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Harmful algal blooms have large impacts on aquatic ecosystem and human health. Nutrient enrichment, in combination with warm water temperatures, high sunlight availability, and low water turbulence, have been proven to be major factors driving algal blooms. In this study, lake eutrophication processes, including phytoplankton production and nutrient cycling, were simulated and coupled with a reservoir operations model to optimize multi‐criteria lake operation goals. The main objective of this study was thus to design reservoir operations that would minimize phosphorus (P), nitrate‐nitrogen (NOx), and phytoplankton loads to downstream water bodies, while meeting other societal water resource demands in eutrophic lakes. We used an open‐source, multi‐objective evolutionary algorithm framework with four optimization objectives (minimizing P, NOx, and phytoplankton loads and water demand deficits), assessing each constituent separately and in combination. In addition, different optimization scenarios associated with each objective were investigated. To effectively demonstrate our findings, we implemented our approach in Lake Okeechobee, the largest subtropical lake in the US. We identified multiple opportunities to reduce downstream loads while minimizing impacts on water demand deficits. Notably, considering combined load objectives yielded substantial reductions in summertime P, NOx, and phytoplankton exports by up to 73%, 82%, and 73%, respectively, with minimal increases in water demand deficits. This supports the idea that alternative operational strategies could provide an effective and economical reservoir management strategy for balancing downstream water quality and societal water resource needs.

Urban water usage spans diverse sectors, requiring effective management strategies to address increasing demand, limited supplies, and sector-specific needs. In this study, a multi-objective urban water resource allocation model is proposed to balance economic, ecological, and social benefits, focusing on social fairness. The model considers water availability, demand diversity, and environmental factors for optimized resource allocation. An improved zebra optimization algorithm-based multi-objective evolutionary algorithm (ZOA-MOEA/D) is developed, integrating zebra optimization with a decomposition-based approach to overcome the traditional methods’ limitations, improving solution diversity and convergence. ZOA-MOEA/D consistently outperforms the NSGA-II, MOPSO, and MOEA/D algorithms in solution distribution, convergence, quality, and diversity across multiple test scenarios. By applying the model to Ningbo, China, key trade-offs between economic growth, social fairness, living standards, and ecological protection are revealed. These findings provide useful insights into urban water resource management, offering a flexible framework for balancing multiple objectives and supporting sustainable development. Despite some limitations, the approach can contribute to the ongoing development of urban water resources.

SUMMARY This study proposes a new strategy to solve the problem of radial power distribution system (RDS) reconfiguration in a multi‐objective and constrained environment. Due to the presence of various conflicting objectives and constraints, the proposed strategy uses the Elitist Non‐Dominated Sorting Genetic Algorithm‐II (NSGA‐II), an effective evolutionary multi‐objective optimization technique. NSGA‐II determines a set of pareto‐optimal solutions for the power distribution system topology, considering power losses, reliability and investment in tie‐switches. The methodology adopted to evaluate the RDS reliability uses a non‐sequential Monte Carlo Simulation and is focused on the impacts of branch failures for interruption energy assessment. The effectiveness of the proposed methodology is demonstrated on a 69 bus RDS. Copyright © 2013 John Wiley & Sons, Ltd.

Financial market has systemic complexity and uncertainty. For investors, return and risk often coexist. How to rationally allocate funds into different assets and achieve excess returns with effectively controlling risk are main problems to be solved in the field of portfolio optimization (PO). At present, due to the influence of modeling and algorithm solving, the PO models established by many researchers are still mainly focused on single-stage single-objective models or single-stage multi-objective models. PO is actually considered as a multi-stage multi-objective optimization problem in real investment scenarios. It is more difficult than the previous single-stage PO model for meeting the realistic requirements. In this paper, the authors proposed a mean-improved stable tail adjusted return ratio-maximum drawdown rate (M-ISTARR-MD) PO model which effectively characterizes the real investment scenario. In order to solve the multi-stage multi-objective PO model with complex multi-constraints, the authors designed a multi-stage constrained multi-objective evolutionary algorithm with orthogonal learning (MSCMOEA-OL). Comparing with four well-known intelligence algorithms, the MSCMOEA-OL algorithm has competitive advantages in solving the M-ISTARR-MD model on the proposed constructed carbon neutral stock dataset. This paper provides a new way to construct and solve the complex PO model.

To integrate massive amounts of heterogeneous biomedical data in biomedical ontologies and to provide more options for clinical diagnosis, this work proposes an adaptive Multi-modal Multi-Objective Evolutionary Algorithm (aMMOEA) to match two heterogeneous biomedical ontologies by finding the semantically identical concepts. In particular, we first propose two evaluation metrics on the alignment’s quality, which calculate the alignment’s statistical and its logical features, i.e., its f-measure and its conservativity. On this basis, we build a novel multi-objective optimization model for the biomedical ontology matching problem. By analyzing the essence of this problem, we point out that it is a large-scale Multi-modal Multi-objective Optimization Problem (MMOP) with sparse Pareto optimal solutions. Then, we propose a problem-specific aMMOEA to solve this problem, which uses the Guiding Matrix (GM) to adaptively guide the algorithm’s convergence and diversity in both objective and decision spaces. The experiment uses Ontology Alignment Evaluation Initiative (OAEI)’s biomedical tracks to test aMMOEA’s performance, and comparisons with two state-of-the-art MOEA-based matching techniques and OAEI’s participants show that aMMOEA is able to effectively determine diverse solutions for decision makers.

Summary This paper presents the solution to the problem in fabricating Environmental and Economic Power Dispatch (EEPD) of thermal generators with valve‐point loading effect and multiple prohibited operating zones (POZ). The valve‐point effect introduces ripples in the input–output characteristics of generating units, and the existence of POZ breaks the operating region of a generating unit into isolated sub‐regions, thus forms a nonconvex decision space. The EEPD problem becomes a nonsmooth optimization problem because of these valve‐point effect and POZ. Accuracy of the solution for a practical system is improved by considering the nonlinearities of valve‐point loading effect and multiple POZ in the EEPD problem. The multi‐objective evolutionary algorithms, namely non‐dominated sorting genetic algorithm‐II (NSGA‐II) and modified NSGA‐II (MNSGA‐II) have been applied for solving the multi‐objective nonlinear optimization EEPD problem. To improve the uniform distribution of non‐dominated solutions, dynamic crowding distance is considered in the NSGA‐II and developed MNSGA‐II. These multi‐objective evolutionary algorithms have been individually examined and applied to the standard IEEE 30‐bus and IEEE 118‐bus test systems. Real‐coded genetic algorithm is used to generate reference Pareto‐front, which is used to compare with the Pareto front obtained using NSGA‐II and MNSGA‐II. Numerical results reveal that MNSGA‐II is effectively capable for appreciable performance than NSGA‐II to solve the different power system nonsmooth EEPD problem. Moreover, three different performance metrics such as convergence, diversity and Inverted Generational Distance are calculated for the evaluation of closeness of obtained Pareto fronts to the reference Pareto‐front. In addition, an approach based on Technique for ordering Preferences by Similarity to Ideal Solution is applied to extract best compromise solution from the obtained non‐domination solutions. Copyright © 2014 John Wiley & Sons, Ltd.

This paper proposes an improved epsilon constraint-handling mechanism and combines it with a decomposition-based multi-objective evolutionary algorithm (MOEA/D) to solve constrained multi-objective optimization problems (CMOPs). The proposed constrained multi-objective evolutionary algorithm (CMOEA) is named MOEA/D-IEpsilon. It adjusts the epsilon level dynamically according to the ratio of feasible to total solutions in the current population. In order to evaluate the performance of MOEA/D-IEpsilon, a new set of CMOPs with two and three objectives is designed, having large infeasible regions (relative to the feasible regions), and they are called LIR-CMOPs. Then, the 14 benchmarks, including LIR-CMOP1-14, are used to test MOEA/D-IEpsilon and four other decomposition-based CMOEAs, including MOEA/D-Epsilon, MOEA/D-SR, MOEA/D-CDP and CMOEA/D. The experimental results indicate that MOEA/D-IEpsilon is significantly better than the other four CMOEAs on all of the test instances, which shows that MOEA/D-IEpsilon is more suitable for solving CMOPs with large infeasible regions. Furthermore, a real-world problem, namely the robot gripper optimization problem, is used to test the five CMOEAs. The experimental results demonstrate that MOEA/D-IEpsilon also outperforms the other four CMOEAs on this problem.

Multi-agent and deteriorating scheduling has gained an increasing concern from academic and industrial communities in recent years. This study addresses a two-agent stochastic flow shop deteriorating scheduling problem with the objectives of minimizing the makespan of the first agent and the total tardiness of the second agent. In the investigated problem, the normal processing time of jobs is a random variable, and the actual processing time of jobs is a linear function of their normal processing time and starting time. To solve this problem efficiently, this study proposes a hybrid multi-objective evolutionary algorithm which is a combination of an evolutionary algorithm and a local search method. It maintains two populations and one archive. The two populations are utilized to execute the global and local searches, where one population employs an evolutionary algorithm to explore the whole solution space, and the other applies a local search method to exploit the promising regions. The archive is used to guide the computation resource allocation in the search process. Some special techniques, i.e., evolutionary methods, local search methods and information exchange strategies between two populations, are designed to enhance the exploration and exploitation ability. Comparing with the classical and popular multi-objective evolutionary algorithms on some test instances, the experimental results show that the proposed algorithm can produce satisfactory solution for the investigated problem.

Due to the scarcity of conventional energy resources and the greenhouse effect, renewable energies have gained more attention. This paper proposes methods for multi-objective optimal design of hybrid renewable energy system (HRES) in both isolated-island and grid-connected modes. In each mode, the optimal design aims to find suitable configurations of photovoltaic (PV) panels, wind turbines, batteries and diesel generators in HRES such that the system cost and the fuel emission are minimized, and the system reliability/renewable ability (corresponding to different modes) is maximized. To effectively solve this multi-objective problem (MOP), the multi-objective evolutionary algorithm based on decomposition (MOEA/D) using localized penalty-based boundary intersection (LPBI) method is proposed. The algorithm denoted as MOEA/D-LPBI is demonstrated to outperform its competitors on the HRES model as well as a set of benchmarks. Moreover, it effectively obtains a good approximation of Pareto optimal HRES configurations. By further considering a decision maker’s preference, the most satisfied configuration of the HRES can be identified.

Evolutionary multi-objective optimization is a field that has experienced a rapid growth in the last two decades. Although an important number of new multi-objective evolutionary algorithms have been designed and implemented by the scientific community, the popular Non-Dominated Sorting Genetic Algorithm (NSGA-II) remains as a widely used baseline for algorithm performance comparison purposes and applied to different engineering problems. Since every evolutionary algorithm needs several parameters to be set up in order to operate, parameter control constitutes a crucial task for obtaining an effective and efficient performance in its execution. However, despite the advancements in parameter control for evolutionary algorithms, NSGA-II has been mainly used in the literature with fine-tuned static parameters. This paper introduces a novel and computationally lightweight self-adaptation mechanism for controlling the distribution index parameter of the polynomial mutation operator usually employed by NSGA-II in particular and by multi-objective evolutionary algorithms in general. Additionally, the classical NSGA-II using polynomial mutation with a static distribution index is compared with this new version utilizing a self-adapted parameter. The experiments carried out over twenty-five benchmark problems show that the proposed modified NSGA-II with a self-adaptive mutator outperforms its static counterpart in more than 75% of the problems using three quality metrics (hypervolume, generalized spread, and modified inverted generational distance).