Dynamic Flexible Job Shop Scheduling (DFJSS) is an important and challenging problem, and can have multiple conflicting objectives. Genetic Programming Hyper-Heuristic (GPHH) is a promising approach to fast respond to the dynamic and unpredictable events in DFJSS. A GPHH algorithm evolves dispatching rules (DRs) that are used to make decisions during the scheduling process (i.e., the so-called heuristic template). In DFJSS, there are two kinds of scheduling decisions: the routing decision that allocates each operation to a machine to process it, and the sequencing decision that selects the next job to be processed by each idle machine. The traditional heuristic template makes both routing and sequencing decisions in a non-delay manner, which may have limitations in handling the dynamic environment. In this article, we propose a novel heuristic template that delays the routing decisions rather than making them immediately. This way, all the decisions can be made under the latest and most accurate information. We propose three different delayed routing strategies, and automatically evolve the rules in the heuristic template by GPHH. We evaluate the newly proposed GPHH with Delayed Routing (GPHH-DR) on a multiobjective DFJSS that optimises the energy efficiency and mean tardiness. The experimental results show that GPHH-DR significantly outperformed the state-of-the-art GPHH methods. We further demonstrated the efficacy of the proposed heuristic template with delayed routing, which suggests the importance of delaying the routing decisions.
{"title":"Genetic Programming with Delayed Routing for Multiobjective Dynamic Flexible Job Shop Scheduling","authors":"Binzi Xu;Yi Mei;Yan Wang;Zhicheng Ji;Mengjie Zhang","doi":"10.1162/evco_a_00273","DOIUrl":"10.1162/evco_a_00273","url":null,"abstract":"<para>Dynamic Flexible Job Shop Scheduling (DFJSS) is an important and challenging problem, and can have multiple conflicting objectives. Genetic Programming Hyper-Heuristic (GPHH) is a promising approach to fast respond to the dynamic and unpredictable events in DFJSS. A GPHH algorithm evolves dispatching rules (DRs) that are used to make decisions during the scheduling process (i.e., the so-called heuristic template). In DFJSS, there are two kinds of scheduling decisions: the routing decision that allocates each operation to a machine to process it, and the sequencing decision that selects the next job to be processed by each idle machine. The traditional heuristic template makes both routing and sequencing decisions in a non-delay manner, which may have limitations in handling the dynamic environment. In this article, we propose a novel heuristic template that delays the routing decisions rather than making them immediately. This way, all the decisions can be made under the latest and most accurate information. We propose three different delayed routing strategies, and automatically evolve the rules in the heuristic template by GPHH. We evaluate the newly proposed GPHH with Delayed Routing (GPHH-DR) on a multiobjective DFJSS that optimises the energy efficiency and mean tardiness. The experimental results show that GPHH-DR significantly outperformed the state-of-the-art GPHH methods. We further demonstrated the efficacy of the proposed heuristic template with delayed routing, which suggests the importance of delaying the routing decisions.</para>","PeriodicalId":50470,"journal":{"name":"Evolutionary Computation","volume":"29 1","pages":"75-105"},"PeriodicalIF":6.8,"publicationDate":"2021-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1162/evco_a_00273","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37907438","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Understanding the behaviour of heuristic search methods is a challenge. This even holds for simple local search methods such as 2-OPT for the Travelling Salesperson Problem (TSP). In this article, we present a general framework that is able to construct a diverse set of instances which are hard or easy for a given search heuristic. Such a diverse set is obtained by using an evolutionary algorithm for constructing hard or easy instances which are diverse with respect to different features of the underlying problem. Examining the constructed instance sets, we show that many combinations of two or three features give a good classification of the TSP instances in terms of whether they are hard to be solved by 2-OPT.
{"title":"Feature-Based Diversity Optimization for Problem Instance Classification","authors":"Wanru Gao;Samadhi Nallaperuma;Frank Neumann","doi":"10.1162/evco_a_00274","DOIUrl":"10.1162/evco_a_00274","url":null,"abstract":"<para>Understanding the behaviour of heuristic search methods is a challenge. This even holds for simple local search methods such as 2-OPT for the Travelling Salesperson Problem (TSP). In this article, we present a general framework that is able to construct a diverse set of instances which are hard or easy for a given search heuristic. Such a diverse set is obtained by using an evolutionary algorithm for constructing hard or easy instances which are diverse with respect to different features of the underlying problem. Examining the constructed instance sets, we show that many combinations of two or three features give a good classification of the TSP instances in terms of whether they are hard to be solved by 2-OPT.</para>","PeriodicalId":50470,"journal":{"name":"Evolutionary Computation","volume":"29 1","pages":"107-128"},"PeriodicalIF":6.8,"publicationDate":"2021-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1162/evco_a_00274","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"38055586","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
To maintain the population diversity of genetic algorithms (GAs), we are required to employ an appropriate population diversity measure. However, commonly used population diversity measures designed for permutation problems do not consider the dependencies between the variables of the individuals in the population. We propose three types of population diversity measures that address high-order dependencies between the variables to investigate the effectiveness of considering high-order dependencies. The first is formulated as the entropy of the probability distribution of individuals estimated from the population based on an m-th--order Markov model. The second is an extension of the first. The third is similar to the first, but it is based on a variable order Markov model. The proposed population diversity measures are incorporated into the evaluation function of a GA for the traveling salesman problem to maintain population diversity. Experimental results demonstrate the effectiveness of the three types of high-order entropy-based population diversity measures against the commonly used population diversity measures.
{"title":"High-Order Entropy-Based Population Diversity Measures in the Traveling Salesman Problem","authors":"Yuichi Nagata","doi":"10.1162/evco_a_00268","DOIUrl":"10.1162/evco_a_00268","url":null,"abstract":"<para>To maintain the population diversity of genetic algorithms (GAs), we are required to employ an appropriate population diversity measure. However, commonly used population diversity measures designed for permutation problems do not consider the dependencies between the variables of the individuals in the population. We propose three types of population diversity measures that address high-order dependencies between the variables to investigate the effectiveness of considering high-order dependencies. The first is formulated as the entropy of the probability distribution of individuals estimated from the population based on an <inline-formula><mml:math><mml:mi>m</mml:mi></mml:math></inline-formula>-th--order Markov model. The second is an extension of the first. The third is similar to the first, but it is based on a variable order Markov model. The proposed population diversity measures are incorporated into the evaluation function of a GA for the traveling salesman problem to maintain population diversity. Experimental results demonstrate the effectiveness of the three types of high-order entropy-based population diversity measures against the commonly used population diversity measures.</para>","PeriodicalId":50470,"journal":{"name":"Evolutionary Computation","volume":"28 4","pages":"595-619"},"PeriodicalIF":6.8,"publicationDate":"2020-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1162/evco_a_00268","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37639325","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Sarah L. Thomson;Gabriela Ochoa;Sébastien Verel;Nadarajen Veerapen
Connection patterns among Local Optima Networks (LONs) can inform heuristic design for optimisation. LON research has predominantly required complete enumeration of a fitness landscape, thereby restricting analysis to problems diminutive in size compared to real-life situations. LON sampling algorithms are therefore important. In this article, we study LON construction algorithms for the Quadratic Assignment Problem (QAP). Using machine learning, we use estimated LON features to predict search performance for competitive heuristics used in the QAP domain. The results show that by using random forest regression, LON construction algorithms produce fitness landscape features which can explain almost all search variance. We find that LON samples better relate to search than enumerated LONs do. The importance of fitness levels of sampled LONs in search predictions is crystallised. Features from LONs produced by different algorithms are combined in predictions for the first time, with promising results for this “super-sampling”: a model to predict tabu search success explained 99% of variance. Arguments are made for the use-case of each LON algorithm and for combining the exploitative process of one with the exploratory optimisation of the other.
{"title":"Inferring Future Landscapes: Sampling the Local Optima Level","authors":"Sarah L. Thomson;Gabriela Ochoa;Sébastien Verel;Nadarajen Veerapen","doi":"10.1162/evco_a_00271","DOIUrl":"10.1162/evco_a_00271","url":null,"abstract":"<para>Connection patterns among <italic>Local Optima Networks</i> (LONs) can inform heuristic design for optimisation. LON research has predominantly required complete enumeration of a fitness landscape, thereby restricting analysis to problems diminutive in size compared to real-life situations. LON <italic>sampling</i> algorithms are therefore important. In this article, we study LON construction algorithms for the Quadratic Assignment Problem (QAP). Using machine learning, we use estimated LON features to predict search performance for competitive heuristics used in the QAP domain. The results show that by using random forest regression, LON construction algorithms produce fitness landscape features which can explain almost all search variance. We find that LON samples better relate to search than enumerated LONs do. The importance of fitness levels of sampled LONs in search predictions is crystallised. Features from LONs produced by different algorithms are combined in predictions for the first time, with promising results for this “super-sampling”: a model to predict tabu search success explained 99% of variance. Arguments are made for the use-case of each LON algorithm and for combining the exploitative process of one with the exploratory optimisation of the other.</para>","PeriodicalId":50470,"journal":{"name":"Evolutionary Computation","volume":"28 4","pages":"621-641"},"PeriodicalIF":6.8,"publicationDate":"2020-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1162/evco_a_00271","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37680158","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Jordan MacLachlan;Yi Mei;Juergen Branke;Mengjie Zhang
Due to its direct relevance to post-disaster operations, meter reading and civil refuse collection, the Uncertain Capacitated Arc Routing Problem (UCARP) is an important optimisation problem. Stochastic models are critical to study as they more accurately represent the real world than their deterministic counterparts. Although there have been extensive studies in solving routing problems under uncertainty, very few have considered UCARP, and none consider collaboration between vehicles to handle the negative effects of uncertainty. This article proposes a novel Solution Construction Procedure (SCP) that generates solutions to UCARP within a collaborative, multi-vehicle framework. It consists of two types of collaborative activities: one when a vehicle unexpectedly expends capacity (route failure), and the other during the refill process. Then, we propose a Genetic Programming Hyper-Heuristic (GPHH) algorithm to evolve the routing policy used within the collaborative framework. The experimental studies show that the new heuristic with vehicle collaboration and GP-evolved routing policy significantly outperforms the compared state-of-the-art algorithms on commonly studied test problems. This is shown to be especially true on instances with larger numbers of tasks and vehicles. This clearly shows the advantage of vehicle collaboration in handling the uncertain environment, and the effectiveness of the newly proposed algorithm.
{"title":"Genetic Programming Hyper-Heuristics with Vehicle Collaboration for Uncertain Capacitated Arc Routing Problems","authors":"Jordan MacLachlan;Yi Mei;Juergen Branke;Mengjie Zhang","doi":"10.1162/evco_a_00267","DOIUrl":"10.1162/evco_a_00267","url":null,"abstract":"<para>Due to its direct relevance to post-disaster operations, meter reading and civil refuse collection, the Uncertain Capacitated Arc Routing Problem (UCARP) is an important optimisation problem. Stochastic models are critical to study as they more accurately represent the real world than their deterministic counterparts. Although there have been extensive studies in solving routing problems under uncertainty, very few have considered UCARP, and none consider collaboration between vehicles to handle the negative effects of uncertainty. This article proposes a novel Solution Construction Procedure (SCP) that generates solutions to UCARP within a collaborative, multi-vehicle framework. It consists of two types of collaborative activities: one when a vehicle unexpectedly expends capacity (<italic>route failure</i>), and the other during the refill process. Then, we propose a Genetic Programming Hyper-Heuristic (GPHH) algorithm to evolve the routing policy used within the collaborative framework. The experimental studies show that the new heuristic with vehicle collaboration and GP-evolved routing policy significantly outperforms the compared state-of-the-art algorithms on commonly studied test problems. This is shown to be especially true on instances with larger numbers of tasks and vehicles. This clearly shows the advantage of vehicle collaboration in handling the uncertain environment, and the effectiveness of the newly proposed algorithm.</para>","PeriodicalId":50470,"journal":{"name":"Evolutionary Computation","volume":"28 4","pages":"563-593"},"PeriodicalIF":6.8,"publicationDate":"2020-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1162/evco_a_00267","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47775196","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Clustering is a difficult and widely studied data mining task, with many varieties of clustering algorithms proposed in the literature. Nearly all algorithms use a similarity measure such as a distance metric (e.g., Euclidean distance) to decide which instances to assign to the same cluster. These similarity measures are generally predefined and cannot be easily tailored to the properties of a particular dataset, which leads to limitations in the quality and the interpretability of the clusters produced. In this article, we propose a new approach to automatically evolving similarity functions for a given clustering algorithm by using genetic programming. We introduce a new genetic programming-based method which automatically selects a small subset of features (feature selection) and then combines them using a variety of functions (feature construction) to produce dynamic and flexible similarity functions that are specifically designed for a given dataset. We demonstrate how the evolved similarity functions can be used to perform clustering using a graph-based representation. The results of a variety of experiments across a range of large, high-dimensional datasets show that the proposed approach can achieve higher and more consistent performance than the benchmark methods. We further extend the proposed approach to automatically produce multiple complementary similarity functions by using a multi-tree approach, which gives further performance improvements. We also analyse the interpretability and structure of the automatically evolved similarity functions to provide insight into how and why they are superior to standard distance metrics.
{"title":"Genetic Programming for Evolving Similarity Functions for Clustering: Representations and Analysis","authors":"Andrew Lensen;Bing Xue;Mengjie Zhang","doi":"10.1162/evco_a_00264","DOIUrl":"10.1162/evco_a_00264","url":null,"abstract":"<para>Clustering is a difficult and widely studied data mining task, with many varieties of clustering algorithms proposed in the literature. Nearly all algorithms use a similarity measure such as a distance metric (e.g., Euclidean distance) to decide which instances to assign to the same cluster. These similarity measures are generally predefined and cannot be easily tailored to the properties of a particular dataset, which leads to limitations in the quality and the interpretability of the clusters produced. In this article, we propose a new approach to automatically evolving similarity functions for a given clustering algorithm by using genetic programming. We introduce a new genetic programming-based method which automatically selects a small subset of features (feature selection) and then combines them using a variety of functions (feature construction) to produce dynamic and flexible similarity functions that are specifically designed for a given dataset. We demonstrate how the evolved similarity functions can be used to perform clustering using a graph-based representation. The results of a variety of experiments across a range of large, high-dimensional datasets show that the proposed approach can achieve higher and more consistent performance than the benchmark methods. We further extend the proposed approach to automatically produce multiple complementary similarity functions by using a multi-tree approach, which gives further performance improvements. We also analyse the interpretability and structure of the automatically evolved similarity functions to provide insight into how and why they are superior to standard distance metrics.</para>","PeriodicalId":50470,"journal":{"name":"Evolutionary Computation","volume":"28 4","pages":"531-561"},"PeriodicalIF":6.8,"publicationDate":"2020-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1162/evco_a_00264","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64541083","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We present a study demonstrating how random walk algorithms can be used for evolutionary image transition. We design different mutation operators based on uniform and biased random walks and study how their combination with a baseline mutation operator can lead to interesting image transition processes in terms of visual effects and artistic features. Using feature-based analysis we investigate the evolutionary image transition behaviour with respect to different features and evaluate the images constructed during the image transition process. Afterwards, we investigate how modifications of our biased random walk approaches can be used for evolutionary image painting. We introduce an evolutionary image painting approach whose underlying biased random walk can be controlled by a parameter influencing the bias of the random walk and thereby creating different artistic painting effects.
{"title":"Evolutionary Image Transition and Painting Using Random Walks","authors":"Aneta Neumann;Bradley Alexander;Frank Neumann","doi":"10.1162/evco_a_00270","DOIUrl":"10.1162/evco_a_00270","url":null,"abstract":"<para>We present a study demonstrating how random walk algorithms can be used for evolutionary image transition. We design different mutation operators based on uniform and biased random walks and study how their combination with a baseline mutation operator can lead to interesting image transition processes in terms of visual effects and artistic features. Using feature-based analysis we investigate the evolutionary image transition behaviour with respect to different features and evaluate the images constructed during the image transition process. Afterwards, we investigate how modifications of our biased random walk approaches can be used for evolutionary image painting. We introduce an evolutionary image painting approach whose underlying biased random walk can be controlled by a parameter influencing the bias of the random walk and thereby creating different artistic painting effects.</para>","PeriodicalId":50470,"journal":{"name":"Evolutionary Computation","volume":"28 4","pages":"643-675"},"PeriodicalIF":6.8,"publicationDate":"2020-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1162/evco_a_00270","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37680160","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Errata: Convergence Analysis of Evolutionary Algorithms That Are Based on the Paradigm of Information Geometry","authors":"Hans-Georg Beyer","doi":"10.1162/evco_x_00281","DOIUrl":"10.1162/evco_x_00281","url":null,"abstract":"","PeriodicalId":50470,"journal":{"name":"Evolutionary Computation","volume":"28 4","pages":"709-710"},"PeriodicalIF":6.8,"publicationDate":"2020-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"38660291","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Michael Garvie;Ittai Flascher;Andrew Philippides;Adrian Thompson;Phil Husbands
For the first time, a field programmable transistor array (FPTA) was used to evolve robot control circuits directly in analog hardware. Controllers were successfully incrementally evolved for a physical robot engaged in a series of visually guided behaviours, including finding a target in a complex environment where the goal was hidden from most locations. Circuits for recognising spoken commands were also evolved and these were used in conjunction with the controllers to enable voice control of the robot, triggering behavioural switching. Poor quality visual sensors were deliberately used to test the ability of evolved analog circuits to deal with noisy uncertain data in realtime. Visual features were coevolved with the controllers to automatically achieve dimensionality reduction and feature extraction and selection in an integrated way. An efficient new method was developed for simulating the robot in its visual environment. This allowed controllers to be evaluated in a simulation connected to the FPTA. The controllers then transferred seamlessly to the real world. The circuit replication issue was also addressed in experiments where circuits were evolved to be able to function correctly in multiple areas of the FPTA. A methodology was developed to analyse the evolved circuits which provided insights into their operation. Comparative experiments demonstrated the superior evolvability of the transistor array medium.
{"title":"Evolved Transistor Array Robot Controllers","authors":"Michael Garvie;Ittai Flascher;Andrew Philippides;Adrian Thompson;Phil Husbands","doi":"10.1162/evco_a_00272","DOIUrl":"10.1162/evco_a_00272","url":null,"abstract":"<para>For the first time, a field programmable transistor array (FPTA) was used to evolve robot control circuits directly in analog hardware. Controllers were successfully incrementally evolved for a physical robot engaged in a series of visually guided behaviours, including finding a target in a complex environment where the goal was hidden from most locations. Circuits for recognising spoken commands were also evolved and these were used in conjunction with the controllers to enable voice control of the robot, triggering behavioural switching. Poor quality visual sensors were deliberately used to test the ability of evolved analog circuits to deal with noisy uncertain data in realtime. Visual features were coevolved with the controllers to automatically achieve dimensionality reduction and feature extraction and selection in an integrated way. An efficient new method was developed for simulating the robot in its visual environment. This allowed controllers to be evaluated in a simulation connected to the FPTA. The controllers then transferred seamlessly to the real world. The circuit replication issue was also addressed in experiments where circuits were evolved to be able to function correctly in multiple areas of the FPTA. A methodology was developed to analyse the evolved circuits which provided insights into their operation. Comparative experiments demonstrated the superior evolvability of the transistor array medium.</para>","PeriodicalId":50470,"journal":{"name":"Evolutionary Computation","volume":"28 4","pages":"677-708"},"PeriodicalIF":6.8,"publicationDate":"2020-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1162/evco_a_00272","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37890892","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Multiobjective evolutionary algorithms (MOEAs) have progressed significantly in recent decades, but most of them are designed to solve unconstrained multiobjective optimization problems. In fact, many real-world multiobjective problems contain a number of constraints. To promote research on constrained multiobjective optimization, we first propose a problem classification scheme with three primary types of difficulty, which reflect various types of challenges presented by real-world optimization problems, in order to characterize the constraint functions in constrained multiobjective optimization problems (CMOPs). These are feasibility-hardness, convergence-hardness, and diversity-hardness. We then develop a general toolkit to construct difficulty adjustable and scalable CMOPs (DAS-CMOPs, or DAS-CMaOPs when the number of objectives is greater than three) with three types of parameterized constraint functions developed to capture the three proposed types of difficulty. In fact, the combination of the three primary constraint functions with different parameters allows the construction of a large variety of CMOPs, with difficulty that can be defined by a triplet, with each of its parameters specifying the level of one of the types of primary difficulty. Furthermore, the number of objectives in this toolkit can be scaled beyond three. Based on this toolkit, we suggest nine difficulty adjustable and scalable CMOPs and nine CMaOPs, to be called DAS-CMOP1-9 and DAS-CMaOP1-9, respectively. To evaluate the proposed test problems, two popular CMOEAs—MOEA/D-CDP (MOEA/D with constraint dominance principle) and NSGA-II-CDP (NSGA-II with constraint dominance principle) and two popular constrained many-objective evolutionary algorithms (CMaOEAs)—C-MOEA/DD and C-NSGA-III—are used to compare performance on DAS-CMOP1-9 and DAS-CMaOP1-9 with a variety of difficulty triplets, respectively. The experimental results reveal that mechanisms in MOEA/D-CDP may be more effective in solving convergence-hard DAS-CMOPs, while mechanisms of NSGA-II-CDP may be more effective in solving DAS-CMOPs with simultaneous diversity-, feasibility-, and convergence-hardness. Mechanisms in C-NSGA-III may be more effective in solving feasibility-hard CMaOPs, while mechanisms of C-MOEA/DD may be more effective in solving CMaOPs with convergence-hardness. In addition, none of them can solve these problems efficiently, which stimulates us to continue to develop new CMOEAs and CMaOEAs to solve the suggested DAS-CMOPs and DAS-CMaOPs.
{"title":"Difficulty Adjustable and Scalable Constrained Multiobjective Test Problem Toolkit","authors":"Zhun Fan;Wenji Li;Xinye Cai;Hui Li;Caimin Wei;Qingfu Zhang;Kalyanmoy Deb;Erik Goodman","doi":"10.1162/evco_a_00259","DOIUrl":"10.1162/evco_a_00259","url":null,"abstract":"<para>Multiobjective evolutionary algorithms (MOEAs) have progressed significantly in recent decades, but most of them are designed to solve unconstrained multiobjective optimization problems. In fact, many real-world multiobjective problems contain a number of constraints. To promote research on constrained multiobjective optimization, we first propose a problem classification scheme with three primary types of difficulty, which reflect various types of challenges presented by real-world optimization problems, in order to characterize the constraint functions in constrained multiobjective optimization problems (CMOPs). These are feasibility-hardness, convergence-hardness, and diversity-hardness. We then develop a general toolkit to construct difficulty adjustable and scalable CMOPs (DAS-CMOPs, or DAS-CMaOPs when the number of objectives is greater than three) with three types of parameterized constraint functions developed to capture the three proposed types of difficulty. In fact, the combination of the three primary constraint functions with different parameters allows the construction of a large variety of CMOPs, with difficulty that can be defined by a triplet, with each of its parameters specifying the level of one of the types of primary difficulty. Furthermore, the number of objectives in this toolkit can be scaled beyond three. Based on this toolkit, we suggest nine difficulty adjustable and scalable CMOPs and nine CMaOPs, to be called DAS-CMOP1-9 and DAS-CMaOP1-9, respectively. To evaluate the proposed test problems, two popular CMOEAs—MOEA/D-CDP (MOEA/D with constraint dominance principle) and NSGA-II-CDP (NSGA-II with constraint dominance principle) and two popular constrained many-objective evolutionary algorithms (CMaOEAs)—C-MOEA/DD and C-NSGA-III—are used to compare performance on DAS-CMOP1-9 and DAS-CMaOP1-9 with a variety of difficulty triplets, respectively. The experimental results reveal that mechanisms in MOEA/D-CDP may be more effective in solving convergence-hard DAS-CMOPs, while mechanisms of NSGA-II-CDP may be more effective in solving DAS-CMOPs with simultaneous diversity-, feasibility-, and convergence-hardness. Mechanisms in C-NSGA-III may be more effective in solving feasibility-hard CMaOPs, while mechanisms of C-MOEA/DD may be more effective in solving CMaOPs with convergence-hardness. In addition, none of them can solve these problems efficiently, which stimulates us to continue to develop new CMOEAs and CMaOEAs to solve the suggested DAS-CMOPs and DAS-CMaOPs.</para>","PeriodicalId":50470,"journal":{"name":"Evolutionary Computation","volume":"28 3","pages":"339-378"},"PeriodicalIF":6.8,"publicationDate":"2020-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1162/evco_a_00259","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37266988","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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