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This article proposes an alternative constraint handling technique for the four-bar linkage path generation problem. The constraint handling technique that is traditionally applied uses an exterior penalty function, and has been found to be inefficient, particularly when dealing with constraints on the input angles. The new technique deals with both input crank rotation and Grashof's criterion. Four classical path generation problems are used to test the performance of the proposed technique. A new adaptive teaching–learning-based optimization (TLBO) scheme is used to solve several optimization problems. This technique is referred to here as teaching–learning-based optimization with a diversity archive (ATLBO-DA), and was specifically developed for this design problem. The results show that this new design concept gives better results than those of previous work, and that ATLBO-DA is superior to the original version and other metaheuristic algorithms. [ABSTRACT FROM AUTHOR]

In this manuscript we present an original implementation of network management functions in the context of Software Defined Networking. We demonstrate a full integration of an artificial intelligence driven management, an SDN control plane, and a programmable data plane. Constraint Programming is used to implement a management operating system that accepts high level specifications, via a northbound interface, in terms of operational objective and directives. These are translated in technology-specific constraints and directives for the SDN control plane, leveraging the programmable data plane, which is enriched with functionalities suited to feed data that enable the most effective operation of the “intelligent” control plane, by exploiting the P4 language. [ABSTRACT FROM AUTHOR]

Summary: This article presents an algorithm for constraining shape deformations in adjoint‐based aerodynamic shape optimization. The algorithm considers known bounding surfaces and constrains the shape undergoing optimization not to intersect with them. For each and every node on the shape, its signed distance to the bounding surfaces is computed. The signed distance function returns a positive value, in case a node lies outside the bounds, or a negative one otherwise. It can, therefore, serve as an inequality constraint, the satisfaction of which ensures that this node does not violate the no‐intersection criteria. To increase the efficiency and make this imposition of constraints usable with any parameterization scheme, the resulting inequality constraints are transformed to a single‐equality constraint by means of a penalty function which is, then, summed over the shape to be optimized. The shape parameterization used in this article is spline‐based but this is not restrictive and any other parameterization type (node‐based, RBF, etc) can be used instead. The gradient of the objective function of the aerodynamic problem with respect to the design variables defined by the parameterization is computed using the continuous adjoint method. The method is demonstrated in the optimization of a 2D manifold case and two industrial‐like cases including the shape optimization of a U‐bend cooling duct, constrained to stay within a box, and the side mirror of a passenger car constrained to retain an almost undeformed reflector glass. [ABSTRACT FROM AUTHOR]

Constrained multiobjective optimization problems (CMOPs) are challenging because of the difficulty in handling both multiple objectives and constraints. While some evolutionary algorithms have demonstrated high performance on most CMOPs, they exhibit bad convergence or diversity performance on CMOPs with small feasible regions. To remedy this issue, this article proposes a coevolutionary framework for constrained multiobjective optimization, which solves a complex CMOP assisted by a simple helper problem. The proposed framework evolves one population to solve the original CMOP and evolves another population to solve a helper problem derived from the original one. While the two populations are evolved by the same optimizer separately, the assistance in solving the original CMOP is achieved by sharing useful information between the two populations. In the experiments, the proposed framework is compared to several state-of-the-art algorithms tailored for CMOPs. High competitiveness of the proposed framework is demonstrated by applying it to 47 benchmark CMOPs and the vehicle routing problem with time windows. [ABSTRACT FROM AUTHOR]

While evolutionary algorithms are known among the best methods for solving both theoretical and real-world optimization problems, constraint handling is still one of the major concerns. Common constraint handling methods reject or devalue infeasible solutions depending on their distance from the feasible space, even if they dominate feasible solutions. Alternatively, repair methods aim to overcome infeasibility, but they are currently limited to specific types of problems. In this paper, we propose a more generic repair approach to improve efficiency of constraint handling in non-dominance based genetic algorithm. We start by identifying variables which influence each constraint. This information is used to replace variable values that caused constraint violation, using other solutions in the current generation. Repairing is carried out on the solutions that dominate all feasible members of the population, or have the smallest constraint violation. The repair approach is implemented into NSGA-II and tested on one optimization test case and an engineering optimization problem. The latter focuses on structural design of a ship hull girder, involving two conflicting objectives, 94 decision variables and 376 nonlinear constraints. The proposed repairing approach reduces drastically the number of function evaluations needed to find the feasible space, and it leads to faster convergence and better spread of the non-dominated front. Starting from different random populations, the new algorithm finds feasible solutions within one generation, while the original algorithm takes between 7 and 72 generations. Effectiveness of the optimization is analyzed in terms of the hypervolume performance metric. The repairing algorithm obtains significantly better hypervolume values throughout the optimization run. The highest improvements are achieved in the initial phase of the optimization, which is important for the practical design. The new algorithm performs better than two constraint handling approaches from the literature. It also outperforms MOEA/D algorithm in the engineering problem. • A new repair-type constraint-handling approach is proposed for multi-objective problems. • Solutions are repaired using information from other members of the population. • User is required to identify which variables influence constraints the most. • Less function evaluations must be performed to find the feasible space. • Faster convergence is obtained with larger spread of the non-dominated front. [ABSTRACT FROM AUTHOR]

In this paper, an efficient fitness-based differential evolution (EFDE) algorithm and a constraint handling technique for dynamic economic emission dispatch (DEED) are proposed. In EFDE, there are three improvements compared to the standard differential evolution (DE) algorithm. First, an archive containing the current and previous population is established to provide more candidate solutions. Second, two mutation strategies are used to generate mutant individuals, where the population similarity is introduced to choose a suitable one between DE/rand/1 and DE/best/1. The fitness-based mutation operation is efficient to balance the exploration and exploitation ability of EFDE. Third, EFDE adopts a random-based mutation factor, and the crossover rate with the learning ability is developed to produce more excellent solutions. In addition, the infeasible solutions can be effectively avoided by the proposed repair technique. Four cases are selected to judge the performance of the proposed EFDE and constraint handling technique. For the fuel cost and emission minimizations of four DEED cases, a normalized approach (NA) is used to help EFDE to find the best compromise solutions in the evolution process. According to the simulation results, EFDE exhibits a huge advantage in comparison with the other approaches for the single-objective and multi-objective optimization problems. • An efficient fitness-based differential evolution (EFDE) algorithm is developed. • EFDE is used to solve dynamic economic emission dispatch problems. • A constraint handling mechanism helps EFDE to rapidly find feasible solutions. • A multi-objective optimization method is used to trade off the cost and emission. • The proposed methods can obtain desirable feasible solutions. [ABSTRACT FROM AUTHOR]

Mixed-variable optimization problems consist of the continuous, integer, and discrete variables generally used in various engineering optimization problems. These variables increase the computational cost and complexity of optimization problems due to the handling of variables. Moreover, there are few optimization algorithms that give a globally optimal solution for non-differential and non-convex objective functions. Initially, the Jaya algorithm has been developed for continuous variable optimization problems. In this paper, the Jaya algorithm is further extended for solving mixed-variable optimization problems. In the proposed algorithm, continuous variables remain in the continuous domain while continuous domains of discrete and integer variables are converted into discrete and integer domains applying bound constraint of the middle point of corresponding two consecutive values of discrete and integer variables. The effectiveness of the proposed algorithm is evaluated through examples of mixed-variable optimization problems taken from previous research works, and optimum solutions are validated with other mixed-variable optimization algorithms. The proposed algorithm is also applied to two-plane balancing of the unbalanced rigid threshing rotor, using the number of balance masses on plane 1 and plane 2. It is found that the proposed algorithm is computationally more efficient and easier to use than other mixed optimization techniques.

Theoretical analyses of evolution strategies are indispensable for gaining a deep understanding of their inner workings. For constrained problems, rather simple problems are of interest in the current research. This work presents a theoretical analysis of a multi-recombinative evolution strategy with cumulative step size adaptation applied to a conically constrained linear optimization problem. The state of the strategy is modeled by random variables and a stochastic iterative mapping is introduced. For the analytical treatment, fluctuations are neglected and the mean value iterative system is considered. Nonlinear difference equations are derived based on one-generation progress rates. Based on that, expressions for the steady state of the mean value iterative system are derived. By comparison with real algorithm runs, it is shown that for the considered assumptions, the theoretical derivations are able to predict the dynamics and the steady state values of the real runs. [ABSTRACT FROM AUTHOR]

Enhanced indexation is an investment strategy that aims to generate moderate and consistent excess returns with respect to a tracked benchmark index. In this work, we introduce an optimization approach where the risk of under-performing the benchmark is separated from the potential over-performance, and the Sharpe ratio measures the profitability of the active management. In addition, a cardinality constraint controls the number of active positions in the portfolio, while a turnover threshold limits the transaction costs. We adopt a polynomial goal programming approach to combine these objectives with the investor's preferences. An improved version of the particle swarm optimization algorithm with a novel constraint-handling mechanism is proposed to solve the optimization problem. A numerical example, where the Euro Stoxx 50 Index is used as the benchmark, shows that our method consistently produces larger returns, with reduced costs and risk exposition, than the standard indexing strategies over a 10-year backtesting period. [ABSTRACT FROM AUTHOR]

Over recent decades, several efficient constraint-handling methods have been proposed in the area of evolutionary computation, and the ε constraint method is considered as a state-of-the-art method for both single and multiobjective optimization. Still, very few attempts have been made to improve this method when applied to the differential evolution algorithm. This study proposes several novel constraint-handling methods following similar ideas, where the ε level is defined based on the current violation in the population, individual ε levels are maintained for every constraint, and a combination of fitness and constraint violation is used for determining infeasible solutions. The proposed approaches demonstrate superior performance compared to other approaches in terms of the feasibility rate in high-dimensional search spaces, as well as convergence to global optima. The experiments are performed using the CEC'2017 constrained suite benchmark functions and a set of Economic Load Dispatch problems. [ABSTRACT FROM AUTHOR]

This study investigates the distributed stochastic model predictive control (DSMPC) algorithm design for a class of networked subsystems with stochastic disturbances and coupled probabilistic constraints, differently from the existing work, the network‐induced imperfections such as time‐varying delays and quantisation process are considered. A probabilistic constraint handling strategy and a novel DSMPC implementation algorithm are presented. In addition, according to the probabilistic distribution of the uncertainties, the probabilistic constraints are transformed into a set of determinate constraints. Although the closed‐loop system is affected by the time‐varying delays and quantisation process, the quadratic stability of the closed‐loop system and the feasibility of the optimisation problem can still be guaranteed with the developed algorithm. Finally, a numerical example is provided to illustrate the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

Combinatorial optimization problems are often considered NP-hard problems in the field of decision science and the industrial revolution. As a successful transformation to tackle complex dimensional problems, metaheuristic algorithms have been implemented in a wide area of combinatorial optimization problems. Metaheuristic algorithms have been evolved and modified with respect to the problem nature since it was recommended for the first time. As there is a growing interest in incorporating necessary methods to develop metaheuristics, there is a need to rediscover the recent advancement of metaheuristics in combinatorial optimization. From the authors’ point of view, there is still a lack of comprehensive surveys on current research directions. Therefore, a substantial part of this paper is devoted to analyzing and discussing the modern age metaheuristic algorithms that gained popular use in mostly cited combinatorial optimization problems such as vehicle routing problems, traveling salesman problems, and supply chain network design problems. A survey of seven different metaheuristic algorithms (which are proposed after 2000) for combinatorial optimization problems is carried out in this study, apart from conventional metaheuristics like simulated annealing, particle swarm optimization, and tabu search. These metaheuristics have been filtered through some key factors like easy parameter handling, the scope of hybridization as well as performance efficiency. In this study, a concise description of the framework of the selected algorithm is included. Finally, a technical analysis of the recent trends of implementation is discussed, along with the impacts of algorithm modification on performance, constraint handling strategy, the handling of multi-objective situations using hybridization, and future research opportunities.

A differential evolution algorithm (DE) is proposed to exactly satisfy the linear equality constraints present in a continuous optimization problem that may also include additional non-linear equality and inequality constraints. The proposed DE technique, denoted by DELEqC-II, is an extension of a previous method developed by the authors. In contrast to the previous approach, it uses both mutation and crossover strategies that maintain feasibility with respect to the linear equality constraints. Also, a procedure to correct numerical errors detected in the previous approach was incorporated in DELEqC-II. In the numerical experiments, scalable test-problems with linear equality constraints are used to analyze the performance of the new proposal. [ABSTRACT FROM AUTHOR]

The notion and characterisation of fitness landscapes has helped us understand the performance of heuristic algorithms on complex optimisation problems. Many practical problems, however, are constrained, and when significant areas of the search space are infeasible, researchers have intuitively resorted to a variety of constraint-handling techniques intended to help the algorithm manoeuvre through infeasible areas and toward feasible regions of better fitness. It is clear that providing constraint-related feedback to the algorithm to influence its choice of solutions overlays the violation landscape with the fitness landscape in unpredictable ways whose effects on the algorithm cannot be directly measured. In this work, we apply metrics of violation landscapes to continuous and combinatorial problems to characterise them. We relate this information to the relative performance of six well-known constraint-handling techniques to demonstrate how some properties of constrained landscapes favour particular constraint-handling approaches. For the problems with sampled feasible solutions, a bi-objective approach was the best performing approach overall, but other techniques performed better on problems with the most disjoint feasible areas. For the problems with no measurable feasibility, a feasibility ranking approach was the best performing approach overall, but other techniques performed better when the correlation between fitness values and the level of constraint violation was high. [ABSTRACT FROM AUTHOR]

This article introduces a new method entitled multi-objective feasibility enhanced partical swarm optimization (MOFEPSO), to handle highly-constrained multi-objective optimization problems. MOFEPSO, which is based on the particle swarm optimization technique, employs repositories of non-dominated and feasible positions (or solutions) to guide feasible particle flight. Unlike its counterparts, MOFEPSO does not require any feasible solutions in the initialized swarm. Additionally, objective functions are not assessed for infeasible particles. Such particles can only fly along sensitive directions, and particles are not allowed to move to a position where any previously satisfied constraints become violated. These unique features help MOFEPSO gradually increase the overall feasibility of the swarm and to finally attain the optimal solution. In this study, multi-objective versions of a classical gear-train optimization problem are also described. For the given problems, the article comparatively evaluates the performance of MOFEPSO against several popular optimization algorithms found in the literature. [ABSTRACT FROM AUTHOR]

In order to optimize multi-pass milling process, selection of optimal values for the parameters of the process is of great importance. The mathematical model for optimization of multi-pass milling process is a multi-constrained nonlinear programing formulation which is hard to be solved. Therefore, a novel robust meta-heuristic algorithm named Robust Grey Wolf Optimizer (RGWO) is proposed. In order to develop a RGWO, a robust design methodology named Taguchi method is utilized to tune the parameters of the algorithm. Therefore, in contradiction to previous researches, there is no need to design costly experiments to obtain the optimal values of the parameters of the GWO. In addition, an efficient constraint handling approach is implemented to handle complex constraints of the problem. A real-world problem is adopted to show the effectiveness and efficiency of the proposed RGWO in optimizing the milling process within different strategies. The results indicated that the RGWO outperforms the other solution methods in the literature as well as two novel meta-heuristic algorithms by obtaining better and feasible solutions for all cutting strategies. [ABSTRACT FROM AUTHOR]

Evolutionary optimization of reservoir operation is subject to complex physical and operational constraints. Constraint-handling techniques (CHTs) in this field are predominantly problem-specific or based on certain evolutionary algorithms; generally applicable CHTs are seldom tested against reservoir scheduling problems. This study proposes an independent CHT to accommodate the reservoir operation constraints, called the nondomination rank-based adaptive method (NRAM). The NRAM is straightforward to use and free of parameter tuning. The process emphasizes exploiting information from infeasible individuals and preserving them to promote convergence to global optima on a feasible space boundary. Moreover, the method adjusts the population composition dynamically to facilitate exploration or local search. The NRAM was applied to the hydropower scheduling of the Three Gorges Reservoir and Gezhouba Reservoir in China. Results show that the NRAM performs slightly better than three other well-regarded CHTs but requires mildly longer computational time. In addition, the genetic algorithm with the NRAM outperforms dynamic programming that is commonly used for hydropower scheduling. The operation schedules the NRAM provides are well suited for maximizing hydropower generation with all constraints satisfied. [ABSTRACT FROM AUTHOR]

We consider a scalable problem that has strong ties with real-world problems, can be compactly formulated and efficiently evaluated, yet is not trivial to solve and has interesting characteristics that differ from most commonly used benchmark problems: packing n circles in a square (CiaS).Recently, a first study that used basic Gaussian EDAs indicated that typically suggested algorithmic parameter settings do not necessarily transfer well to the CiaS problem. In this article, we consider also AMaLGaM, an enhanced Gaussian EDA, as well as arguably the most powerful real-valued black-box optimization algorithm to date, CMA-ES, which can also be seen as a further enhanced Gaussian EDA. We study whether the well-known performance on typical benchmark problems extends to the CiaS problem. We find that although the enhancements over a basic Gaussian EDA result in superior performance, the further efficiency enhancements in CMA-ES are not highly impactful. Instead, the most impactful features are how constraint handling is performed, how large the population size is, whether a full covariance matrix is used and whether restart techniques are used. We further show that a previously published version of AMaLGaM that does not require the user to set the the population size parameter is capable of solving the problem and we derive the scalability of the required number of function evaluations to solve the problem up to 99.99% of the known optimal value for up to 30 circles. [ABSTRACT FROM AUTHOR]

An empirical study of the algorithm dynamic differential evolution with combined variants with a repair method (DDECV $$+$$ Repair) in the solution of dynamic constrained optimization problems is presented. Unexplored aspects of the algorithm are of particular interest in this work: (1) the role of each one of its elements, (2) its sensitivity to different change frequencies and change severities in the objective function and the constraints, (3) its ability to detect a change and recover after it, besides its diversity handling (percentage of feasible and infeasible solutions) during the search, and (4) its performance with dynamism present in different parts of the problem. Seven performance measures, eighteen recently proposed test problems and eight algorithms found in the specialized literature are considered in four experiments. The statistically validated results indicate that DDECV $$+$$ Repair is robust to change frequency and severity variations, and that it is particularly fast to recover after a change in the environment, but highly depends on its repair method and its memory population to provide competitive results. DDECV $$+$$ Repair shows evidence on the convenience of keeping a proportion of infeasible solutions in the population when solving dynamic constrained optimization problems. Finally, DDECV $$+$$ Repair is highly competitive particularly when dynamism is present in both, objective function and constraints. [ABSTRACT FROM AUTHOR]

The artificial bee colony (ABC) algorithm is a global stochastic optimization algorithm inspired by simulating the foraging behavior of honey bees. It has been successfully applied to solve the constrained optimization problems (COPs) with a constraint handling technique (Deb's rules). However, it may also lead to premature convergence. In order to improve this problem, we propose an improved artificial bee colony (I-ABC) algorithm for COPs. In I-ABC algorithm, we firstly relax the Deb's rules by introducing the approximate feasible solutions to suitably utilize the information of the infeasible solutions with better objective function value and small violation. Next, we construct a selection strategy based on rank selection and design a search mechanism using the information of the best-so-far solution to balance the exploration and the exploitation at different stages. In addition, periodic boundary handling mode is used to repair invalid solutions. To verify the performance of I-ABC algorithm, 24 benchmark problems are employed and two comparison experiments have been carried out. The numerical results show that the proposed I-ABC algorithm has an outstanding performance for the COPs. [ABSTRACT FROM AUTHOR]

This paper describes the application of an evolutionary algorithm, Restart Covariance Matrix Adaptation Evolution Strategy (RCMA-ES) to the Generation Expansion Planning (GEP) problem. RCMA-ES is a class of continuous Evolutionary Algorithm (EA) derived from the concept of self-adaptation in evolution strategies, which adapts the covariance matrix of a multivariate normal search distribution. The original GEP problem is modified by incorporating Virtual Mapping Procedure (VMP). The GEP problem of a synthetic test systems for 6-year, 14-year and 24-year planning horizons having five types of candidate units is considered. Two different constraint-handling methods are incorporated and impact of each method has been compared. In addition, comparison and validation has also made with dynamic programming method.

This paper presents an alternative constraint handling approach within a specialized genetic algorithm (SGA) for the optimal reactive power dispatch (ORPD) problem. The ORPD is formulated as a nonlinear single-objective optimization problem aiming at minimizing power losses while keeping network constraints. The proposed constraint handling approach is based on a product of sub-functions that represents permissible limits on system variables and that includes a specific goal on power loss reduction. The main advantage of this approach is the fact that it allows a straightforward verification of both feasibility and optimality. The SGA is examined and tested with the recommended constraint handling approach and the traditional penalization of deviations from feasible solutions. Several tests are run in the IEEE 30, 57, 118 and 300 bus test power systems. The results obtained with the proposed approach are compared to those offered by other metaheuristic techniques reported in the specialized literature. Simulation results indicate that the proposed genetic algorithm with the alternative constraint handling approach yields superior solutions when compared to other recently reported techniques.