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Economic dispatch (ED) has received considerable interest in the field of energy management and optimization. The problem aims to determine the most cost-effective power allocation strategy that satisfies the power demand and all physical constraints of the power system. To solve this problem, we propose an algorithm based on differential evolution and adopt a hybrid mutation strategy, a linear population size reduction mechanism, and an improved single-unit repair mechanism. Experimental results confirmed that these mechanisms are useful for performance improvement. The proposed algorithm (L -HMDE) showed good performance when compared with more than 90 algorithms in solving 22 test cases. It could provide high-quality solutions stably and efficiently. In addition to designing a good algorithm, we present a review of over 100 papers and highlight their algorithm features. We also provide a comprehensive collection of test cases in the literature. Through careful examination and verification, data coefficients of these test cases and solutions to them are included in this paper as a useful reference for researchers who are interested in this problem. • A differential evolution-based algorithm (L-HMDE) is proposed to address the economic dispatch problem. • The L-HMDE integrates a hybrid mutation strategy, a population size reduction mechanism, and an improved repair procedure. • It shows good solution quality and high efficiency when compared with more than 90 existing algorithms on 22 test cases. • A comprehensive collection of test cases and solutions is also provided. [ABSTRACT FROM AUTHOR]

This paper proposes an adaptive uniform search framework designed for constrained multi-objective optimization. The framework comprises three key components: a global uniform exploration strategy, a local greedy exploitation strategy, and a search switch mechanism. These components work together to facilitate comprehensive exploration of promising areas while maintaining a balance between global exploration and local exploitation. Specifically, the global uniform exploration strategy ensures even distribution within promising areas, preventing any oversights during exploration. The local greedy exploitation strategy divides these areas into sub-areas and employs a feasibility-led constraint handling technique to enhance efficiency in identifying optimal solutions. Additionally, the search switch dynamically adjusts the search strategy between global exploration and local exploitation. Numerical simulations on various benchmark suites and real-world problem demonstrate the strong performance of the framework in addressing constrained multi-objective optimization problems. The comparison results show that compared with eight recently proposed algorithms, the proposed framework is more robust in solving diverse constrained multi-objective optimization problems. • GUE removes close individuals, promoting even distribution. • LGE divides areas for effective local optimization. • A novel switch adapts search between GUE and LGE. [ABSTRACT FROM AUTHOR]

This paper is the second one of the two papers entitled “Weighted Superposition Attraction (WSA) Algorithm”, which is about the performance evaluation of the WSA algorithm in solving the constrained global optimization problems. For this purpose, the well-known mechanical design optimization problems, design of a tension/compression coil spring, design of a pressure vessel, design of a welded beam and design of a speed reducer, are selected as test problems. Since all these problems were formulated as constrained global optimization problems, WSA algorithm requires a constraint handling method for tackling them. For this purpose we have selected 6 formerly developed constraint handling methods for adapting into WSA algorithm and analyze the effect of the used constraint handling method on the performance of the WSA algorithm. In other words, we have the aim of producing concluding remarks over the performance and robustness of the WSA algorithm through a set of computational study in solving the constrained global optimization problems. Computational study indicates the robustness and the effectiveness of the WSA in terms of obtained results, reached level of convergence and the capability of coping with the problems of premature convergence, trapping in a local optima and stagnation. [ABSTRACT FROM AUTHOR]

This paper presents an approach for tackling constrained underwater glider path planning (UGPP), where the feasible path area is defined as a corridor around the border of an ocean eddy. The objective of the glider here is to sample the oceanographic variables more efficiently while keeping a bounded trajectory. Therefore, we propose a solution based on differential evolution (DE) algorithm mechanisms, including in its configuration self-adaptation of control parameters, population size reduction, ϵ -constraint handling with adjustment, and mutation based on elitistic best vector. Different aspects of this DE configuration are studied for the constrained UGPP challenge, on a prepared benchmark set comprised of 28 different specialized scenarios. The DE configurations were tested over a benchmark set over 51 independent runs for each DE configuration aspect. Comparison and suitability for the combination of these mechanisms is reported, through the per-scenario and aggregated statistical performance differences, including different constraint handling definition strategies, different DE mutation strategies’ configurations, and population sizing parameterizations. Our proposed solution outranked all other compared algorithms, keeping a trajectory within the limits with 100% success rate in all physically feasible scenarios; on average, it improved the randomly initialized trajectories fitness by roughly 50%, even reaching perfect fitness (all-around, 360-degree eddy corridor sampling) in some scenarios. [ABSTRACT FROM AUTHOR]

Differential evolution (DE) refers to a class of population based stochastic optimization algorithms. In order to solve practical problems involving constraints, such algorithms are typically coupled with a constraint handling scheme. Such constraints often emerge out of user requirements, physical laws, statutory requirements, resource limitations etc and are routinely evaluated using computationally expensive analysis i.e., solvers relying on finite element methods, computational fluid dynamics, computational electromagnetics etc. In this paper, we introduce a novel scheme of constraint handling, wherein every solution is assigned a random sequence of constraints and the evaluation process is aborted whenever a constraint is violated. The solutions are sorted based on two measures i.e., the number of satisfied constraints and the violation measure. The number of satisfied constraints takes precedence over the amount of violation. We illustrate the performance of the proposed scheme and compare it with other state of the art constraint handling methods using a common framework based on differential evolution. The results are compared using CEC-2006 , CEC-2010 and CEC-2011 test functions with inequality constraints. The results clearly highlight two key aspects (a) the ability to identify feasible solutions earlier than other constraint handling schemes and (b) potential savings in computational cost offered by the proposed strategy. [ABSTRACT FROM AUTHOR]

The classical optimal power flow problem is usually formulated with only thermal generators, in which the fuel used to generate power is limited and emissions from the network system are often ignored. Due to several promising features like renewability, richness, and cleanness, renewable energy sources have been drew growing attention. As a result, more and more renewable energy sources are penetrated into the electrical grid. In this paper, the standard IEEE-30 bus system is modified by integrating renewable energy sources as the case study, where the traditional thermal generators on buses 5 and 11 are replaced by wind generators, and bus 13 is replaced by solar generators. In addition, to address the intermittence and uncertainty of renewable sources, the Weibull probability density function is used to calculate the available wind power. Meanwhile, the lognormal probability density function is employed to calculate the available solar power. The optimal power flow with stochastic wind and solar energy is formulated as a multi-objective optimization problem. A multi-objective evolutionary algorithm based on non-dominated sorting with constraint handling technique are presented to solve it. In addition, another larger test system i.e., IEEE-57 bus system is selected to further verify the performance of the proposed approach in handling large dimensional problem. Simulation results indicate that proposed approach can obtain competitive compromise solution on different optimization objectives. • OPF incorporating renewable energy sources such as wind and solar is formulated. • The intermittent and uncertain of wind and solar power is matched by different density function. • The superiority of feasible solutions (SF) is used to effectively handle constraints in OPF. • Two effective constraint multi-objective methods are proposed. [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]