Non-dominated Solutions Research Articles

Bounds and convex heuristics for bi-objective optimal experiment design in water networks

Optimal Experiment Design for parameter estimation in water networks has been traditionally formulated to maximize either hydraulic model accuracy or spatial coverage. Because a unique sensor configuration that optimizes both objectives may not exist, these approaches inevitably result in sub-optimal configurations with respect to one of the objectives. This paper presents a new bi-objective optimization problem formulation to investigate the trade-offs between these conflicting objectives. We develop a convex heuristic to approximate the Pareto front, and compute guaranteed bounds to discard portions of the criterion space that do not contain non-dominated solutions. Our method relies on a Chebyshev scalarization scheme and convex optimization. We implement the proposed methods for optimal experiment design in an operational water network from the UK. For this case study, the convex heuristic computes near-optimal solutions for the individual objective minimization problems, and tight bounds on the true Pareto front of the considered bi-objective optimization problem.

Batched Data-Driven Evolutionary Multiobjective Optimization Based on Manifold Interpolation

Multiobjective optimization problems are ubiquitous in real-world science, engineering, and design optimization problems. It is not uncommon that the objective functions are as a black box, the evaluation of which usually involve time-consuming and/or costly physical experiments. Data-driven evolutionary optimization can be used to search for a set of nondominated tradeoff solutions, where the expensive objective functions are approximated as a surrogate model. In this article, we propose a framework for implementing batched data-driven evolutionary multiobjective optimization (EMO). It is so general that any off-the-shelf EMO algorithms can be applied in a plug-in manner. There are two unique components: 1) based on the Karush–Kuhn–Tucker conditions, a manifold interpolation approach that explores more diversified solutions with a convergence guarantee along the manifold of the approximated Pareto-optimal set and 2) a batch recommendation approach that reduces the computational time of the data-driven evolutionary optimization process by evaluating multiple samples at a time in parallel. Comparing against seven state-of-the-art surrogate-assisted evolutionary algorithms, experiments on 168 benchmark test problem instances with various properties and a real-world application on hyper-parameter optimization fully demonstrate the effectiveness and superiority of our proposed framework, which is featured with a faster convergence and a stronger resilience to various Pareto-optimal front shapes.

Improving locational decision making: a heuristic that optimizes access and coverage

Siting decisions can influence access, logistics, supply chains and transportation and other qualities, making them critical to the success of a service system. Often access to resources or opportunities is the primary concern, but other performance characteristics can be equally important. This paper considers access combined with service coverage in site selection as a bi-objective spatial optimization model. Specifically, the access objective aims to minimize demand proximity to its closest sited facility and the coverage objective seeks to maximize demand within a service distance standard. Solution of the problem is challenging due to the nature of facility location, where siting may occur anywhere in continuous space. Further complicating matters is the need to identify tradeoffs, or nondominated solutions, as the problem involves two objectives being simultaneously optimized. This research introduces a heuristic approach to solve a multi-facility, bi-objective location-allocation problem involving facility location in continuous space, where access and coverage are simultaneously considered. A unique case study is reported involving the strategic positioning of outfielders in baseball, where fielder access and coverage to batted balls are fundamentally important. The heuristic is found to perform exceptionally well, identifying the best range of solutions for this problem from which strategic placement of fielders can be planned.

Service Composition and Optimal Selection of Low-Carbon Cloud Manufacturing Based on NSGA-II-SA Algorithm

As a new model of networked manufacturing services, cloud manufacturing (CMfg) aims to allocate enterprise manufacturing resources, realize rational utilization of manufacturing resources, and adapt to increasingly complex user needs. However, previous studies on service composition and optimal selection (SCOS) in CMfg environments do not incorporate carbon emissions into the quality of service (QoS) evaluation indicators. Therefore, a SCOS model for CMfg under a low-carbon environment is firstly proposed in this paper. Secondly, based on the Non-dominated Sorting Genetic Algorithm (NSGA-II) algorithm, a hybrid multi-objective evolutionary algorithm, named the NSGA-II-SA algorithm, is proposed to solve the model and obtain the Pareto optimal solution set. Then, an algorithm result optimization strategy combining subjective and objective is proposed to filter the Pareto optimal solution set, so as to make the final decision. Finally, taking natural gas cylinder head production as an example, the proposed algorithm is compared with other algorithms, and the results show that the proposed algorithm can obtain more non-dominated solutions, and the quality of the solutions in the four dimensions is better than the other. Therefore, it is proved that the proposed algorithm has better comprehensive performance in SCOS under a low-carbon environment.

Optimal Design of Agricultural Mobile Robot Suspension System Based on NSGA-III and TOPSIS

The stability of vehicles is influenced by the suspension system. At present, there are many studies on the suspension of traditional passenger vehicles, but few are related to agricultural mobile robots. There are structural differences between the suspension system of agricultural mobile robots and passenger vehicles, which requires structural simplification and modelling concerning suspension of agricultural mobile robots. This study investigates the optimal design for an agricultural mobile robot’s suspension system designed based on a double wishbone suspension structure. The dynamics of the quarter suspension system were modelled based on Lagrange’s equation. In our work, the non-dominated sorting genetic algorithm III (NSGA-III) was selected for conducting multi-objective optimization of the suspension design, combined with the Technique for Order Preference by Similarity to the Ideal Solution (TOPSIS) to choose the optimal combination of parameters in the non-dominated solution set obtained by NSGA-III. We compared the performance of NSGA-III with that of other multi-objective evolutionary algorithms (MOEAs). Compared with the second-scoring solution, the score of the optimal solution obtained by NSGA-III increased by 4.92%, indicating that NSGA-III has a significant advantage in terms of the solution quality and robustness for the optimal design of the suspension system. This was verified by simulation in Adams that our method, which utilizes multibody dynamics, NSGA-III and TOPSIS, is feasible to determine the optimal design of a suspension system for an agricultural mobile robot.

A strength pareto evolutionary algorithm based on adaptive reference points for solving irregular fronts

Evolutionary algorithms have proven to be extremely effective at tackling multi-objective optimization problems (MOPs). However, when dealing with many-objective optimization problems (MaOPs), their performance frequently degrades, especially when the Pareto marking irregular shapes. The population pressure to choose the Pareto optimal front and address the generalizability of different Pareto front shapes becomes more challenging as the number of objectives increases. We present a strength Pareto evolutionary algorithm based on adaptive reference points (SPEA/ARP) to address this problem. First, the reference points are updated using current and historical population information. The angles between the current demographic information and the predefined uniform reference points are used to select the active reference points, and the adaptive reference points are selected from the historical population information projected onto the reference plane. Second, the fitness function values are applied to classify the environmental selection criteria into two categories: 1) The angle distance scaling function using adaptive reference points is utilized to increase selection pressure, and the diversity of non-dominated solutions is balanced using the angle-based secondary selection technique. 2) Otherwise, the fitness function values are employed to choose the next generation of non-dominated solutions. Third, an aggregate fitness r-value generated by the angle distance scaling function is employed to construct matching pools that produce valid offsprings. Finally, extensive experiments are carried out to demonstrate SPEA/ARP performance by comparing it with six state-of-the-art many-objective evolutionary algorithms on 5-, 10-, 15-objective of 31 benchmark MaOPs. The experiments show that SPEA/ARP outperforms the compared algorithms.

A Many-Objective Evolutionary Algorithm Based on Indicator and Decomposition

In the field of many-objective evolutionary optimization algorithms (MaOEAs), how to maintain the balance between convergence and diversity has been a significant research problem. With the increase of the number of objectives, the number of mutually nondominated solutions increases rapidly, and multi-objective evolutionary optimization algorithms, based on Pareto-dominated relations, become invalid because of the loss of selection pressure in environmental selection. In order to solve this problem, indicator-based many-objective evolutionary algorithms have been proposed; however, they are not good enough at maintaining diversity. Decomposition-based methods have achieved promising performance in keeping diversity. In this paper, we propose a MaOEA based on indicator and decomposition (IDEA) to keep the convergence and diversity simultaneously. Moreover, decomposition-based algorithms do not work well on irregular PFs. To tackle this problem, this paper develops a reference-points adjustment method based on the learning population. Experimental studies of several well-known benchmark problems show that IDEA is very effective compared to ten state-of-the-art many-objective algorithms.

Multiple sparse detection-based evolutionary algorithm for large-scale sparse multiobjective optimization problems

AbstractSparse multiobjective optimization problems are common in practical applications. Such problems are characterized by large-scale decision variables and sparse optimal solutions. General large-scale multiobjective optimization problems (LSMOPs) have been extensively studied for many years. They can be well solved by many excellent custom algorithms. However, when these algorithms are used to deal with sparse LSMOPs, they often encounter difficulties because the sparse nature of the problem is not considered. Therefore, aiming at sparse LSMOPs, an algorithm based on multiple sparse detection is proposed in this paper. The algorithm applies an adaptive sparse genetic operator that can generate sparse solutions by detecting the sparsity of individuals. To improve the deficiency of sparse detection caused by local detection, an enhanced sparse detection (ESD) strategy is proposed in this paper. The strategy uses binary coefficient vectors to integrate the masks of nondominated solutions. Essentially, the mask is globally and deeply optimized by coefficient vectors to enhance the sparsity of the solutions. In addition, the algorithm adopts an improved weighted optimization strategy to fully optimize the key nonzero variables to balance exploration and optimization. Finally, the proposed algorithm is named MOEA-ESD and is compared to the current state-of-the-art algorithm to verify its effectiveness.

Optimal planning of hybrid electric-hydrogen energy storage systems via multi-objective particle swarm optimization

Abstract: In recent years, hydrogen is rapidly developing because it is environmentally friendly and sustainable. In this case, hydrogen energy storage systems (HESSs) can be widely used in the distribution network. The application of hybrid electric-hydrogen energy storage systems can solve the adverse effects caused by renewable energy access to the distribution network. In order to ensure the rationality and effectiveness of energy storage systems (ESSs) configuration, economic indicators of battery energy storage systems (BESSs) and hydrogen energy storage systems, power loss, and voltage fluctuation are chosen as the fitness function in this paper. Meanwhile, multi-objective particle swarm optimization (MOPSO) is used to solve Pareto non-dominated set of energy storage systems’ optimal configuration scheme, in which the technique for order preference by similarity to ideal solution (TOPSIS) based on information entropy weight (IEW) is used select the optimal solution in Pareto non-dominated solution set. Based on the extended IEEE-33 system and IEEE-69 system, the rationality of energy storage systems configuration scheme under 20% and 35% renewable energy penetration rate is analyzed. The simulation results show that the power loss can be reduced by 7.9%–22.8% and the voltage fluctuation can be reduced by 40.0%–71% when the renewable energy penetration rate is 20% and 35% respectively in IEEE-33 and 69 nodes systems. Therefore, it can be concluded that the locations and capacities of energy storage systems obtained by multi-objective particle swarm optimization can improve the distribution network stability and economy after accessing renewable generation.

A new method for intuitionistic fuzzy multi-objective linear fractional optimization problem and its application in agricultural land allocation problem

This paper presents a new method for solving an intuitionistic fuzzy multi-objective linear fractional optimization (IFMOLFO) problem with crisp and intuitionistic fuzzy constraints. Here, all uncertain parameters are represented as triangular intuitionistic fuzzy numbers. We used an accuracy ranking function and variable transformation in the proposed method to convert an IFMOLFO problem into a crisp multi-objective linear optimization problem. Then, we formulated the first phase of the weighted intuitionistic fuzzy goal programming (WIFGP) model to obtain an intuitionistic fuzzy non-dominant (IFND) solution for the IFMOLFO problem. Several strategies for obtaining an IFND solution to the IFMOLFO problem have been proposed in the literature. However, in addition to constructing the phase-I WIFGP model, this study shows that the IFND solution may not be Pareto-optimal when some of the under-deviation variables are zero. As a result, the second phase of the WIFGP model is applied to address this issue. The benefits of both models are merged to provide a novel method, unlike any other method in the literature, for producing optimal solutions that satisfy both IFND and Pareto-optimal requirements. The suggested algorithm’s efficiency and reliability are demonstrated by addressing a real-life case study of an agricultural production planning problem and followed by solving a numerical example from literature.

A performance approximation assisted expensive many-objective evolutionary algorithm

Surrogate-assisted multi-objective evolutionary algorithms have been paid much attention to solve expensive multi-objective problems in recent years. However, with the number of objectives increasing, an improper solution may be picked for expensive objective evaluation due to the accumulation error of approximated values on objective functions. Furthermore, the time to construct surrogate models for all objectives will significantly increase. Thus, in this paper, Gaussian process (GP) models are proposed for performance indicators instead of for objective functions. Furthermore, solutions are selected from either of two ways to be evaluated using the expensive objective function. When there are non-dominated solutions found so far that are approximated, they will be exactly evaluated using the objective function. Otherwise, the solution with the maximum approximation uncertainty among the current population will be evaluated using the real objective functions. The efficiency of the presented approach is validated on the DTLZ test suite with 3, 6, 10, 15, and 20 objectives, MaF benchmark problems with 3, 6, 10, 15, and 20 objectives, and a real-world optimization problem called filter design. The experimental results show that the method proposed in this paper is competitive compared to recently proposed peer algorithms for expensive many-objective problems.

A semi-desirable location and sizing model for hydrogen fuel storage areas: A case study for Istanbul

Due to their sustainable nature and high energy efficiency, hydrogen fuel vehicles (HFVs) gradually replace gasoline internal combustion engine vehicles. The increasing number of HFVs brings out the need for installing hydrogen fuel storage areas (HFSAs) that serve as local suppliers for the fuel retail stations. In this study, we consider the HFSA locating and sizing problem for the Anatolian side of Istanbul and pose it as a bi-objective semi-desirable facility location problem which incorporates both social and transshipment costs as push and pull objectives. Next, by adopting a weighted goal programming framework, we minimize the total weighted unwanted deviations from each goal for years between 2021 and 2030 while accounting for several organizational and governmental rules. Our modelling approach is also supported by a structured demand prediction methodology which accounts for the HFV market penetration rates and other parameters such as predicted population, number of HFVs on road, etc. Having two conflicting objectives, we adopt a posteriori approach and generate a representative set of non-dominated solutions to provide decision support to planners and investors. Finally, we perform a sensitivity analysis to account for the uncertainty in the hydrogen fuel demands of districts by defining an uncertainty set for the demand of each district. Sensitivity analysis reveals how and how much change in the district demands modify the most preferred solution.

Feature Selection Using Diversity-Based Multi-objective Binary Differential Evolution

By identifying relevant features from the original data, feature selection methods can maintain or improve the classification accuracy and reduce the dimensionality. Recently, many multi-objective evolutionary methods have been proposed for feature selection. However, effectively handling the trade-offs between convergence and diversity of the non-dominated solutions remains a major challenge, especially for high-dimensional datasets. To cover this issue, this work studies a diversity-based multi-objective differential evolution approach to feature selection. During the environmental selection process, each of the solutions in the candidate pool will have a diversity score, and solutions with large diversity score values will be preferred so as to improve the population diversity. To reduce the search space, irrelevant and weakly relevant features are detected and removed in the proposed method. A new binary mutation operator using the neighborhood information of individuals is also proposed, aiming to produce better feature subsets. Experimental results on 14 datasets with varying difficulties show that the proposed feature selection method can obtain significantly better feature selection performance than current popular multi-objective feature selection methods.

Multi-Strategy Dynamic Evolution-Based Improved MOEA/D Algorithm for Solving Multi-Objective Fuzzy Flexible Job Shop Scheduling Problem

A scheduling model was developed to optimize the maximum completion time, total machine load, and maximum machine load for the fuzzy flexible job shop problem with uncertain processing times. To solve this problem, a multi-strategy dynamic evolution-based improved multi-objective evolutionary algorithm based on decomposition(IMOEA/D) was proposed. In order to enhance the quality of the non-dominated solution set and improve the algorithm efficiency. The algorithm firstly employs a strategy based on minimum processing time and workload, along with a non-dominated solution prioritization mechanism to generate the initial population. Secondly, three evolutionary strategies are incorporated, and their probabilities are dynamically adjusted with the increase of evolution generations. Finally, a variable neighborhood search method is introduced to improve the search performance of the algorithm. The effectiveness of the proposed algorithm was demonstrated through experimental validation.

An Improved Hyperplane Assisted Multiobjective Optimization for Distributed Hybrid Flow Shop Scheduling Problem in Glass Manufacturing Systems

To solve the distributed hybrid flow shop scheduling problem (DHFS) in raw glass manufacturing systems, we investigated an improved hyperplane assisted evolutionary algorithm (IhpaEA). Two objectives are simultaneously considered, namely, the maximum completion time and the total energy consumptions. Firstly, each solution is encoded by a three-dimensional vector, i.e., factory assignment, scheduling, and machine assignment. Subsequently, an efficient initialization strategy embeds two heuristics are developed, which can increase the diversity of the population. Then, to improve the global search abilities, a Pareto-based crossover operator is designed to take more advantage of non-dominated solutions. Furthermore, a local search heuristic based on three parts encoding is embedded to enhance the searching performance. To enhance the local search abilities, the cooperation of the search operator is designed to obtain better non-dominated solutions. Finally, the experimental results demonstrate that the proposed algorithm is more efficient than the other three state-of-the-art algorithms. The results show that the Pareto optimal solution set obtained by the improved algorithm is superior to that of the traditional multiobjective algorithm in terms of diversity and convergence of the solution.

Picker routing optimization of storage stacker based on improved multi-objective iterative local search algorithm

<p style='text-indent:20px;'>In the process of warehouse automation, the efficient picker routing strategy is one of the key factors to improve warehouse efficiency. According to the order and the picking characteristics of the warehouse stacker, the picker routing of the stacker is regarded as the prize-collecting vehicle routing problem (PCVRP). According to the path and order for stacker picking, we designed a picker routing optimization strategy based on improved multi-objective iterative local search (IMOILS) algorithm. An elite pool strategy was set to save the high-quality solutions in the iterative process, and the nondominated solutions in the iterative evolution were stored and updated. Adding the adaptive enhanced perturbation strategy was beneficial to the current solution to escape from local optimum. In the local search procedure, to limit the excessively large search space, the epsilon constraint was adopted to limit the significant deterioration in another objective direction. The computational results showed that the proposed algorithm is superior to the comparison algorithms in the number of nondominated solutions, the hypervolume, and the spacing metric, and the stability of the algorithm is also good, which not only verifies the effectiveness of the proposed algorithm, but also provides a feasible optimization scheme for the storage stacker's picker routing problem.</p>

Bi-Objective simplified swarm optimization for fog computing task scheduling

In the face of burgeoning data volumes, latency issues present a formidable challenge to cloud computing. This problem has been strategically tackled through the advent of fog computing, shifting computations from central cloud data centers to local fog devices. This process minimizes data transmission to distant servers, resulting in significant cost savings and instantaneous responses for users. Despite the urgency of many fog computing applications, existing research falls short in providing time-effective and tailored algorithms for fog computing task scheduling. To bridge this gap, we introduce a unique local search mechanism, Card Sorting Local Search (CSLS), that augments the non-dominated solutions found by the Bi-objective Simplified Swarm Optimization (BSSO). We further propose Fast Elite Selecting (FES), a ground-breaking one-front non-dominated sorting method that curtails the time complexity of non-dominated sorting processes. By integrating BSSO, CSLS, and FES, we are unveiling a novel algorithm, Elite Swarm Simplified Optimization (EliteSSO), specifically developed to conquer time-efficiency and non-dominated solution issues, predominantly in large-scale fog computing task scheduling conundrums. Computational evidence reveals that our proposed algorithm is both highly efficient in terms of time and exceedingly effective, outstripping other algorithms on a significant scale.

MaOMFO: Many-objective moth flame optimizer using reference-point based non-dominated sorting mechanism for global optimization problems

Many-objective optimization (MaO) deals with a large number of conflicting objectives in optimization problems to acquire a reliable set of appropriate non-dominated solutions near the true Pareto front, and for the same, a unique mechanism is essential. Numerous papers have reported multi-objective evolutionary algorithms to explain the absence of convergence and diversity variety in many-objective optimization problems. One of the most encouraging methodologies utilizes many reference points to segregate the solutions and guide the search procedure. The above-said methodology is integrated into the basic version of the Moth Flame Optimization (MFO) algorithm for the first time in this paper. The proposed Many-Objective Moth Flame Optimization (MaOMFO) utilizes a set of reference points progressively decided by the hunt procedure of the moth flame. It permits the calculation to combine with the Pareto front yet synchronize the decent variety of the Pareto front. MaOMFO is employed to solve a wide range of unconstrained and constrained benchmark functions and compared with other competitive algorithms, such as non-dominated sorting genetic algorithm, multi-objective evolutionary algorithm based on dominance and decomposition, and novel multi-objective particle swarm optimization using different performance metrics. The results demonstrate the superiority of the algorithm as a new many-objective algorithm for complex many-objective optimization problems.

MULTIOBJECTIVE OPTIMIZATION OF CASCADE REFRIGERATION SYSTEM USING NH3-CO2 AND NH3-N2O REFRIGERANT PAIRS

In this paper a comparative analysis based on multiobjective optimization of a cascade refrigeration system using NH<sub>3</sub>-CO<sub>2</sub> and NH<sub>3</sub>-N<sub>2</sub>O refrigerant pairs has been done. Exergetic effciciency and overall cost rate have been taken as the two conflicting objective functions, and evaporator temperature, condenser temperature, LTC condenser temperature, and cascade heat exchanger temperature difference are the four design variables. The optimization work has been carried out using genetic algorithm, which results in a nondominated optimal solution represented in the form of pareto-optimal curve, and the technique for order performance by similarity to ideal solution (TOPSIS) method is used to select a unique solution. The results show that NH<sub>3</sub>-N<sub>2</sub>O is a better alternative as compared to NH<sub>3</sub>-CO<sub>2</sub> refrigerant pair from a multiobjective optimization point of view. The corresponding optimal operating conditions have also been suggested for both the refrigerant pairs.

Dynamic Resource Allocation Using an Adaptive Multi-Objective Teaching-Learning Based Optimization Algorithm in Cloud

Resource allocation is a non-polynomial complete problem in the cloud data center that selects the proper resources to execute many fine computational granularity tasks. Customer requirements and capacity of applications change frequently. To bridge the gap between frequently changing customer requirement and available infrastructure for the services, we propose a dynamic resource allocation strategy using an adaptive multi-objective teaching-learning based optimization (AMO-TLBO) algorithm in Cloud computing. To improve the exploration and exploitation capacities, AMO-TLBO introduces the concept of number of teachers, adaptive teaching factor, tutorial training and self-motivated learning. Moreover, a grid-based approach to adaptively assess the non-dominated solutions maintained in an external archive is used. The objectives of AMO-TLBO include minimizing makespan, cost and maximizing utilization using well-balanced load across virtual machines. The evaluation results show that the proposed algorithm outperforms TLBO, MOPSO and NSGA-II algorithms in terms of different performance metrics.