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Sugarcane is one of the main commodities in the world economy. An important step in the sugarcane supply chain is the harvest stage, requiring the support of mathematical modeling and optimization tools. Integrating the process of choosing the areas for harvesting according to the sugarcane maturation with the formation of the harvesting fronts and associating them with machine relocation costs is challenging. This paper contributes with a novel integer mathematical model that considers these concerns using three conflicting objectives. The first is that the sugarcane should be harvested as close as possible to its maturity, considering the sugarcane should be harvested as close as possible to its maturity by considering a combined measure of temperature and time since planting. The second aims to minimize the number of harvest fronts. The third objective is to minimize the costs involved with the relocation of the harvesters that cut the cane. Different strategies for obtaining Pareto-optimal solutions were proposed using exact methods, including MIP start and a decomposition technique. In the worst case, solutions with tolerable integrality gaps were obtained (inferior to 3%) in less than 1.5 h. Computational tests in real case studies were conducted in the sugarcane industry in two countries, indicating strong trade-offs in the determined solutions. In the Brazilian case, harvesting as close to maturation as possible, for example, causes an increase of 158% in the number of harvest fronts and 47% in the transportation costs, considering the minimum values for these objectives. Other trade-offs were seen and discussed when one of the other objectives was prioritized. These different compromise solutions help the decision-makers choose the most appropriate harvesting schedule according to their preferences. • We propose a new MIP optimization model to determine the harvesting of sugarcane. • The model aims to optimize three conflicting objectives. • A new method of computing cane maturation is used: the concept of degree-days. • A procedure for determining Pareto solutions by exact methods is proposed. [ABSTRACT FROM AUTHOR]

Real-world optimization problems typically involve multiple objectives to be optimized simultaneously under multiple constraints and with respect to several variables. While multi-objective optimization itself can be a challenging task, equally difficult is the ability to make sense of the obtained solutions. In this two-part paper, we deal with data mining methods that can be applied to extract knowledge about multi-objective optimization problems from the solutions generated during optimization. This knowledge is expected to provide deeper insights about the problem to the decision maker, in addition to assisting the optimization process in future design iterations through an expert system. The current paper surveys several existing data mining methods and classifies them by methodology and type of knowledge discovered. Most of these methods come from the domain of exploratory data analysis and can be applied to any multivariate data. We specifically look at methods that can generate explicit knowledge in a machine-usable form. A framework for knowledge-driven optimization is proposed, which involves both online and offline elements of knowledge discovery. One of the conclusions of this survey is that while there are a number of data mining methods that can deal with data involving continuous variables, only a few ad hoc methods exist that can provide explicit knowledge when the variables involved are of a discrete nature. Part B of this paper proposes new techniques that can be used with such datasets and applies them to discrete variable multi-objective problems related to production systems. [ABSTRACT FROM AUTHOR]

Due to its practicality, hybrid flowshop scheduling problem (HFSP) with productivity objective has been extensively explored. However, studies on HFSP considering green objective in distributed production environment are quite limited. Moreover, the current manufacturing mode is gradually evolving toward distributed co-production mode. Thus, this paper investigated a distributed hybrid flowshop scheduling problem (DHFSP) with objectives of minimization the makespan and total energy consumption (T E C). To address this problem, this paper designed a Pareto-based multi-objective hybrid iterated greedy algorithm (MOHIG) by integrating the merits of genetic operator and iterated greedy heuristic. In this MOHIG, firstly, one cooperative initialization strategy is proposed to boost initial solutions' quality based on the previous experience and rules. Secondly, one knowledge-based multi-objective local search method is invented to enhance the exploitation capability according to characteristics of problem. Thirdly, an energy-saving technique is developed to decrease the idle energy consumption of machine tools. Furthermore, the effectiveness of each improvement component of MOHIG is assessed by three common indicators. Finally, the proposed MOHIG algorithm is compared with other multi-objective optimization algorithms, including SPEA2, MOEA/D, and NSGAII. Experimental results indicate that the proposed MOHIG outperforms its compared algorithms in solving this problem. In addition, this research can better guide practical production in some certain environments. • Considering green scheduling in distributed hybrid flowshop environment. • Designing a new energy-saving strategy into this problem. • Proposing a Pareto-based multi-objective hybrid iterated greedy algorithm (MOHIG). • Evaluating performance of the proposed MOHIG by conducting comparison experiments. [ABSTRACT FROM AUTHOR]

Highlights • A heuristic search strategy was proposed for optimal learning group formation. • NSGA-II, a multi-objective optimization tool, was utilized for optimal grouping. • It was capable of enhancing inter-group homogeneity and Intra-group Heterogeneity. • Efficient and reliable fitness functions were defined to stop iterations. • Various characteristics of any data types and range of variations can be handled. Abstract In modern education systems, plenty of research suggests that clustering the learners into optimal learning groups based on their multiple characteristics is a determining effort in enhancing the effectiveness of collaborative learning. Although there have been several evidences on developing and implementing appropriate computational tools to handle classification processes in expert and intelligent systems, the effectiveness and accuracy of optimal grouping algorithms are still worth improving. For instance, the majority of grouping processes in collaborative learning environments is orchestrated through single-objective optimization algorithms, which need to be revisited due to some intrinsic limitations. In this paper, we propose a novel algorithm capable of properly addressing a variety of optimization problems in optimal learning group formation processes. To this end, a multi-objective version of Genetic Algorithms, i.e. Non-dominated Sorting Genetic Algorithm, NSGA-II, was successfully implemented and applied to improve the performance and accuracy of optimally formed learning groups. In contrast to the previous related works applying single-objective algorithms, the main advantage of our work is simultaneous satisfaction of multiple targets predefined for the formation of optimal learning groups, especially the inter-homogeneity and intra-heterogeneity of each learning group, which significantly enhance both effectiveness and accuracy of optimal grouping processes in the underlying intelligent systems. Challenging the proposed optimization algorithms, both single- and multi-objective optimizers, with a similar grouping problem, clearly proved that the single-objective optimization technique has limited control and sensitivity to the quality of individual groups. Contrary to single-objective optimization techniques, which are mainly governed by adjusting the quality of the groups altogether in average, the proposed multi-objective algorithm not only takes the average desirability of all formed groups into account but also precisely monitors the fitness of each group in a potential solution distinctively. The generality of the proposed algorithm makes it a suitable candidate not only to handle optimal grouping in learning environments but also to be competent enough for grouping problems in other domains as well. [ABSTRACT FROM AUTHOR]

Gene clustering is a prerequisite in the analysis of microarray data where sets of co-expressed genes are clustered. In this paper, a multi-objective clonal selection optimization algorithm (MCSOA) is developed based on the immune system behavior for gene clustering purposes in which the number of clusters can vary in a predefined range. To achieve a reliable clustering outcome on various gene expression (GE) datasets, the most effective clustering validity indexes are incorporated and represented in terms of two conflicting objective functions. For the sake of fast convergence to the optimal solutions, a new population updating mechanism is iteratively applied to select the less-dominate solutions of the previous iteration. The proposed clustering technique is implemented on various publicly available microarray datasets. Comparing the results with those of the widely used gene clustering techniques confirms the superiority and efficacy of the proposed technique. [ABSTRACT FROM AUTHOR]

This paper investigates a new approach for finding efficient solutions of a multi-objective programming problem (MOPP) in intuitionistic fuzzy environment (IFE) based on decision maker’s different views, viz., optimistic, pessimistic and mixed. Firstly, the point operator F α , which transforms intuitionistic fuzzy set (IFS) into the equivalent fuzzy set (FS), is introduced and some desirable properties of F α are studied. Subsequently, the formulation of MOPP, accuracy function and value function in IFE have been introduced. For resolving the mutual conflicting nature of objectives in MOPP in IFE, we introduce the membership and non-membership functions governed by reference function which do not depend on the upper and lower levels of acceptability. Then a new method is proposed to find the efficient solutions of MOPP in IFE based on different viewpoints. Finally, an illustrative example is given to demonstrate the practicality and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The primary task of a memory-based collaborative filtering (CF) recommendation system is to select a group of nearest (similar) user neighbors for an active user. Traditional memory-based CF schemes tend to only focus on improving as much as possible the accuracy by recommending familiar items ( i.e ., popular items over the group). Yet, this may reduce the number of items that could be recommended and consequently weakens the chances of recommending novel items. To address this problem, it is desirable to consider recommendation coverage when selecting the appropriate group. This could help in simultaneously making both accurate and diverse recommendations. In this paper, we propose to focus mainly on the growing of the large search space of users’ profiles and to use an evolutionary multi-objective optimization-based recommendation system to pull up a group of profiles that maximizes both similarity with the active user and diversity between its members. In such manner, the recommendation system will provide high performances in terms of both accuracy and diversity. The experimental results on the Movielens benchmark and on a real-world insurance dataset show the efficiency of our approach in terms of accuracy and diversity compared to state-of-the-art competitors. [ABSTRACT FROM AUTHOR]

Based on the concept of performance-price ratio, we propose a quantitative method to solve multi-objective optimization problems. A new hypothesis is established in this paper: market rules that seek a higher-performing product with a lower price are used to compare and select Pareto non-inferior solutions. After carefully observing the distribution of the Pareto front, we find that the distribution is monotonically increasing or decreasing. This means that different variability exists in the Pareto front and that new inherent disciplines can be found. Based on this discovery, we use the performance-price ratio as a reference to construct the average variability that adjacent non-inferior solutions correspond to the objective function values. Then, the sensitivity ratio that is similar to the performance-price ratio is obtained, and a quantitative method is developed to evaluate Pareto non-inferior solutions. Two important achievements are derived: (1) based on the sensitivity ratio, a new subset of the Pareto non-inferior solution set is formed in accordance with the dominance relationship. The number of Pareto non-inferior solutions is reduced, and the bias degree corresponding to every Pareto non-inferior solution is obtained for different objectives. Thus, it is convenient for decision makers to select Pareto non-inferior solutions based on their preferences. (2) In the new subset of Pareto non-inferior solutions, the solution that corresponds to the minimal absolute value difference of the sensitivity ratio for different optimization objectives is defined as an unbiased and good solution. Accordingly, we obtain the optimal solution that is acceptable for every objective. Finally, the method is illustrated with a numerical example. [ABSTRACT FROM AUTHOR]

In many real-world optimization problems, several conflicting objectives must be achieved and optimized simultaneously and the solutions are often required to satisfy certain restrictions or constraints. Moreover, in some applications, the numerical values of the objectives and constraints are obtained from computationally expensive simulations. Many multi-objective optimization algorithms for continuous optimization have been proposed in the literature and some have been incorporated or used in conjunction with expert and intelligent systems. However, relatively few of these multi-objective algorithms handle constraints, and even fewer, use surrogates to approximate the objective or constraint functions when these functions are computationally expensive. This paper proposes a surrogate-assisted evolution strategy (ES) that can be used for constrained multi-objective optimization of expensive black-box objective functions subject to expensive black-box inequality constraints. Such an algorithm can be incorporated into an intelligent system that finds approximate Pareto optimal solutions to simulation-based constrained multi-objective optimization problems in various applications including engineering design optimization, production management and manufacturing. The main idea in the proposed algorithm is to generate a large number of trial offspring in each generation and use the surrogates to predict the objective and constraint function values of these trial offspring. Then the algorithm performs an approximate non-dominated sort of the trial offspring based on the predicted objective and constraint function values, and then it selects the most promising offspring (those with the smallest predicted ranks from the non-dominated sort) to become the actual offspring for the current generation that will be evaluated using the expensive objective and constraint functions. The proposed method is implemented using cubic radial basis function (RBF) surrogate models to assist the ES. The resulting RBF-assisted ES is compared with the original ES and to NSGA-II on 20 test problems involving 2–15 decision variables, 2–5 objectives and up to 13 inequality constraints. These problems include well-known benchmark problems and application problems in manufacturing and robotics. The numerical results showed that the RBF-assisted ES generally outperformed the original ES and NSGA-II on the problems used when the computational budget is relatively limited. These results suggest that the proposed surrogate-assisted ES is promising for computationally expensive constrained multi-objective optimization. [ABSTRACT FROM AUTHOR]

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 . [ABSTRACT FROM AUTHOR]

In this paper, the concept of multi-objective optimization is introduced in the automation of the placement task in analog integrated circuits layout design. To bridge the difficulties found on state-of-the-art works on fulfilling proximity constraints, here, cells are organized into proximity groups which implement the desired set of symmetry and proximity requirements. Then, an innovative archived-based multi-objective simulated annealing algorithm, operating over an absolute representation, is proposed to optimize the placement of each proximity group. In contrast to traditional single-objective placement approaches, the resulting Pareto fronts of placements, representing the tradeoffs between the optimization objectives of each group, are combined, bottom-up, through the design hierarchy, until a final front is obtained. This way, the problem's complexity is reduced, and split over multiple executions of the optimization kernel with less design variables, and also, analog designer becomes aware of the design tradeoffs. The proposed multi-objective and hierarchical methodology was implemented, and, experimental results prove that previous efforts on single-objective absolute representations are no match for the obtained floorplans. Furthermore, the obtained Pareto fronts contain the solutions found with the most recent published topological representations for the well-known Microelectronics Center of North Carolina benchmark sets, and, allowed an improvement of placement area up to 23% on a previously optimized folded cascode operational amplifier for the United Microelectronics Corporation 0.13 μm fabrication process. [ABSTRACT FROM AUTHOR]

In the quest for greater autonomy, there is an increasing need for solutions that would enable a large set of robots to coalesce and perform complicated multi-robot tasks. This problem, also known as the multi-robot coalition formation problem has been traditionally approached as a single objective optimization problem. However, robots in the real world have to optimize multiple conflicting criteria such as battery life, number of completed tasks, and distance traveled. Researchers have only recently addressed the robot coalition formation problem as a multi-objective optimization problem, however the proposed solutions have computational bottlenecks that make them unsuitable for real time robotic applications. In this paper we address the issue of scalability by proposing parallelized algorithms in the CUDA programming framework. NSGA-II and PAES algorithm have been parallelized due to their suitability to the coalition formation domain as outlined in our previous work. The parallelized versions of these algorithms have been applied to both the additive and non-additive coalition formation environments. Simulations have been performed in the player/stage environment to validate the applicability of our approach to real robot situations. Results establish that the multi-point PAES parallel variant yields significant performance gains in terms of running time and solution quality when the problem is scaled to deal with large inputs. This suggests that the algorithm may be viable for real time robotic applications. Experiments demonstrate significant speedup when the proposed parallel algorithms were compared with the serial solutions proposed earlier. [ABSTRACT FROM AUTHOR]

Students generally attempt to improve themselves with different manners in their spare time. Inspired by this fact, this paper presents a multi-objective elitist feedback teaching–learning-based optimization (MEFTO) algorithm for multi-objective optimization problems. To promote the exploration capacity and convergence of the basic teaching–learning-based optimization (TLBO), a feedback phase that simulates the spare-time learning phenomenon is introduced at the end of the learner phase. Students should compare their score with the average class score to select an appropriate means for further improvement. Poorly performing students can learn from the teacher directly for rapid improvement, whereas high-performing students prefer to motivate themselves for reinforcement learning. Non-dominated sorting is incorporated to permit this heuristic to solve problems with several objectives. Crowding distance calculation is adopted to maintain the diversity of the obtained solution set in a single run. Elitism strategy is also employed to provide a great improvement for the algorithm. The performance of the MEFTO algorithm is compared with seven other well-known algorithms by using a set of unconstrained benchmark test problems and three constrained engineering optimization problems. The qualitative and quantitative results indicate that the proposed algorithm can provide considerably competitive results and outperforms the other algorithms. • A novel multi-objective evolutionary algorithm (MEFTO) is developed. • The developed algorithm is evaluated on a series of benchmark functions. • The performance of the MEFTO is demonstrated using various metrics. • The developed algorithm is applied to solve three constrained engineering problem. [ABSTRACT FROM AUTHOR]

• A two-stage evolution strategy is proposed for solving multi-objective problem. • The convergence and diversity should be balanced in multi-objective optimization. • A local searching method can improve the diversity of solutions in the space. • Experimental results have been presented by using statistical method. The balance of convergence and diversity plays a significant role to the performance of multi-objective evolutionary algorithms (MOEAs). The MOEA/D is a very popular multi-objective optimization algorithm and has been used to solve various real world problems. Like many other algorithms, the MOEA/D also has insufficient ability of convergence and diversity when tackling certain complex multi-objective optimization problems (MOPs). In this paper, a novel algorithm named MOEA/D-TS is proposed for effectively solving MOPs. The new algorithm adopts two stages evolution strategies, the first stage is focused on pushing the solutions into the area of the Pareto front and speeding up its convergence ability, after that, the second stage conducts in the operating solution's diversity and makes the solutions distributed uniformly. The performance of MOEA/D-TS is validated in the ZDT, DTLZ and IMOP problems. Compared with others popular and variants algorithms, the experimental results demonstrate that the proposed algorithm has advantage over other algorithms with regard to the convergence and diversity in most of the tested problems. [ABSTRACT FROM AUTHOR]

• A novel multi-objective feature selection algorithm is proposed. • It hybridizes filter and wrapper models into whale optimization algorithm. • It has been validated through ten datasets and compared against five algorithms. • Yields solutions with fewer features and improves the classification accuracy. Feature selection aims at finding the minimum number of features that result in high classification accuracy. Accordingly, the feature selection is considered as a multi-objective problem. However, most existing approaches treat feature selection as single-objective problem, and they are often divided into two main categories: filter and wrapper methods. Filters are known as fast methods but less accurate, while wrappers are computationally expensive but with high classification performance. This paper proposes a novel hybrid filter-wrapper feature selection approach using whale optimization algorithm (WOA). The proposed method is a multi-objective algorithm in which a filter and wrapper fitness functions are optimized simultaneously. Our algorithm's efficiency is demonstrated through an extensive comparison with seven well-known algorithms on twelve benchmark datasets. Experimental results show the ability of the proposed algorithm to obtain several subsets that include smaller number of features with excellent classification accuracy. [ABSTRACT FROM AUTHOR]

• A new multi-objective wrapper method based on Forest Optimization (MOFOA) is proposed. • MOFOA uses archive, grid, and region-based selection to maintain Pareto front. • Two continues and binary versions of MOFOA is presented to solve features selection. • Continuous version of MOFOA outperforms other multi-objective algorithms. • The performance of MOFOA was confirmed by quantitative and qualitative analyses. Feature selection is one of the important techniques of dimensionality reduction in data preprocessing because datasets generally have redundant and irrelevant features that adversely affect the performance and complexity of classification models. Feature selection has two main objectives, i.e., reducing the number of features and increasing classification performance due to its inherent nature. In this paper, we propose a multi-objective feature selection algorithm based on forest optimization algorithm (FOA) using the archive, grid, and region-based selection concepts. For this purpose, two versions of the proposed algorithm are developed using continuous and binary representations. The performance of the proposed algorithms is investigated on nine UCI datasets and two microarray datasets. Next, the obtained results are compared with seven traditional single-objective and five multi-objective methods. Based on the results, both proposed algorithms have reached the same performance or even outperformed the single-objective methods. Compared with other multi-objective algorithms, MOFOA with continuous representation has managed to reduce the classification error in most cases by selecting less number of features than other methods. [ABSTRACT FROM AUTHOR]

Manufacturing industries frequently encounter production scheduling problems containing device dynamic reconfiguration processes (DRP). DRP refers to dynamic device adjustments (such as replacement of tools), leading to changes in the devices' actual processing time. It has a severe impact on the production schedule. Nevertheless, there is scarcely research upon hybrid flow shop scheduling problem (HFSP) with DRP. Besides, it is necessary to consider multiple conflict objectives in the HFSP. Thus, the multi-objective HFSP with DRP (MOHFSP-DRP) is significant in both theoretical research and application. This paper first proposes a multi-objective mathematical model (MOHFSP-DRP) that simultaneously considers the DRP and devices' adjustable processing modes. The bi-objective of this model is to minimize both the makespan and the whole device's energy consumption. This study then proposes an improved multi-objective whale optimization algorithm (IMOWOA) to solve the MOHFSP-DRP and obtain the Pareto-based optimal solution set. After that, to verify the proposed method's effectiveness, numerical experiments are implemented based on the real-world cases in a Chinese company's digital hot-rolling workshop. Results denote that the presented IMOWOA is superior to SPEA2 and NSGA-II. Finally, the MOHFSP-DRP model and IMOWOA are applied to a real-world hot-rolling shop successfully. The real-world cases verify the proposed IMOWOA can tackle the presented MOHFSP-DRP very well. [ABSTRACT FROM AUTHOR]

• A new multi-objective optimization method used OBL strategy, WOA and DE algorithms • It combines DE and the OBL to improve the performance of the WOA • The MWDEO results outperformed all other algorithms in most of the test problems • 32 multi-objective test problems are used in the experiments and CEC2017 problems The optimization problems are divided into a single objective and multi-objective. Single objective optimization has only one objective function; whereas, multi-objective optimization has multiple objective functions that generate the Pareto set; therefore, solving a multi-objective problem is a challenging problem. This paper presents a new multi-objective optimization method (called MWDEO) based on improved whale optimization algorithm (WOA) by combining the differential evolution (DE) algorithm and the opposition-based learning (OBL). The MWDEO uses the WOA to perform a global exploration, whereas DE is used to exploit the search space; while the OBL is applied to improve the exploration and exploitation by generating the opposite values. The proposed algorithm is evaluated using 32 multi-objective test problems besides a set of benchmark problems of CEC'2017. The experimental results are compared with nine state-of-the-art multi-objective methods. The analysis of the results showed that the proposed MWDEO outperformed all other algorithms in most of the test problems which indicates that the proposed MWDEO is competitive and effective in solving different types of multi-objective problems. [ABSTRACT FROM AUTHOR]

• The proposed algorithm ranks the optimal solutions based on its quality. • All non-dominated (optimal) solutions are completely ranked. • User can choose to have top K solutions. K = user defined value. • This algorithm is parameter-free and easy to use to find the best solution(s). This paper presents a solution ranking algorithm to find the outstanding solutions in given set of non-dominated solutions of multi-objective optimization problems, which are the results from either Multi-Objective Evolutionary Algorithms (MOEAs) or exact methods. The algorithm enables the decision makers to identify outstanding solutions without a deep understanding of the problem. The algorithm provides a ranking for all solutions so that they can obtain any top K ranked solutions to implement. This novel parameter-free solution ranking approach is based on two concepts: an extended angle-based dominance technique from the algorithm called ADaptive angle-based pruning Algorithm (ADA) for discovering the knee solutions and the inverse-square law of light for enhancing the diversity of solutions. We evaluate the performance of the approach on several well-known test problems against well-known knee finding algorithms as well as on a practical system design and optimization problem to demonstrate the usefulness of the algorithm. [ABSTRACT FROM AUTHOR]