Multi-objective Problem Research Articles

New Mean and Median Techniques to Solve Multiobjective Linear Fractional Programming Problem and Comparison with Other Techniques

In the field of operation research, both linear and fractional programming problems have been more encountered in recent years because they are more realistic in expressing real-life problems. Fractional programming problem is used when several rates need to be optimized simultaneously such as resource allocation planning, financial and corporate planning, healthcare, and hospital planning. There are several techniques to solve the multiobjective linear fractional programming problem. However, because of the use of scalarization, these techniques have some limitations. This paper proposed two new mean and median techniques to solve the multiobjective linear fractional programming problem by overcoming the limitations. After utilizing mean and median techniques, the problem is converted into an equivalent linear fractional programming problem; then, the linear fractional programming problem is transformed into linear programming problem and solved by the conventional simplex method or mathematical software. Some numerical examples have been illustrated to show the efficiency of the proposed techniques and algorithm. The performance of these solutions was evaluated by comparing their results with other existing methods. The numerical results have shown that the proposed techniques are better than other techniques. Furthermore, the proposed techniques solve a pure multiobjective maximization problem, which is even impossible with some existing techniques. The present investigation can be improved further, which is left for future research.

Multi-objective reinforcement learning-based approach for pressurized water reactor optimization

A novel method, the Pareto Envelope Augmented with Reinforcement Learning (PEARL), has been developed to address the challenges posed by multi-objective problems, particularly in the field of engineering where the evaluation of candidate solutions can be time-consuming. PEARL distinguishes itself from traditional policy-based multi-objective Reinforcement Learning methods by learning a single policy, eliminating the need for multiple neural networks to independently solve simpler sub-problems. Several versions inspired from deep learning and evolutionary techniques have been crafted, catering to both unconstrained and constrained problem domains. Curriculum Learning (CL) is harnessed to effectively manage constraints in these versions. PEARL’s performance is first evaluated on classical multi-objective benchmarks. Additionally, it is tested on two practical PWR core Loading Pattern (LP) optimization problems to showcase its real-world applicability. The first problem involves optimizing the Cycle length (LC) and the rod-integrated peaking factor (FΔh) as the primary objectives, while the second problem incorporates the mean average enrichment as an additional objective. Furthermore, PEARL addresses three types of constraints related to boron concentration (Cb), peak pin burnup (Bumax), and peak pin power (Fq). The results are systematically compared against conventional approaches from stochastic optimization. Notably, PEARL, specifically the PEAL-NdS ( ▪ ) variant, efficiently uncovers a Pareto front without necessitating additional efforts from the algorithm designer, as opposed to a single optimization with scaled objectives. It also outperforms the classical approach across multiple performance metrics, including the Hyper-volume. Future works will encompass a sensitivity analysis of hyper-parameters with statistical analysis to optimize the application of PEARL and extend it to more intricate problems.

Labeling methods for partially ordered paths

The landscape of applications and subroutines relying on shortest path computations continues to grow steadily. This growth is driven by the undeniable success of shortest path algorithms in theory and practice. It also introduces new challenges as the models and assessing the optimality of paths become more complicated. Hence, multiple recent publications in the field adapt existing labeling methods in an ad hoc fashion to their specific problem variant without considering the underlying general structure: they always deal with multi-criteria scenarios, and those criteria define different partial orders on the paths. In this paper, we introduce the partial order shortest path problem (POSP), a generalization of the multi-objective shortest path problem (MOSP) and in turn also of the classical shortest path problem. POSP captures the particular structure of many shortest path applications as special cases. In this generality, we study optimality conditions or the lack of them, depending on the objective functions’ properties. Our final contribution is a big lookup table summarizing our findings and providing the reader with an easy way to choose among the most recent multi-criteria shortest path algorithms depending on their problems’ weight structure. Examples range from time-dependent shortest path bottleneck path problems to the electric vehicle shortest path problem with recharging and complex financial weight functions studied in the public transportation community. Our results hold for general digraphs and, therefore, surpass previous generalizations that were limited to acyclic graphs.

A deep reinforcement learning algorithm framework for solving multi-objective traveling salesman problem based on feature transformation

As a special type of multi-objective combinatorial optimization problems (MOCOPs), the multi-objective traveling salesman problem (MOTSP) plays an important role in practical fields such as transportation and robot control. However, due to the complexity of its solution space and the conflicts between different objectives, it is difficult to obtain satisfactory solutions in a short time. This paper proposes an end-to-end algorithm framework for solving MOTSP based on deep reinforcement learning (DRL). By decomposing strategies, solving MOTSP is transformed into solving multiple single-objective optimization subproblems. Through linear transformation, the features of the MOTSP are combined with the weights of the objective function. Subsequently, a modified graph pointer network (GPN) model is used to solve the decomposed subproblems. Compared with the previous DRL model, the proposed algorithm can solve all the subproblems using only one model without adding weight information as input features. Furthermore, our algorithm can output a corresponding solution for each weight, which increases the diversity of solutions. In order to verify the performance of our proposed algorithm, it is compared with four classical evolutionary algorithms and two DRL algorithms on several MOTSP instances. The comparison shows that our proposed algorithm outperforms the compared algorithms both in terms of training time and the quality of the resulting solutions.

A multiobjective beam angle optimization framework for intensity-modulated radiation therapy

Radiation therapy treatment planning is inherently a multiobjective problem, aiming to obtain the best tradeoffs between irradiating the tumor with the prescribed dose and sparing as much as possible the surrounding healthy organs. Many different multiobjective approaches have been proposed for the optimization of radiation intensities for fixed beam irradiation directions. However, multiobjective beam angle optimization is seldom considered. The purpose of this paper is to introduce a new multiobjective optimization framework that explicitly and simultaneously considers the optimization of intensities and also beam directions. Whilst multiobjective optimization of radiation intensities considering a fixed set of beam directions gives rise to a single Pareto front, beam angle optimization gives rise to the appearance of multiple Pareto fronts, each one associated with a given beam angle set. Our framework proposes a beam angle set choice based on the evaluation of non-dominated solutions belonging to different Pareto fronts, using a tree-based approach and a performance indicator to assess the quality of each Pareto front. The proposed approach, illustrated by head-and-neck cancer cases, allows for more flexibility in the calculation of solutions and a better understanding of the existing compromises between different objectives.

Sensitivity Analysis of the Cost Coefficients in Multiobjective Integer Linear Optimization

This paper considers sensitivity analysis of the cost coefficients in multiobjective integer linear programming problems. We define the sensitivity region as the set of simultaneous changes to the coefficients for which the efficient set and its structure remain the same. In particular, we require that the component-wise relation between efficient solutions is preserved and that inefficient solutions remain inefficient, and we show that this is sufficient for the efficient set to be the same upon changes. For a single coefficient, we show that a subset of the inefficient solutions can be excluded from consideration. More specifically, we prove that it suffices to inspect the inefficient solutions of a q-objective problem that are efficient in one of two related q + 1-objective problems. Finally, we show that the sensitivity region is a convex set (an interval). Our approach generalizes to simultaneous changes in multiple coefficients. For illustration, we consider mean-variance capital budgeting and determine the region for which the set of efficient portfolios remains the same, despite a misspecification or a change in the net present values of the projects. Further computational experience with multiobjective binary and integer knapsack problems demonstrates the general applicability of our technique. For instance, we obtain all sensitivity intervals for changes to single coefficients of biobjective problems with 500 binary variables in less than half an hour of CPU time by excluding a large number of inefficient solutions. In fact, the number of excluded solutions is above 100 orders of magnitude larger than the number of remaining solutions. This paper was accepted by Chung Piaw Teo, optimization. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2021.01406 .

Multi-objective model transformation chain exploration with MOMoT

Context:The increasing complexity of modern systems leads to an increasing amount of artifacts that are used along the model-based software and systems development lifecycle. This also includes model transformations, which serve for mapping models between representations, e.g., for verification and validation purposes. Objectives:Model repositories manage this variety of artifacts and promote reusability, but should also enable the bundling of compatible artifacts. Therefore, model transformations should be reused and arranged into transformation chains to support more complex transformation scenarios. The resulting transformation should correspond to the user’s interest in terms of quality criteria such as model coverage, transformation coverage, and number of transformation steps, thus assembling such chains becomes a multi-objective problem. Methods:A novel multi-objective approach for exploring possible transformation chains residing in model repositories is presented. MOMoT, a model-driven optimization framework, is leveraged to explore the transformation space spanned by the repository. For demonstration, three differently populated repositories are considered. Results:We have extended MOMoT with an exhaustive, multi-objective search that explores the entire model transformation space defined by graph transformation rules, allowing all possible transformation chains to be considered as solution. Accordingly, the optimal solutions were identified in the demonstration cases with negligible computation time. Conclusion:The approach assists modelers when there are multiple chains for transforming an input model to a specified output model to consider. Our evaluation shows that the approach elicits all legitimate transformation chains, thus enabling the modelers to consider trade-offs in view of multiple criteria selection.

Approximation schemes for scheduling jobs on identical parallel machines to minimize the maximum lateness and makespan

We consider a multiobjective scheduling problem, with the aim of minimizing the maximum lateness and the makespan on identical machines, when the number of machines is fixed. This paper proposes an exact algorithm (based on a dynamic programming) to generate the complete Pareto Frontier in a pseudo-polynomial time. Moreover, four heuristics have been proposed in order to optimize our algorithm. Then, we present a Polynomial Time Approximation Scheme (PTAS) to generate an approximate Pareto Frontier. In this scheme, we use a simplification technique based on the merging of jobs. Furthermore, we present a Fully Polynomial Time Approximation Scheme (FPTAS) to generate an approximate Pareto Frontier, based on the conversion of the dynamic programming algorithm. The proposed FPTAS is strongly polynomial. Finally, some numerical experiments are provided in order to compare the proposed approaches.

Long Short-Term Memory Parameter Optimization Based on Improved Sparrow Search Algorithm for Molten Iron Quality Prediction

Blast furnace (BF) ironmaking is a key process in iron and steel production. Because BF ironmaking is a dynamic time series process, it is more appropriate to use a recurrent neural network for modeling. The long short-term memory (LSTM) network is commonly used to model time series data. However, its model performance and generalization ability heavily depend on the parameter configuration. Therefore, it is necessary to study parameter optimization for the LSTM model. The sparrow search algorithm (SSA) holds advantages over traditional optimization algorithms in several aspects, such as no need for prior knowledge, fewer parameters, fast convergence, and high scalability. However, the algorithm still faces some challenges, such as the tendency to become trapped in the local optimum and the imbalance between global search ability and local search ability. Therefore, on the basis of SSA, this study examined the Levy flight strategy, sine search strategy, and step size factor adjustment strategy to improve it. This algorithm, improved by three strategies, is called the improved sparrow search algorithm (ISSA). Then, the ISSA-LSTM model was established. Furthermore, considering the limitations of SSA in dealing with multi-objective problems, the fast non-dominated sorting genetic algorithm (NSGAII) was introduced, and the ISSA-NSGAII model was established. Finally, experimental validation was performed using real blast furnace operation data, which demonstrated the proposed algorithm’s superiority in parameter optimization for the LSTM model and prediction for real industrial data.

Preventive Maintenance Decision-Making Optimization Method for Airport Runway Composite Pavements

Long-term preventive maintenance planning using finite annual budgets is vital for maintaining the service performance of airport runway composite pavements. Using the pavement condition index (PCI) to quantify composite pavement performance, this study investigated the PCI deterioration tendencies of middle runways, terminal runways, and taxiways and developed prediction models related to structural thickness and air traffic. Performance jump (PJ) and deterioration rate reduction (DRR) were used to measure maintenance benefits. Based on 112 composite pavement sections in the Long-term Pavement Performance Program, this study analyzed the influences of five typical preventive maintenance technologies on PJ, DRR, and PCI deterioration rates. The logarithmic regression relationship between PJ and PCI was obtained. For sections treated with crack sealing and crack filling, the DRR was nearly 0. For sections treated with fog seal, thin HMA overlay, and hot-mix recycled AC, the DRR was 0.2, 0.7, and 0.8, respectively. To solve the multi-objective maintenance problem, this study proposed a decision-making optimization method based on dynamic programming, and the solution algorithm was optimized, which was applied in a five-year maintenance plan. Considering different PCI deterioration tendencies of airport regions, as well as PJ, DRR, and costs of maintenance technologies, the preventive maintenance decision-making optimization method meets performance and financial requirements sufficiently.

A techno-economic scheduling of distribution system including multi-microgrids considering system reconfiguration and bus selector switches

The Microgrid (MG) as an alternative energy system, would reduce power loss, enhance energy consumption efficiency, and improve the system reliability for a sustainable city. Energy scheduling of distribution systems (DSs) including multi-microgrids (MMGs), would result in a multi-objective problem from DS operators’ point of view for a techno-economic operation. In this regard, a multi-objective model for operation scheduling of DS and connected MGs, is proposed in this paper, which also considers the system management solutions such as reconfiguration and determination of the energy trading points for MGs connection. The proposed model is applied to a modified IEEE 33-bus distribution system including 4 MGs. Simulation results and analysis based on the fuzzy satisfying method indicate that the simultaneous consideration of distribution system reconfiguration and Bus Selector Switches (BSSs) for MGs can improve the social welfare function by 4.58 % and reduces the energy losses by 15.82 %.

Coordination of protections as a multi-objective problem, and Pareto frontiers relating speed and selectivity in the particular case of directional overcurrent functions

Coordination of protections as a multi-objective problem, and Pareto frontiers relating speed and selectivity in the particular case of directional overcurrent functions

Robust simulation-based optimization for multiobjective problems with constraints

Robust simulation-based optimization for multiobjective problems with constraints

Research on the Construction of Emergency Relief Center Site Selection Model Based on Firefly Algorithm

Aiming at the problem of site selection of rescue center under multi-objective after natural disaster, this paper constructs a site selection model to minimize the freight cost and maximize the time satisfaction of disaster victims. Firstly, the site selection model framework will be constructed according to the objectives, secondly, the model framework will be set up with specific constraints, and finally, the improved firefly optimization algorithm (SGSO) will be applied to conduct virtual simulation experiments. The SGSO algorithm is only used with the theory of the set of good points for the algorithm to initialize the population, and at the same time, it combines the inverse chord function with the step convergence factor, and it designs a formula for updating the position of the individuals in the population. On the basis of passing 8 standard test functions, virtual simulation experiments are carried out, and it is concluded that the SGSO algorithm can effectively solve the multi-objective siting problem, and provide more ideas and guarantees for the future research.

Evolutionary Computation in bioinformatics: A survey

Bioinformatics is a subject that studies life phenomena by using mathematical and information science theories and techniques. Its main tasks, such as DNA sequence comparison, protein structure prediction and cell metabolism analysis, can be regarded as complex optimization problems with different characteristics. Evolutionary computing is a kind of global optimization algorithm inspired by nature. Over the years, scholars have accumulated fruitful results in solving complex optimization problems such as large-scale, dynamic, multi-modal, multi-objective and multi-constrained problems by using Evolutionary Computation algorithms, and have successfully applied to the above optimization tasks in bioinformatics. This paper mainly summarizes the work of Evolutionary Computation technologies in bioinformatics from 2019 to 2023 at multiple levels, including Genomics, Proteomics, metabolomics and molecular networks related optimization tasks, as well as further applications in disease diagnosis and drug development.

Metaheuristic approach to multi-objective ergonomic workforce scheduling for Bi-hazard industrial tasks

ABSTRACT This paper considers the daily scheduling of workers who are simultaneously exposed to two ergonomic hazards when performing their assigned tasks. Safe daily rotating work schedules are generated to minimize the maximum exposure amounts of both hazards simultaneously. A non-dominated sorting genetic algorithm II (NSGA-II) method is employed to generate near-optimal workforce scheduling solutions. A numerical example shows that for a small multi-objective problem, the NSGA-II is able to yield the same set of non-dominated Pareto points as those obtained from a multi-objective optimization model with ε-constraint method. A computational experiment further demonstrates that the NSGA-II can yield acceptable non-dominated Pareto points in reasonable computation times irrespective of the problem size.

An improved MOEA/D for multi-objective flexible job shop scheduling by considering efficiency and cost

To achieve cost reduction and efficiency improvement in the production process of the aerospace industry, this study establishes a mathematical model for the multi-objective flexible job shop scheduling problem (MOFJSP). The model comprehensively considers four optimisation objectives: completion time, tool number, machine load, and machine energy consumption. For solving the MOFJSP, an improved MOEA/D (IMOEA/D) algorithm is proposed. To improve the quality of solutions, the algorithm introduces another global update strategy in addition to the original substitution operation. The population is initialised using four allocation rules, and the neighbourhood is dynamically updated based on the degree of population evolution. The simulation results on a single instance indicate that the simulation time of IMOEA/D has decreased by 10.5% and machine energy consumption has reduced by 9.5%. Moreover, when compared to various classic multi-objective algorithms on 25 benchmark instances, the IMOEA/D algorithm achieved optimal results in 19 instances for inverted generational distance comparisons, 15 instances for hypervolume comparisons and nearly all instances for set coverage comparisons. The results reveal that the proposed IMOEA/D is effective and competitive in solving MOFJSP.

Solving multi-objective green flexible job shop scheduling problem by an improved chimp optimization algorithm

As environmental contamination becomes more and more severe, enterprises need to consider optimizing environmental criteria while optimizing production criteria. In this study, a multi-objective green flexible job shop scheduling problem (MO_GFJSP) is established with two objective functions: the makespan and the carbon emission. To effectively solve the MO_GFJSP, an improved chimp optimization algorithm (IChOA) is designed. The proposed IChOA has four main innovative aspects: 1) the fast non-dominated sorting (FDS) method is introduced to compare the individuals with multiple objectives and strengthen the solution accuracy. 2) a dynamic convergence factor (DCF) is introduced to strengthen the capabilities of exploration and exploitation. 3) the position weight (PW) is used in the individual position updating to enhance the search efficiency. 4) the variable neighborhood search (VNS) is developed to strengthen the capacity to escape the local optimum. By executing abundant experiments using 20 benchmark instances, it was demonstrated that the developed IChOA is efficient to solve the MO_GFJSP and effective for reducing carbon emission in the flexible job shop.

A comparative study of fuzzy multi-objective investment project portfolio selection and optimization based on financial return and different risk measurements

Competitiveness in the global market is getting more intense. Due to resource and budget constraints, firms need to achieve their expected goals and satisfy all investment constraints under uncertainty. Selecting the set of projects among other candidates to get the most efficient portfolio requires a lot of attention from the Decision Makers (DMs) as this consideration no longer relies purely on the financial term. This problem becomes a multi-objective problem under uncertainty where the financial return and risk from uncertainty are required into the trading off consideration. Due to the financial uncertainty, the chance-constrained programming has been employed in this study for defuzzifying and solving uncertain optimization problems at a specified confidence level that is defined by the DMs. Then, various kinds of investment or financial risk measures, Lower-Semi Variance Index (LSVI), the absolute deviation with the expected FNPV, and the absolute mean-Conditional Value at Risk (CVaR) gap are provided in the selection of such risk measures to show their differences in characteristics and performances in the obtained results. Since, such problems can consist of many project candidates and complex constraints, which may grow beyond the application of the exact optimization approach, a meta-heuristic method, Genetic Algorithm (GA), is introduced to optimize this problem through designing and constructing a decision support tool for the investment portfolio selection and optimization. The applicability of the proposed comparative approach and the constructed tool are illustrated through examples.

Multi-objective RIME algorithm-based techno economic analysis for security constraints load dispatch and power flow including uncertainties model of hybrid power systems

In recent times, the landscape of power systems has undergone significant evolution, particularly with the integration of diverse renewable energy sources (RESs). This advancement presents an invaluable opportunity to enhance energy efficiency in the modern power grid, primarily by bolstering the role of stochastic RESs. The challenge lies in the optimal power flow (OPF), a multifaceted and non-linear optimization challenge that grows more complex with the inclusion of stochastic RESs that aims to optimize the allocation of power system resources to minimize the operational cost while maintaining the stability and security of the system. Addressing this, the current study introduces an innovative optimization approach, the Multi-Objective RIME (MORIME) algorithm. Drawing inspiration from the physical phenomenon of rime-ice, called the RIME, the MORIME seeks to effectively tackle OPF issues. This algorithm enhances solution accuracy by smartly dividing with non-dominated sorting and crowding distance mechanism. The proposed OPF model incorporates three types of RESs: solar photovoltaic, wind and small-scale hydropower units. While uncertainties in wind speed and solar irradiation are managed through Monte Carlo simulations, the small hydro unit is considered a constant power source. The efficacy of the MORIME algorithm is tested on IEEE 30 bus systems and results indicate that the MORIME method identifies the optimal solution for the multi-objective OPF problem while satisfying the power system constraints, thereby proving its effectiveness and superiority over MOWOA, MOGWO, MOALO, MOMRFO and MOAGDE in terms of Hyper Volume (HV) and reciprocal of Pareto Sets Proximity (1/PSP) metrices. The MORIME source code is available at: https://github.com/kanak02/MORIME