Conventional Multi-objective Evolutionary Algorithms Research Articles

Multiobjective multihydropower reservoir operation optimization with transformer-based deep reinforcement learning

The paper introduces a transformer-based deep reinforcement learning (T-DRL) approach designed to address the multiobjective multihydropower reservoir operation optimization (MMROO) problem. Unlike existing literature that primarily focuses on maximizing power generation from individual reservoirs, the MMROO model in this study considers the broader context of multiple reservoirs, encompassing total power generation, ecological protection, and residential area water supply. The computational challenges posed by the numerous constraints and nonlinearities of multiple reservoirs render conventional multiobjective evolutionary algorithms both expensive and lacking in generalization capabilities for solving the MMROO problem. To overcome these challenges, the paper proposes a T-DRL approach that leverages the multihead attention mechanism within the encoder module to adeptly extract complex information from reservoirs and residential areas. The two-stage encoder effectively processes diverse information separately. The multireservoir network of the decoder then generates optimal decisions based on contextual information. The case study focusing on Lake Mead and Lake Powell in the Colorado River Basin demonstrates the efficacy of the T-DRL approach, producing operation strategies that outperform a state-of-the-art method. Specifically, the proposed approach yields a 10.11% increase in electricity generation, a 39.69% reduction in amended annual proportional flow deviation, and a 4.10% rise in water supply revenue. Overall, the T-DRL approach emerges as an effective method for the multiobjective operation of multihydropower reservoir systems.

Dual-Fuzzy-Classifier-Based Evolutionary Algorithm for Expensive Multiobjective Optimization

Multiobjective evolutionary algorithms (MOEAs) have been widely used to solve multiobjective optimization problems (MOPs). Conventional MOEAs usually require a large number of function evaluations (FEs) for evaluating the quality of solutions. However, only a limited number of FEs are affordable in many real-world optimization problems where the FEs are computationally or economically expensive. The use of a large number of FEs decreases the effectiveness of MOEAs in solving these problems. This article proposes a dual fuzzy classifier-based surrogate model (DFC) and a DFC-based multiobjective evolutionary algorithm framework (DFC-MOEA) for expensive optimization problems. The DFC model is used for offspring pre-selection to choose high-quality offspring solutions and for categorization to divide unevaluated solutions into three categories. In the proposed framework, two fuzzy classifiers are built to predict the quality of each unevaluated solution. To strike a balance between convergence and diversity, one classifier is designed for predicting the dominance relation of unevaluated solutions (i.e., convergence), and another classifier is designed for predicting the crowdedness of unevaluated solutions (i.e., diversity). The integration of the proposed framework in three different types of MOEAs (i.e., a dominance-based MOEA, an indicator-based MOEA, and a decomposition-based MOEA) demonstrates its usefulness in handling expensive optimization problems. Comprehensive experiments on four well-known test suites and several real-world optimization problems demonstrate that the proposed framework is able to improve the performance of MOEAs under a limited number of FEs.

Competitive Decomposition-Based Multiobjective Architecture Search for the Dendritic Neural Model.

The dendritic neural model (DNM) is computationally faster than other machine-learning techniques, because its architecture can be implemented by using logic circuits and its calculations can be performed entirely in binary form. To further improve the computational speed, a straightforward approach is to generate a more concise architecture for the DNM. Actually, the architecture search is a large-scale multiobjective optimization problem (LSMOP), where a large number of parameters need to be set with the aim of optimizing accuracy and structural complexity simultaneously. However, the issues of irregular Pareto front, objective discontinuity, and population degeneration strongly limit the performances of conventional multiobjective evolutionary algorithms (MOEAs) on the specific problem. Therefore, a novel competitive decomposition-based MOEA is proposed in this study, which decomposes the original problem into several constrained subproblems, with neighboring subproblems sharing overlapping regions in the objective space. The solutions in the overlapping regions participate in environmental selection for the neighboring subproblems and then propagate the selection pressure throughout the entire population. Experimental results demonstrate that the proposed algorithm can possess a more powerful optimization ability than the state-of-the-art MOEAs. Furthermore, both the DNM itself and its hardware implementation can achieve very competitive classification performances when trained by the proposed algorithm, compared with numerous widely used machine-learning approaches.

A fast sampling based evolutionary algorithm for million-dimensional multiobjective optimization

With their complexity and vast search space, large-scale multiobjective optimization problems (LSMOPs) challenge existing multiobjective evolutionary algorithms (MOEAs). Recently, several large-scale multiobjective evolutionary algorithms have been developed to tackle LSMOPs. Unlike conventional MOEAs that concentrate on selection operations in the objective space, large-scale MOEAs emphasize operations in the decision space, such as offspring generation, to tackle the large number of decision variables. Nevertheless, most present large-scale MOEAs experience difficulty effectively and efficiently solving LSMOPs with tens of thousands or more decision variables or exhibit poor versatility in solving different LSMOPs. We propose a fast large-scale MOEA framework with reference-guided offspring generation, named FLEA, aiming at these issues. Generally, FLEA constructs several reference vectors in the decision space to steer the sampling of promising solutions during offspring generation. A parameter is used to allocate computation resources between the convergence and diversity of the offspring population adaptively. Without computationally expensive problem reformulation or decision variable analysis techniques, the proposed method can significantly accelerate the search speed of conventional MOEAs in solving LSMOPs. FLEA is examined on various LSMOPs with up to 1.6 million decision variables, demonstrating its superior effectiveness, efficiency, and versatility in large-scale multiobjective optimization.

Methods for constrained optimization of expensive mixed-integer multi-objective problems, with application to an internal combustion engine design problem

Engineering design optimization problems increasingly require computationally expensive high-fidelity simulation models to evaluate candidate designs. The evaluation budget may be small, limiting the effectiveness of conventional multi-objective evolutionary algorithms. Bayesian optimization algorithms (BOAs) are an alternative approach for expensive problems but are underdeveloped in terms of support for constraints and non-continuous design variables—both of which are prevalent features of real-world design problems. This study investigates two constraint handling strategies for BOAs and introduces the first BOA for mixed-integer problems, intended for use on a real-world engine design problem. The new BOAs are empirically compared to their closest competitor for this problem—the multi-objective evolutionary algorithm NSGA-II, itself equipped with constraint handling and mixed-integer components. Performance is also analysed on two benchmark problems which have similar features to the engine design problem, but are computationally cheaper to evaluate. The BOAs offer statistically significant convergence improvements of between 5.9% and 31.9% over NSGA-II across the problems on a budget of 500 design evaluations. Of the two constraint handling methods, constrained expected improvement offers better convergence than the penalty function approach. For the engine problem, the BOAs identify improved feasible designs offering 36.4% reductions in nitrogen oxide emissions and 2.0% reductions in fuel consumption when compared to a notional baseline design. The use of constrained mixed-integer BOAs is recommended for expensive engineering design optimization problems.

A knee-guided algorithm to solve multi-objective economic emission dispatch problem

Environmental protection and climate change have addressed tremendous pressure on thermal plants. So, the Economic Emission Dispatch (EED) problem has to consider bi-objective: the fuel cost and emission dispatch, which can be solved by the conventional Multi-Objective Evolutionary Algorithms (MOEAs). However, these MOEAs often provide well-distributed Pareto Optimal Front (POF), which may be a burden to thermal plants policymakers to select an optimal solution from a lot of candidate solutions. We develop a Knee-Guided Algorithm (KGA) to handle the EED problem, in which the knee solution is defined as the optimal by using the minimum Manhattan distance approach. The proposed KGA searches around the knee solution to boost the convergence and outputs the knee solution instead of the whole POF, which is convenient to thermal plant policymakers. Through four test cases, including six-unit, ten-unit, eleven-unit, and fourteen-unit, the proposed KGA is compared with some latest algorithms. The results have demonstrated that the KGA is superior.

Adaptive simulated binary crossover for rotated multi-objective optimization

Abstract Crossover is a crucial operation for generating promising offspring solutions in evolutionary multi-objective optimization. Among various crossover operators, the simulated binary crossover (SBX) is the most widely used in evolutionary multi-objective optimization. Despite that SBX is effective in solving problems with regular Pareto sets, its performance degenerates dramatically on problems with rotated Pareto sets.To address this issue, we propose a modified SBX, named the rotation-based simulated binary crossover (RSBX), to improve the performance of multi-objective evolutionary algorithms (MOEAs) on rotated problems whose Pareto sets are not parallel with the decision variables. The main idea is to introduce the rotation property into the SBX, and then an adaptive selection strategy is proposed to make use of both SBX and RSBX. The proposed method is embedded in three representative MOEAs, and they are compared with their original versions on some problems with rotated Pareto sets, respectively. Experimental results demonstrate that the proposed method is efficient in promoting the performance of conventional MOEAs for handling rotated multi-objective optimization problems.

Multi-objective energy management of multiple microgrids under random electric vehicle charging

In view of the increasing development of decentralized power systems and electric vehicles, this paper seeks to improve the energy management performance of multiple microgrid systems under the uncertainty associated with electric vehicle charging. A multi-objective optimization model is established for minimizing the transmission losses, operating costs, and carbon emissions of multiple microgrid systems. Firstly, a novel method is proposed for forecasting electric vehicle charging loads based on a back propagation neural network improved by long short-term memory deep learning. Based on the forecast data, a double layer solution algorithm is proposed, which consists of an adaptive multi-objective evolutionary algorithm based on decomposition and differential evolution at the multiple microgrids layer and a modified consistency algorithm for fast economic scheduling at the single microgrid layer. Finally, a model system composed of four interconnected IEEE microgrids is simulated as a case study, and the performance of the proposed algorithm is compared with that of conventional multi-objective evolutionary algorithms based on decomposition. The simulation results demonstrate the superiority of the global search performance and the rapid convergence performance of the proposed improved algorithm.

A Dynamic Multiobjective Evolutionary Algorithm Based on Decision Variable Classification.

In recent years, dynamic multiobjective optimization problems (DMOPs) have drawn increasing interest. Many dynamic multiobjective evolutionary algorithms (DMOEAs) have been put forward to solve DMOPs mainly by incorporating diversity introduction or prediction approaches with conventional multiobjective evolutionary algorithms. Maintaining a good balance of population diversity and convergence is critical to the performance of DMOEAs. To address the above issue, a DMOEA based on decision variable classification (DMOEA-DVC) is proposed in this article. DMOEA-DVC divides the decision variables into two and three different groups in static optimization and changes response stages, respectively. In static optimization, two different crossover operators are used for the two decision variable groups to accelerate the convergence while maintaining good diversity. In change response, DMOEA-DVC reinitializes the three decision variable groups by maintenance, prediction, and diversity introduction strategies, respectively. DMOEA-DVC is compared with the other six state-of-the-art DMOEAs on 33 benchmark DMOPs. The experimental results demonstrate that the overall performance of the DMOEA-DVC is superior or comparable to that of the compared algorithms.

Using multi-objective metaheuristics for the optimal selection of positioning systems

The interworking between cellular and wireless local area networks, as well as the spreading of mobile devices equipped with several positioning technologies pave the ground to new and more favorable indoor/outdoor location-based services (LBSs). Thus, wireless internet service providers are required to take several positioning methods into account at the same time, to leverage the different features of existing technologies. This would allow providing LBSs satisfying the user-required quality of position in terms of accuracy, privacy, power consumption, and often, conflicting features. Therefore, this paper presents GlobalPreLoc, a multi-objective strategy for the dynamic and optimal selection of positioning technologies. The strategy exploits a pattern-mining algorithm for future position prediction combined with conventional multi-objective evolutionary algorithms, for choosing continuously the best location providers, accounting for the user requirements, the terminal capabilities, and the surrounding positioning infrastructures. To practically implement the strategy, we also designed an architecture based on secure user plane location specification to provide indoor and outdoor LBSs in interworking wireless networks exploiting GlobalPreLoc features.

A hybrid multi-objective evolutionary algorithm for wind-turbine blade optimization

A concurrent-hybrid non-dominated sorting genetic algorithm (hybrid NSGA-II) has been developed and applied to the simultaneous optimization of the annual energy production, flapwise root-bending moment and mass of the NREL 5 MW wind-turbine blade. By hybridizing a multi-objective evolutionary algorithm (MOEA) with gradient-based local search, it is believed that the optimal set of blade designs could be achieved in lower computational cost than for a conventional MOEA. To measure the convergence between the hybrid and non-hybrid NSGA-II on a wind-turbine blade optimization problem, a computationally intensive case was performed using the non-hybrid NSGA-II. From this particular case, a three-dimensional surface representing the optimal trade-off between the annual energy production, flapwise root-bending moment and blade mass was achieved. The inclusion of local gradients in the blade optimization, however, shows no improvement in the convergence for this three-objective problem.

A simulated annealing based genetic local search algorithm for multi-objective multicast routing problems

This paper presents a new hybrid evolutionary algorithm to solve multi-objective multicast routing problems in telecommunication networks. The algorithm combines simulated annealing based strategies and a genetic local search, aiming at a more flexible and effective exploration and exploitation in the search space of the complex problem to find more non-dominated solutions in the Pareto Front. Due to the complex structure of the multicast tree, crossover and mutation operators have been specifically devised concerning the features and constraints in the problem. A new adaptive mutation probability based on simulated annealing is proposed in the hybrid algorithm to adaptively adjust the mutation rate according to the fitness of the new solution against the average quality of the current population during the evolution procedure. Two simulated annealing based search direction tuning strategies are applied to improve the efficiency and effectiveness of the hybrid evolutionary algorithm. Simulations have been carried out on some benchmark multi-objective multicast routing instances and a large amount of random networks with five real world objectives including cost, delay, link utilisations, average delay and delay variation in telecommunication networks. Experimental results demonstrate that both the simulated annealing based strategies and the genetic local search within the proposed multi-objective algorithm, compared with other multi-objective evolutionary algorithms, can efficiently identify high quality non-dominated solution set for multi-objective multicast routing problems and outperform other conventional multi-objective evolutionary algorithms in the literature.

A Pareto Corner Search Evolutionary Algorithm and Dimensionality Reduction in Many-Objective Optimization Problems

Many-objective optimization refers to the optimization problems containing large number of objectives, typically more than four. Non-dominance is an inadequate strategy for convergence to the Pareto front for such problems, as almost all solutions in the population become non-dominated, resulting in loss of convergence pressure. However, for some problems, it may be possible to generate the Pareto front using only a few of the objectives, rendering the rest of the objectives redundant. Such problems may be reducible to a manageable number of relevant objectives, which can be optimized using conventional multiobjective evolutionary algorithms (MOEAs). For dimensionality reduction, most proposals in the paper rely on analysis of a representative set of solutions obtained by running a conventional MOEA for a large number of generations, which is computationally overbearing. A novel algorithm, Pareto corner search evolutionary algorithm (PCSEA), is introduced in this paper, which searches for the corners of the Pareto front instead of searching for the complete Pareto front. The solutions obtained using PCSEA are then used for dimensionality reduction to identify the relevant objectives. The potential of the proposed approach is demonstrated by studying its performance on a set of benchmark test problems and two engineering examples. While the preliminary results obtained using PCSEA are promising, there are a number of areas that need further investigation. This paper provides a number of useful insights into dimensionality reduction and, in particular, highlights some of the roadblocks that need to be cleared for future development of algorithms attempting to use few selected solutions for identifying relevant objectives.

Multi-Objective Genetic Programming with Redundancy-Regulations for Automatic Construction of Image Feature Extractors

We propose a new multi-objective genetic programming (MOGP) for automatic construction of image feature extraction programs (FEPs). The proposed method was originated from a well known multi-objective evolutionary algorithm (MOEA), i.e., NSGA-II. The key differences are that redundancy-regulation mechanisms are applied in three main processes of the MOGP, i.e., population truncation, sampling, and offspring generation, to improve population diversity as well as convergence rate. Experimental results indicate that the proposed MOGP-based FEP construction system outperforms the two conventional MOEAs (i.e., NSGA-II and SPEA2) for a test problem. Moreover, we compared the programs constructed by the proposed MOGP with four human-designed object recognition programs. The results show that the constructed programs are better than two human-designed methods and are comparable with the other two human-designed methods for the test problem.