Non-dominated Solutions Research Articles

Bi-objective carbon-efficient distributed flow-shop scheduling with multistep electricity pricing

A bi-objective distributed flow-shop scheduling problem with multistep electricity pricing and carbon emissions is studied. One objective is to minimise the completion time of production, and the other is to minimise the total cost of multistep electricity pricing and carbon emissions. A mixed integer programming model and a two-stage knowledge based cooperative algorithm with a local reinforcement strategy are proposed for the problem. The extensive numerical experiments show that the two-stage algorithm was effective statistical significantly in generating non-dominated solution sets and Pareto frontiers. Simulations on Electricity Prices are applied to examine different multistep electricity pricing schemes, and management implications were drawn for both government and companies.

Investigating Methods for ASPmT-Based Design Space Exploration in Evolutionary Product Design

Nowadays, product development is challenged by increasing system complexity and stringent time-to-market. To handle the demanding market requirements, knowledge from prior product generations is used to derive new, but partially similar product versions. The concept of product generation engineering, hence, allows manufacturers to release high-quality products within short development times. Therefore, in this paper, we propose a novel approach to evaluate the similarity of two product implementations based on the concept of the Hamming distance. This allows the usage of similarity information in various heuristics as well as in strategies and thus, to improve the product design process. In a wide set of cases, we investigate the quality and similarity of design points. In the experiments, the use of strategies leads to significantly short searching times, but also tends to be too restrictive in certain cases. Simultaneously, the quality of the solutions found in the heuristic design space exploration has been shown to be as good or better than for the search from scratch and considerably closer solutions as part of the non-dominated solution front have been found.

Bilevel optimization with a multi-objective lower-level problem: risk-neutral and risk-averse formulations

In this work, we propose different formulations and gradient-based algorithms for deterministic and stochastic bilevel problems with conflicting objectives in the lower level. Such problems have received little attention in the deterministic case and have never been studied from a stochastic approximation viewpoint despite the recent advances in stochastic methods for single-level, bilevel, and multi-objective optimization. To solve bilevel problems with a multi-objective lower level, different approaches can be considered depending on the interpretation of the lower-level optimality. An optimistic formulation that was previously introduced for the deterministic case consists of minimizing the upper-level function over all non-dominated lower-level solutions. In this paper, we develop new risk-neutral and risk-averse formulations, address their main computational challenges, and develop the corresponding deterministic and stochastic gradient-based algorithms.

A Multi-Objective Sine Cosine Algorithm Based on a Competitive Mechanism and Its Application in Engineering Design Problems.

There are a lot of multi-objective optimization problems (MOPs) in the real world, and many multi-objective evolutionary algorithms (MOEAs) have been presented to solve MOPs. However, obtaining non-dominated solutions that trade off convergence and diversity remains a major challenge for a MOEA. To solve this problem, this paper designs an efficient multi-objective sine cosine algorithm based on a competitive mechanism (CMOSCA). In the CMOSCA, the ranking relies on non-dominated sorting, and the crowding distance rank is utilized to choose the outstanding agents, which are employed to guide the evolution of the SCA. Furthermore, a competitive mechanism stemming from the shift-based density estimation approach is adopted to devise a new position updating operator for creating offspring agents. In each competition, two agents are randomly selected from the outstanding agents, and the winner of the competition is integrated into the position update scheme of the SCA. The performance of our proposed CMOSCA was first verified on three benchmark suites (i.e., DTLZ, WFG, and ZDT) with diversity characteristics and compared with several MOEAs. The experimental results indicated that the CMOSCA can obtain a Pareto-optimal front with better convergence and diversity. Finally, the CMOSCA was applied to deal with several engineering design problems taken from the literature, and the statistical results demonstrated that the CMOSCA is an efficient and effective approach for engineering design problems.

Enhanced watershed model evaluation incorporating hydrologic signatures and consistency within efficient surrogate multi-objective optimization

This paper presents a new framework for calibrating computationally expensive watershed models with multi-objective optimization methods and hydrological consistency analysis. The analysis evaluates different algorithms' efficiencies for finding watershed model calibration solutions within a limited budget. Two surrogate multi-objective algorithms GOMORS and ParEGO are compared to five evolutionary algorithms without surrogates on two watershed models. We test the algorithms’ performance with two multi-objective formulations (i.e., threshold-based flow separation and decomposition of the Nash-Sutcliffe Efficiency (NSE)). Results indicate that the surrogate-based GOMORS is the most computationally efficient overall. We also propose a framework to select among the calibration solutions obtained from multi-objective optimization using different hydrologic signatures. GOMORS is assessed for its ability to identify hydrologically acceptable calibrations. The decomposition of NSE is the most effective calibration formulation in terms of hydraulic consistency analysis. In addition, hydrologic signatures could be used effectively to filter non-dominated solutions obtained from multi-objective optimization.

Multi-objective simulation-optimization for integrated automated storage and retrieval systems planning considering energy consumption

An Automated Storage and Retrieval System (AS/RS) is one of modern technologies in warehouse operation. Despite many advantages offered by AS/RS such as improving accuracy, efficiency, and safety, AS/RS operation is very complex started from strategical, tactical, to operational level. Reaching optimal combination for all decisions become important. However, due to the dynamic and combinatorial complexity as well as uncertainty in supply – demand, it cannot be solved through the general mathematical optimization. Therefore, this study introduces simulation–optimization (SO) framework for integrated AS/RS planning considering 7 decisions at a time. Furthermore, a comprehensive mathematical model for measuring AS/RS energy consumption is formulated. The proposed framework is implemented in the China’s warehouse company for optimizing multi-objective namely energy consumption and travel time per unit. Non-dominated Sorting Genetic Algorithm II (NSGA-II) is developed as metaheuristics algorithm and discrete-event simulation is modeled based on FlexSim. The results produce non-dominated solutions that are further summarized through clustering algorithm resulting in 4 different clusters with significantly different impacts. This study provides insightful analysis and managerial implications for reaching near-global optimum in AS/RS planning towards green operation.

Multi-criteria Scheduling in Parallel Environment with Learning Effect

Abstract This paper is devoted to the study of a multi-criteria scheduling problem on unrelated processors with machines’ learning effect, with the goal of minimizing makespan, machine cost and maximal flow-time simultaneously, which is an NP-hard problem. An improved particle swarm optimization algorithm equipped with the overloaded operators, as well as a procedure of Levy flight, is proposed to generate the Pareto-optimal solutions. The experimental results show that the Levy flight strategy can effectively improve the performance of the algorithm, which can generate more non-dominated solutions, and slightly reduce the execution time of the process.

Multi-objective particle swarm optimization algorithm based on multi-strategy improvement for hybrid energy storage optimization configuration

In order to fully leverage the advantages of hybrid energy storage systems in mitigating voltage fluctuations, reducing curtailment rates of wind and solar power, minimizing active power losses, and enhancing power quality within distributed generation systems, while effectively balancing the economic and security aspects of the system, this paper establishes a multi-objective hybrid energy storage optimization configuration model that comprehensively considers the lifecycle economic costs, node voltage deviations, and system active power losses. To address the limitations of single-objective solution algorithms and the lack of diversity and premature convergence in multi-objective optimization processes, a multi-objective particle swarm optimization by multi-strategy improvements (CMOPSO-MSI) is proposed to solve the model. By introducing adaptive grid crowding distance and roulette wheel selection strategies to dynamically update the Pareto solution set, population uniformity and diversity are ensured. An improved dynamic nonlinear weighting strategy is introduced to enhance the algorithm's global search capability and convergence performance. A Gaussian mutation strategy is incorporated into the iteration process to enhance the uniformity of non-dominated solutions and particle search capabilities The aim is to achieve an optimal balance between the configuration cost and stability of hybrid energy storage systems. A simulation analysis under multiple cases is performed, taking an IEEE 33-node power distribution system as an example, with introducing photovoltaic and wind energy sources. The results demonstrate that the proposed algorithm achieves better Pareto frontiers and convergence performance compared to conventional multi-objective particle swarm optimization algorithms MOPSO, and classical multi-objective optimization algorithm NSGA-II, validating the effectiveness and accuracy of the proposed model and algorithm strategies in solving the hybrid energy storage optimization configuration problems. The approach concurrently considers system economics and grid stability while improving power quality.

A process capability function approach to multiple response surface optimization based on a posterior procedure

Multiple response surface optimization (MRSO) aims to determine a setting of input variables that simultaneously optimizes multiple responses. The process capability function (PCF) approach is an attractive alternative to MRSO because it considers both the mean and variance of the responses systematically through the process capability index. In MRSO, the responses are often in conflict. Thus, the preference information of a decision maker (DM) on the tradeoffs among the responses should be considered. However, the existing PCF methods are based on an unrealistic assumption that all DM preference information is given in advance. In this article, a posterior preference articulation procedure based on the PCF approach, called P-PCF, is proposed. P-PCF first generates nondominated solutions using the ε-constraint method and then allows the DM to select his/her preferred cluster or final solution using the K-means clustering method. The proposed method is illustrated using a well-known MRSO problem.

Evolutionary algorithms for solving single- and multiple-objective political redistricting problems: The case study of Poland

We propose novel evolutionary algorithms for solving single- and multi-objective political redistricting problems. The objectives include population equality, compactness of districts, deviation from the current districting, and an expected number of mandates attainable by some parties. The former two ensure the constructed solutions are reasonable, while the latter pair is meaningful for the post-analysis on how the alternation of existing districts may affect election outcomes. We operate on data concerning geography, demography, and politics in Poland. The experiments reveal that our algorithms efficiently handle the four-objective variant of the problem. In a single test run, we evaluate around one million solutions in nearly two hours on an average class computer, which is satisfactory given the problem’s complexity. The methods construct high-quality non-dominated solutions, outperforming the current districting and revealing the trade-offs between the objectives. The post-analysis allows us to observe connections between the expected number of mandates and the remaining three objectives. Specifically, attaining a greater number of mandates requires more significant changes in delineating the districts and potential violations of constraints. We also exhibit that the space for possible political manipulations increases when more districts can be determined.

Study on the Basic Form of Reservoir Operation Rule Curves for Water Supply and Power Generation

Reservoir operation rule curves are crucial for managing water supply and power generation in reservoirs. As the number of objectives and management requirements increase, there is a growing demand for optimized operation rule curves. The objective of this study is to explore the most effective forms of reservoir operation rule curves, focusing on the case of the Nierji Reservoir and considering the dual objectives of water supply and power generation. The parameter–simulation–optimization framework, specifically employing the NSGA-II algorithm, was used to analyze and compare two basic forms of operation rule curves: the shared type and independent type. The impact of these curves on water supply potential and multi-objective optimization results with various water demand scenarios was assessed. The analysis revealed that the choice of operation rule curve form can influence the maximum water supply potential of the reservoir to some extent. The independent type operation rule curve was significantly more effective in enhancing the water supply potential for industrial and domestic users, resulting in a notable increase of 3.5 × 108 m3. Additionally, it also proved beneficial for environmental users, with an increase of 1 × 108 m3. Conversely, the shared type operation rule curve demonstrated similar functionality to the independent type curve with fewer decision variables, particularly when the water demand was relatively low. In scenarios with high water demand, the independent type curve outperformed the shared type curve by generating 6549 superior, non-dominated solutions for multi-objective optimization, specifically focused on maximizing reservoir operation benefits. In conclusion, selecting the appropriate form of reservoir operation rule curve is crucial to balance different reservoir functional objectives and achieve optimal results. Further research could focus on quantifying the specific benefits and trade-offs associated with each type of curve in order to provide more robust evidence for the advantages of a complex reservoir system.

Automatic Column Grouping of 3D Steel Frames via Multi-Objective Structural Optimization

Formulations of structural optimization problems are proposed in this paper to automatically find the best grouping of columns in 3D steel buildings. In these formulations, the conflicting objective functions, minimized simultaneously, are the weight of the structure and the number of different groups of columns. In other words, the smaller the number of different groups of columns, the greater the weight of the structure, and the greater the number of groups, the smaller the structure’s weight. The design variables are the bracing system configuration, column cross-section orientation, and assigned W-shaped profile indices for columns, beams, and braces. The design constraints are the allowable displacements, strength, and geometric considerations. After solving the multi-objective optimization problem, the result is a Pareto front, presenting non-dominated solutions. Three evolutionary algorithms based on differential evolution are adopted in this paper to solve three computational experiments. Even if preliminary groupings of columns are adopted, considering architectural aspects such as the symmetry of the structure, it is possible to discover other interesting structural configurations that will be available to the decision maker, who will be able to make their choices based on the impacts on manufacturing, cutting, transporting, checking and welding.

Knowledge-transfer based genetic programming algorithm for multi-objective dynamic agile earth observation satellite scheduling problem

The multi-objective dynamic agile earth observation satellite scheduling problem (MO-DAEOSSP) aims to schedule a set of real-time arrival requests and form a reasonable observation plan to satisfy various criteria. According to the requirements in practical applications, the total profit and the average image quality of scheduled requests are taken as optimization goals in this study. Compared to manually designed heuristics and iterative-based methods used in previous research, genetic programming based hyper heuristics (GPHH) can automatically evolve high-quality heuristic rules (HRs) for real-time scheduling without being highly dependent on expert knowledge. In this paper, a knowledge-transfer based multi-objective GPHH framework (KT-MOGP) is proposed, equipped with a heuristic-based simulation considering the idle monitoring, to evolve non-dominated HRs for solving MO-DAEOSSP. The heuristic-based simulation generates feasible schedules and returns fitness values for given HRs, which are the individuals evolved by KT-MOGP. KT-MOGP applies a knowledge transfer mechanism to accelerate convergence. Once a source problem is trained, its non-dominated solutions are extracted and their feature importance is transferred to guide the initialization of another target problem, by which the knowledge generated during the training process can be fully utilized. Experimental results on three sets of instances show that KT-MOGP outperforms the existing GPHH-based method and that the evolved HRs are competitive compared to several classical constructive heuristics and multi-objective evolutionary algorithms. The results also show the effectiveness of the proposed knowledge transfer-based initialization. To the best of our knowledge, this study is the first attempt to consider both multi-objective scenarios and real-time arrival requests.

Trajectory planning of tire laser engraving orthogonal robot based on an improved multi-objective grasshopper optimization algorithm

The traditional tire laser engraving robots have the low and stable running capability and discontinuous motion trajectory during operation, leading to long running time, high energy consumption, and uneven operation. In order to solve these problems, this paper proposes an orthogonal robot trajectory planning method based on an improved multi-objective grasshopper optimization algorithm (IMOGOA) with the orthogonal robot as the research object. Firstly, this paper used the quintic non-uniform rational b-splines (NURBS) curves to construct the trajectory. Secondly, the optimization objectives of the orthogonal robot’s running time, energy consumption, and smoothness were used to obtain the Pareto optimal solution by using the IMOGOA to establish the objective function. Then, the optimization method was simulated and analyzed, and the optimal solution was selected to compare with the rest of the non-dominated solution sets. The simulation results showed that the proposed method reduced the running time by 33.68%, improved the energy consumption and smoothness performance by 34.48% and 56.58%, and achieved multi-objective comprehensive optimization of the orthogonal robot. Thus, the effectiveness and feasibility of the proposed method were verified. Finally, a tire laser engraving orthogonal robot experimental platform was built for physical verification experiments. The experimental results showed that the experimental trajectory deviated from the simulated trajectory by only 5.63%, further proving the proposed method’s practicality.

The optimization method of CNC lathe performance based on Morris sensitivity analysis and improved GA algorithm

This study achieved the goal of guiding bed design and optimization by conducting multi-objective optimization research on the performance of CNC lathe beds. In this study, Morris analysis was first performed on the sensitivity of the parameters, and then out to optimize the parameters using a combination of neural network and genetic algorithm. The loss function value, RMSE error accumulation, recall, sensitivity and specificity of the ASSGA-BP optimization model were better. The maximum error between the predicted and true values of the ASSGA-BP model was 0.28 mm. In the performance study of the multi-objective optimization method based on the Morris sensitivity analysis and the improved GA algorithm, the average MAE value is 0.91 %. The average RMSE value is 0.59 %. Also, the new model is significantly better than the NSGA-II, EGA, and FGA algorithms in terms of both the number of final non-dominated solutions and the speed of reaching convergence. The above results demonstrate that the model proposed in this study has high performance, can achieve faster convergence and has the best stability of the convergence state. The innovation of this article lies in the use of the Morris method to screen and evaluate numerous parameters in order to improve the accuracy of the calculation results and ensure the effectiveness of the optimization results. The improved algorithm overcomes the problems of BP neural network and can effectively improve the generalization performance of the neural network, thereby improving the prediction accuracy of the model.

Integrated remanufacturing scheduling of disassembly, reprocessing and reassembly considering energy efficiency and stochasticity through group teaching optimization and simulation approaches

The energy crisis and environmental pollution are receiving increasing attention from governments and communities. This study researches energy-aware remanufacturing systems. Remanufacturing aims to reuse valuable resources from end-of-life products and produce as-new products. Since remanufacturing systems involve a series of disassembly, processing and assembly operations, remanufacturing schedule integrates disassembly, processing and assembly shops. A multi-objective scheduling of remanufacturing systems is proposed, considering workstation use, energy consumption and customer satisfaction simultaneously. A chance-constrained programming model is established to minimize makespan and energy consumption while satisfying total tardiness requirements. A hybrid method is developed, using group teaching optimization and a discrete event simulation system, which can seek and evaluate potentially favourable solutions. The approach is validated on a group of test instances using well-known methods. The results reveal that this method can find non-dominated solutions with well-converged and well-diversified performance, verifying its advantages in providing informed decisions for managers and engineers.

Genetic Multi-Objective Optimization of Sensor Placement for SHM of Composite Structures

Increasingly often, due to the high sensitivity level of diagnostic systems, they are also sensitive to the occurrence of a significant number of false alarms. In particular, in structural health monitoring (SHM), the problem of optimal sensor placement (OSP) is appearing due to the need to reach a balance between performance and cost of the diagnostic system. The applied approach of considering nondominated solutions allows for adaption of the system parameters to the user’s expectations, treating this optimization problem as multi-objective. For this purpose, the NSGA-II algorithm was selected for the determination of an optimal set of parameters in the OSP problem for the detection of delamination in composite structures. The objectives comprise minimization of type-I and type-II errors, and number of sensors to be placed. The advantage of the proposed approach is that it is based on experimental data from the healthy structure, whereas all cases with a presence of delamination were acquired from numerical experiments. This makes it possible to develop a customized SHM system for the arbitrary location of damage.

Constrained Multiobjective Optimization with Escape and Expansion Forces

Constraints may scatter the Pareto optimal solutions of a constrained multiobjective optimization problem (CMOP) into multiple feasible regions. To avoid getting trapped in local optimal feasible regions or a part of the global optimal feasible regions, a constrained multiobjective evolutionary algorithm (CMOEA) should consider both the escape force and the expansion force carefully during the search process. However, most CMOEAs fail to provide these two forces effectively. As a remedy for this limitation, this article proposes a method called TPEA. TPEA maintains three populations, termed Pop1, Pop2, and Pop3. Pop1 is a regular population, updated with a constrained NSGA-II variant. Pop2 and Pop3 are two auxiliary populations, containing the innermost and outermost nondominated infeasible solutions, respectively. The analysis reveals that these two types of nondominated infeasible solutions can contribute to the generation of escape and expansion forces, respectively. Due to these two forces, TPEA is likely to identify more global optimal feasible regions, which is crucial for constrained multiobjective optimization. Also, a mating selection strategy is developed in TPEA to coordinate the interaction among these three populations. Extensive experiments on 58 benchmark CMOPs and 35 real-world ones demonstrate that TPEA is significantly superior or comparable to six state-of-the-art CMOEAs on most test instances.

Bi-objective Sustainable Crowdshipping with Multi Types of Occasional Drivers

The current work presents a deterministic bi-objective sustainable crowdshipping problem optimizing both the cost and CO2 emissions, referred to as the Bi-Objective Vehicle Routing Problem with Multi types of Occasional Drivers and Time Windows (BO-VRPMODTW). The goals of this work are to verify the trade-of between transportation cost and environmental emissions generation, considering different types of ODs, and to verify the impact in different location spreading for customers. Preliminary experimental results show the gain both in terms of cost and CO2 emissions of having ODs of different types. The use of ODs in the non-dominated solutions is also analyzed.

High-Dimensional Multi-Objective Bayesian Optimization With Block Coordinate Updates: Case Studies in Intelligent Transportation System

Many transportation system problems can be formulated as high-dimensional expensive multi-objective problems. They are challenging for Gaussian process-based Bayesian optimization methods to find the Pareto fronts due to the curse of dimensionality and the boundary issue in the acquisition function optimization. This paper presents a multi-objective Bayesian optimization method with block coordinate updates, Block-MOBO, to solve high-dimensional expensive multi-objective problems. Block-MOBO first partitions the decision variable space into different blocks, each of which includes a low-dimensional multi-objective problem. At each iteration, one block is considered and the decision variables not in this block are approximated by context-vector generation embedded with the Pareto prior knowledge thus promoting convergence. To tackle the boundary issue, we present <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\epsilon$</tex-math> </inline-formula> -greedy acquisition function in a Bayesian and multi-objective fashion, which recommends candidates either from the exploitation-exploration trade-off perspective or with probability <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\epsilon$</tex-math> </inline-formula> from the Pareto dominance relationship perspective. We verify the effectiveness of Block-MOBO by comparing it with other multi-objective Bayesian methods on two real-world optimization problems in transportation system and three multi-objective synthetic test suites. The experimental results show that Block-MOBO can find more evenly distributed and non-dominated solutions in the whole search space with lower complexity compared with other state-of-the-art approaches. Our analyses illustrate that block coordinate updates and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\epsilon$</tex-math> </inline-formula> -greedy acquisition function contribute to computational complexity reduction and convergence-diversity trade-offs, respectively.