, integer valued objectives. The procedures compute a subset of the efficient points such that any other efficient point is within an arbitrary factor from a computed one with respect to both objectives. Both schemes are simple modifications of classical algorithms for the construction of the whole efficient set. In both procedures, a properly defined single objective subproblem has to be solved at every iteration. We show that, in both cases, the number of subproblems to be solved and the number of returned efficient points are polynomial in the input size and the reciprocal of the allowed error. We also show that a fast post-processing guarantees that the number of returned efficient points is at most three times the minimum possible number needed to approximate the efficient set within the specified tolerance. We test the procedures on the Traveling Salesman Problem with Profits, where profits and costs are treated as conflicting objectives. Results are taken on randomly generated instances and on TSPLIB instances. We show that both algorithms return a guaranteed approximation with significant time sparing with respect to exact procedures. We also give empirical evidence that in the specific application the number of points returned by the approximation schemes is close to the minimum. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： multi-objective combinatorial optimization Complexity Approximation TSP with profits

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Using Dominance in Solving Complex, combinatorial optimization Problems: Applications from Healthcare Provider Scheduling and Vehicle Routing

Using Dominance in Solving Complex, Combinatorial Optimizati...

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作者： Hong, Young-Chae University of Michigan

学位级别：Ph.D.

The focus of this dissertation is to develop mathematical methods for the multi-criteria optimization problem and the vehicle routing problem. We approach these problems through the concept of Pareto dominance. Our goal is to develop general algorithms that utilize Pareto dominance and solve the problems in reasonable time. We first consider the problem of assigning medical residents to shifts within a pediatric emergency department. This problem is challenging to solve for a number of reasons. First, like many other healthcare personnel scheduling problems, it has a non-homogeneous work force, with each resident having different characteristics, requirements, and capabilities. Second, residency scheduling problems must not only ensure adequate resources for patient care but must also meet educational training needs, adding further complexity and constraints. Finally, since many factors should be taken into account when selecting the "best" schedule, there is no one clear, well-defined single objective function under which to optimize. Thus, it is difficult, if not impossible, to pre-assign weights that allow these factors and the preferences of the scheduler (typically, a Chief Resident) to be captured in a mathematical objective function. We propose an integer programming formulation and an iterative, interactive approach in which we use this integer program for ill-defined multiple objective criteria which are often in conflict with each other. After we identify quantifiable metrics through the interactive approach, we develop an integer programming-based approach embedded within a recursive algorithm to provide the Chief with a set of Pareto-dominant schedules from which to select. We then present our collaborative work with the University of Michigan C.S. Mott Children's Hospital in building monthly schedules, focusing on both the tractability of our methods and a case study to study how a Chief Resident would evaluate the Pareto set. When building schedules, a

关键词： Residency scheduling multi-objective combinatorial optimization Pareto set vehicle routing problem column generation dynamic programming Thesis

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Cost-aware generative design for urban 'cool spots': A random forest-principal component analysis-augmented combinatorial optimization approach

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ENERGY AND BUILDINGS 2023年第1期295卷

作者： Peng, Ziyu Lu, Weisheng Hao, Tongping Tang, Xu Huang, Jianxiang Webster, Chris Univ Hong Kong Fac Architecture Dept Real Estate & Construct Hong Kong Peoples R China Univ Hong Kong Fac Architecture Dept Urban Planning & Design Hong Kong Peoples R China Univ Hong Kong Fac Architecture Hong Kong Peoples R China Univ Hong Kong Fac Architecture Dept Real Estate & Construct Pokfulam Knowles Bldg Hong Kong Peoples R China

Whilst designing cool small neighborhoods (called 'cool spots' in this paper) remains an enormous technical challenge, clients and their designers are also confronting with the perpetual burden of the financial sphere. This research aims to develop a novel methodological approach for designers to search for affordable cool spots in dense urban areas. It does so by conducting genetic combinatorial optimizations augmented by Random Forest (RF) and Principal Component Analysis (PCA) algorithms. What is particularly innovative is to develop a massbased generative design approach to produce neighborhood options for the subsequent combinatorial optimization. The methodology is tested in a real-world urban renewal project in Hong Kong, which is epitomized by high density and hot and humid weather in the summer. The results show that the design approach can automatically identify high-performance schemes of cool spot design, reducing the daily average thermophysiological equivalent temperature from averagely 29.76 degrees C to at lowest 29.59 degrees C, and decreasing the construction cost by 82.57%. With proper translation, the approach can serve as a useful and robust design assisting tool for designing and developing cool and cost-aware buildings and neighborhoods in urban areas.

关键词： Generative design Outdoor thermal comfort Construction cost multi-objective combinatorial optimization Design assistance tool

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A GRASP heuristic for the multi-objective permutation flowshop scheduling problem

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INTERNATIONAL JOURNAL OF ADVANCED MANUFACTURING TECHNOLOGY 2011年第5-8期55卷 741-753页

作者： Claudio Arroyo, Jose Elias de Souza Pereira, Ana Amelia Univ Fed Vicosa Dept Informat BR-36570000 Vicosa MG Brazil

This paper presents a multi-objective greedy randomized adaptive search procedure (GRASP)-based heuristic for solving the permutation flowshop scheduling problem in order to minimize two and three objectives simultaneously: (1) makespan and maximum tardiness;(2) makespan, maximum tardiness, and total flowtime. GRASP is a competitive metaheuristic for solving combinatorial optimization problems. We have customized the basic concepts of GRASP algorithm to solve a multi-objective problem and a new algorithm named multi-objective GRASP algorithm is proposed. In order to find a variety of non-dominated solutions, the heuristic blends two typical approaches used in multi-objective optimization: scalarizing functions and Pareto dominance. For instances involving two machines, the heuristic is compared with a bi-objective branch-and-bound algorithm proposed in the literature. For instances involving up to 80 jobs and 20 machines, the non-dominated solutions obtained by the heuristic are compared with solutions obtained by multi-objective genetic algorithms from the literature. Computational results indicate that GRASP is a promising approach for multi-objective optimization.

关键词： Flowshop scheduling multi-objective combinatorial optimization Heuristics GRASP

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Pruned Pareto-optimal sets for the system redundancy allocation problem based on multiple prioritized objectives

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JOURNAL OF HEURISTICS 2008年第4期14卷 335-357页

作者： Kulturel-Konak, Sadan Coit, David W. Baheranwala, Fatema Penn State Berks Management Informat Syst Reading PA 19610 USA Rutgers State Univ Dept Ind & Syst Engn Piscataway NJ 08844 USA

In this paper, a new methodology is presented to solve different versions of multi-objective system redundancy allocation problems with prioritized objectives. multi-objective problems are often solved by modifying them into equivalent single objective problems using pre-defined weights or utility functions. Then, a multi-objective problem is solved similar to a single objective problem returning a single solution. These methods can be problematic because assigning appropriate numerical values (i.e., weights) to an objective function can be challenging for many practitioners. On the other hand, methods such as genetic algorithms and tabu search often yield numerous non-dominated Pareto optimal solutions, which makes the selection of one single best solution very difficult. In this research, a tabu search meta-heuristic approach is used to initially find the entire Pareto-optimal front, and then, Monte-Carlo simulation provides a decision maker with a pruned and prioritized set of Pareto-optimal solutions based on user-defined objective function preferences. The purpose of this study is to create a bridge between Pareto optimality and single solution approaches.

关键词： multi-objective combinatorial optimization pruned Pareto-optimal front decision making uncertainty tabu search redundancy allocation problem

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