Kalyanmoy Deb's research while affiliated with Michigan State University and other places
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Publications (155)
Various dominance structures have been proposed in the multi-objective optimization literature. However, a systematic procedure to understand their effect in determining the resulting optimal set for generic domination principles, besides the standard Pareto-dominance principle, is lacking. In this paper, we analyze and lay out properties of genera...
The insights and benefits to be realised through the optimisation of multiple independent, but conflicting objectives are well recognised by practitioners seeking effective and robust solutions to real-world application problems. Key issues encountered by users of many-objective optimisation (>3 objectives) in a real-world environment are discussed...
The series of non-dominated sorting based genetic algorithms (NSGA-series) has clearly shown their niche in solving multi- and many-objective optimization problems since mid-nineties. Of them, NSGA-III was designed to solve problems having three or more objectives efficiently. It is well established that with an increase in number of objectives, an...
Evolutionary multi-objective and many-objective optimization (EMO and EMaO) algorithms are increasingly being used to identify the true shape and location of the Paretooptimal front using a few representative well-converged and welldistributed solutions. The reason for their popularity is due to their ability to provide a better understanding of ob...
To solve complex real-world problems, heuristics and concept-based approaches can be used to incorporate information into the problem. In this study, a concept-based approach called variable functioning ( Fx ) is introduced to reduce the optimization variables and narrow down the search space. In this method, the relationships among one or more sub...
This work aims at reviewing the state of the art of the field of lex-icographic multi/many-objective optimization. The discussion starts with a review of the literature, emphasizing the numerous application in the real life and the recent burst received by the advent of new computational frameworks which work well in such contexts, e.g., Grossone M...
The practicality of Pareto-dominance in solving many-objective optimization problems becomes questionable due to its inability to factor the critical Human Decision-making (HDM) elements, including, the number of better objectives, the degree of betterment in objectives, and objectives’ relative preference. Relevant dominance principles are recentl...
One of the crucial challenges of solving many-objective optimization problems is uniformly well covering of the Pareto-front (PF). However, many the state-of-the-art optimization algorithms are capable of approximating the shape of many-objective PF by generating a limited number of non-dominated solutions. The exponential increase of the populatio...
To solve complex real-world problems, heuristics and concept-based approaches can be used in order to incorporate information into the problem. In this study, a concept-based approach called variable functioning Fx is introduced to reduce the optimization variables and narrow down the search space. In this method, the relationships among one or mor...
In the context of optimization, visualization techniques can be useful for understanding the behaviour of optimization algorithms and can even provide a means to facilitate human interaction with an optimizer. Towards this goal, an image-based visualization framework, without dimension reduction, that visualizes the solutions to large-scale global...
NSGA-II is an evolutionary multi-objective optimization algorithm that has been applied to a wide variety of search and optimization problems since its publication in 2000. This study presents a review and bibliometric analysis of numerous NSGA-II adaptations in addressing scheduling problems. This paper is divided into two parts. The first part di...
This chapter introduces a new class of optimization problems, called Mixed Pareto-Lexicographic Multi-objective Optimization Problems (MPL-MOPs), to provide a suitable model for scenarios where some objectives have priority over some others. Specifically, this work focuses on two relevant subclasses of MPL-MOPs, namely optimization problems having...
Innovization is a task of learning common relationships among some or all of the Pareto-optimal (PO) solutions in multi-and many-objective optimization problems. A recent study has shown that a chronological sequence of non-dominated solutions obtained along the successive generations of an optimizer possesses salient patterns that can be learnt us...
Visual representation of a many-objective Pareto-optimal front in a high-dimensional (four or more) objective space requires a large number of data points. Choosing a single point from a large number of data points even with preference information is problematic, as it causes a large cognitive burden on the part of the decision-makers. Therefore, m...
Dominance move (DoM) is a binary quality indicator that can be used in multiobjective and many-objective optimization to compare two solution sets obtained from different simulations. The DoM indicator can differentiate the sets for certain important features, such as
convergence
,
spread
,
uniformity
, and
cardinality
. DoM does not requir...
Multi-objective evolutionary algorithms (MOEAs) are commonly applied to treat multi-objective optimization problems (MOPs) due to their global nature, robustness, and reliability. However, it is also well known that MOEAs need quite a few resources to compute a good approximation of the Pareto set/front. Even more, MOEAs may exhibit difficulties wh...
This paper concerns the study of Mixed Pareto-Lexicographic Multi-objective Optimization Problems where the objectives must be partitioned in multiple priority levels. A priority level (PL) is a group of objectives having the same importance in terms of optimization and subsequent decision-making, while between PLs a lexicographic ordering exists....
This paper studies a class of mixed Pareto-Lexicographic multi-objective optimization problems where the preference among the objectives is available in different priority levels (PLs) before the start of the optimization process – akin to many practical problems involving domain experts. Each priority level (PL) is a group of objectives having an...
Most optimization-based community detection approaches formulate the problem in a single- or bi-objective framework. In this paper, we propose two variants of a three-objective function optimization formulation using a customized non-dominated sorting genetic algorithm III (NSGA-III) to find community structures in a network. The first variant, nam...
Bioenergy is becoming increasingly relevant as an alternative to fossil fuels. Various bioenergy feedstocks are suggested as environmentally friendly solutions due to their positive impact on stream health and ability to sequester carbon, but most evaluations for bioenergy feedstocks have not evaluated the implications of bioenergy crop production...
This paper presents a new method to solve the Maximum Edge Disjoint Paths (MEDP) problem. Given a set of node pairs within a network, the MEDP problem is the task of finding the largest number of pairs that can be connected by paths, using each edge within the network at most once. We present a heuristic algorithm that builds a hybridisation of Lag...
Dominance move (DoM) is a binary quality indicator that can be used in multi-objective and many-objective optimization to compare two solution sets obtained from different algorithms. The DoM indicator can differentiate the sets for certain important features, such as \textit{convergence}, \textit{spread}, \textit{uniformity}, and \textit{cardinali...
In this paper, we address an online dimensionality reduction approach to deal with a many-objective formulation of a Vehicle Routing Problem with a Demand Responsive Transport (VRPDRT). The problem relates to a mode of transport similar to available carpooling services in which passengers are transported from their origin to their destination shari...
In the context of optimization, visualization techniques can be useful for understanding the behaviour of optimization algorithms and can even provide a means to facilitate human interaction with an optimizer. Towards this goal, an image-based visualization framework, without dimension reduction, that visualizes the solutions to large-scale global...
Automated Innovization procedure aims to extract hidden, non-intuitive, closed-form relationships from a design task without human intervention. Existing procedures involve the application of an Evolutionary Multi-objective Optimization Algorithm (EMOA) in two phases. The first phase of EMOA leads to a set of Pareto-optimal (PO) solutions, while th...
One of the main success stories in the evolutionary computation (EC) field is the use of EC framework to solve multi-criterion optimization problems. These problems give rise to a set of trade-off Pareto-optimal solutions, instead of a single optimal solution; hence a population-based EC framework is a natural choice for solving them. Starting in t...
The ranking of multi-metric scientific achievements is a challenging task. For example, the scientific ranking of researchers utilizes two major types of indicators; namely, number of publications and citations. In fact, they focus on how to select proper indicators, considering only one indicator or combination of them. The majority of ranking met...
Most optimization-based community detection approaches formulate the problem in a single or bi-objective framework. In this paper, we propose two variants of a three-objective formulation using a customized non-dominated sorting genetic algorithm III (NSGA-III) to find community structures in a network. In the first variant, named NSGA-III-KRM, we...
Real-world optimization problems usually involve constraints and sometimes even finding a single feasible solution is a challenging task. This study introduces a new approach for implicitly handling constraints. The proposed approach reduces the consideration of infeasible solutions by directly updating variable bounds with constraints, which is ca...
Considerable academic research has been conducted on truss design optimization by standard metaheuristic methods; however, the generic nature of these methods becomes inefficient for problems with many decision variables. This may explain the simplicity of the relevant test problems in the academic literature in comparison with real structures. To...
The ultimate goal of multiobjective optimization is to help a decision maker (DM) identify solution(s) of interest (SOI) achieving satisfactory tradeoffs among multiple conflicting criteria. This can be realized by leveraging DM’s preference information in evolutionary multiobjective optimization (EMO). No consensus has been reached on the effectiv...
Scalarization refers to a generic class of methods to combine multiple conflicting objectives into one in order to find a Pareto optimal solution to the original problem. Augmented achievement scalarizing function (AASF) is one such method used popularly in the multi-criterion decision-making (MCDM) field. In evolutionary multi-objective optimizati...
Search-Based Software Engineering (SBSE) is a promising paradigm that exploits computational search to optimize different processes when engineering complex software systems. Self-adaptive system (SAS) is one category of such complex systems that permits to optimize different functional and non-functional objectives/criteria under changing environm...
Network models are widely used for solving difficult real-world problems. The minimum cost flow problem (MCFP) is one of the fundamental network optimisation problems with many practical applications. The difficulty of MCFP depends heavily on the shape of its cost function. A common approach to tackle MCFPs is to relax the non-convex, mixed-integer...
The ultimate goal of multi-objective optimisation is to help a decision maker (DM) identify solution(s) of interest (SOI) achieving satisfactory trade-offs among multiple conflicting criteria. This can be realised by leveraging DM's preference information in evolutionary multi-objective optimisation (EMO). No consensus has been reached on the effec...
Multi-objective problems (MOP) are of significant interest to both multi-criteria decision making (MCDM) and evolutionary multi-objective (EMO) research communities. A core technique common in both is scalarization, which combines multiple objectives into one in a way that solving it provides a solution to the original MOP. In this paper, we look c...
Currently, evolutionary multiobjective optimization (EMO) algorithms have been successfully used to find a good approximation of many-objective optimization problems (MaOPs). To measure the performance of EMO algorithms, many benchmark multiobjective test problems have been constructed. Among them, DTLZ and WFG are two representative test suites wi...
In this study, the concept of a semi-independent variable (SIV) problem representation is investigated that embodies a set of expected or desired relationships among the original variables, with the goal of increasing search effectiveness and efficiency. The proposed approach intends to eliminate the generation of infeasible solutions associated wi...
Scheduling and planning problems are generally complex, large-scale, challenging issues, and involve several constraints. To find a practical solution for these problems, most real-world problems must be formulated as discrete or mixed variable optimization problems. Moreover, finding efficient and lower cost procedures for frequent use of the syst...
Distributing of the multi-objective evolutionary algorithms into various computational devices in a parallel fashion is a method for speeding up the execution time of the algorithms. When the processors are increased in number, the gain from parallelization decreases. For this reason, the aim of the parallelization method is not only to decrease th...
Due to the significant costs associated with stream health monitoring, hydrological modeling is widely used to calculate ecologically-relevant hydrologic indices to better understand the overall condition of streams within large and diverse watersheds. However, hydrologic modeling's ability to replicate these indices is limited, especially when cal...
Testing and performance comparisons for optimization algorithms and methods are an important part of demonstrating accurate behavior. These tests are accomplished using numerical and graphical illustrations of the results obtained from the proposed algorithms. To emphasize the advantages and disadvantages of the proposed approaches and algorithms,...
As the number of objectives and/or dimension of a given problem increases, or a real-world optimization problem is modeled in more detail, the optimization algorithm requires more computation time if the computational resources are fixed. Therefore, some more tools are needed to be developed for deployment of these resources. The parallelization is...
One of the main difficulties in applying an optimization algorithm to a practical problem is that evaluation of objectives and constraints often involve computationally expensive procedures. To handle such problems, a metamodel is first formed from a few exact (high-fidelity) solution evaluations and then optimized by an algorithm in a progressive...
Nondominated sorting is a key operation used in multiobjective evolutionary algorithms (MOEA). Worst case time complexity of this algorithm is O(MN
<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup>
), where N is the number of solutions and M is the number of objectives. For stochastic algorithms...
Solutions to most practical numerical optimization problems must be evaluated for their performance over a number of different loading or operating conditions, which we refer here as scenarios. Therefore, a meaningful and resilient optimal solution must be such that it remains feasible under all scenarios and performs close to an individual optimal...
This study proposes a novel procedure for generating parametric scalable functions with diverse properties to strengthen numerical evaluation of niching methods. It combines three simple basic functions to form a composite multimodal function, in which the function parameter controls the number of global minima. The resultant composite function may...
This report presents the benchmarking results of Covariance Matrix Self Adaption Evolution Strategy with Repelling Subpopulations (RS-CMSA) on the CEC2013 test suite. The benchmarking follows restrictions required by GECCO 2017 competition on multimodal optimization. In particular, no problem dependent parameter tuning is performed. A few minor mod...
Mapping irrigated area, frequency, timing, and amount is important for sustainable management of water resources in semi-arid and arid regions. Various studies exist on the mapping of irrigation using remote sensing and census statistics, but they mainly focus on the mapping of irrigation extent without taking frequency and timing into account. In...
This paper proposes a push and pull search (PPS) framework for solving constrained multi-objective optimization problems (CMOPs). To be more specific, the proposed PPS divides the search process into two different stages, including the push and pull search stages. In the push stage, a multi-objective evolutionary algorithm (MOEA) is adopted to expl...
Opposition-based Learning (OBL) is a new concept in machine learning, inspired from the opposite relationship among entities. In 2005, for the first time the concept of opposition was introduced which has attracted a lot of research efforts in the last decade. Variety of soft computing algorithms such as, optimization methods, reinforcement learnin...
So far the focus of almost all multi- or many-objective performance metrics has been the convergence and distribution of solutions in the objective space (Pareto-surface). Pareto-surface metrics such as IGD, HV, and Spread are simple and provide knowledge about the overall performance of the solution set. However, these measures do not provide any...
MATLAB code of the niching test problems proposed in ”A Novel Class of Test Problems for Performance Evaluation of Niching Methods”
Most real-world optimization problems involve computationally expensive simulations for evaluating a solution. Despite significant progress in the use of metamodels for single-objective optimization, metamodeling methods have received a lukewarm attention for multi-objective optimization. A recent study classified various metamodeling approaches, o...
In many optimization problems, one of the goals is to determine the optimal number of analogous components to include in the system. Examples include the number of sensors in a sensor coverage problem, the number of turbines in a wind farm problem, and the number of plies in a laminate stacking problem. Using standard approaches to solve these prob...
Financial Time Series Prediction is a complex and a challenging problem. In this paper, we propose two 3-stage hybrid prediction models wherein Chaos theory is used to construct phase space (Stage-1) followed by invoking Multi-Layer Perceptron (MLP) (Stage-2) and Multi-Objective Particle Swarm Optimization (MOPSO) / elitist Non-dominated Sorting Ge...
Inspired by the lateral line of aquatic vertebrates, an artificial lateral line (ALL) system can localize and track an underwater moving object by analyzing the ambient flow caused by its motion. There are several studies on object detection, localization and tracking by ALL systems, but only a few have investigated the optimal design of the ALL sy...
In many practical optimization problems, evaluation of ob-
jectives and constraints often involve computationally expensive proce-
dures. To handle such problems, a metamodel-assisted approach is usu-
ally used to complete an optimization run in a reasonable amount of
time. A metamodel is an approximate mathematical model of an ob-
jective or a con...
Material flow in a chemical processing plant often follows complicated control laws and involves plant capacity constraints. Importantly, the process involves discrete scenarios which when modelled in a programming format involves if–then–else statements. Therefore, a formulation of an optimization problem of such processes becomes complicated with...
This paper investigates a curious case of informed initialization technique to solve difficult multi-objective optimization (MOP) problems. The initial population was injected with non-exact (i.e. approximated) nadir objective vectors, which are the boundary solutions of a Pareto optimal front (PF). The algorithm then successively improves those bo...
In many practical optimization problems, evaluation of objectives and constraints often involve computationally expensive procedures. To handle such problems, a metamodel-assisted approach is usually used to complete an optimization run in a reasonable amount of time. A metamodel is an approximate mathematical model of an objective or a constrained...
This publication investigates characteristics of and algorithms for the quite new and complex Bi-Objective Traveling Thief Problem, where the well-known Traveling Salesman Problem and Binary Knapsack Problem interact. The interdependence of these two components builds an interwoven system where solving one subproblem separately does not solve the o...
With recent advancements of multi- or many-objective optimization algorithms, researchers and decision-makers are increasingly faced with the dilemma of choosing the best algorithm to solve their problems. In this paper, we propose a simple hybridization of population-based multi- or many-objective optimization algorithms called fusion of non-domin...
Among various complexities affecting the performance of an optimization algorithm, the search space dimension is a major factor. Another key complexity is the discreteness of the search space. When these two complexities are present in a single problem, optimization algorithms have been demonstrated to be inefficient, even in linear programming (LP...
In order to better understand the advantages and disadvantages of a constrained multi-objective evolutionary algorithm (CMOEA), it is important to understand the nature of difficulty of a constrained multi-objective optimization problem (CMOP) that the CMOEA is going to deal with. In this paper, we first propose three primary types of difficulty to...
Multi-Modal Optimization (MMO) aiming to locate multiple optimal (or near-optimal) solutions in a single simulation run has practical relevance to problem solving across many fields. Population-based meta-heuristics have been shown particularly effective in solving MMO problems, if equipped with specificallydesigned diversity-preserving mechanisms,...
Opposition based learning (OBL) has been gaining significant attention in machine learning, specially, in metaheuristic optimization algorithms to take OBL's advantage for enhancing their performance. In OBL, all variables are changed to their opposites while some variables are currently holding proper values which are discarded and converted to wo...
There are two main tasks involved in addressing a multi-objective optimization problem (MOP) by evolutionary multi-objective (EMO) algorithms: (i) make the population converge close to the Pareto-optimal front (PF), and (ii) maintain adequate population diversity. However, most state-of-the-art EMO algorithms are designed based on the ‘convergence...
With the availability of different types of power generators to be used in an electric micro-grid system, their operation scheduling as the load demand changes with time becomes an important task. Besides satisfying load balance constraints and the generator's rated power, several other practicalities, such as limited availability of grid power and...
Reference point based optimization offers tools for the effective treatment of preference based multi-objective optimization problems, e.g. when the decision-maker has a rough idea about the target objective values. For the numerical solution of such problems, specialized evolutionary strategies have become popular, despite their possible slow conv...
