Diversity Of Non-dominated Solutions Research Articles

Multi-objective continuous review inventory policy using MOPSO and TOPSIS methods

In the dynamic business environment of today, decision-making involves considering various conflicting aspects. Inventory planning problems aim to determine how much and when to order products to satisfy customer demand at the lowest possible cost while maintaining a desirable service level. These problems can be formulated as a MOPSO algorithm, which is used to handle multiple objectives in a continuous review stochastic inventory control system (r, Q). Unfortunately, most multi-objective inventory models have been solved by aggregating objectives using specific weights or by optimizing only one objective and treating the others as constraints. Considering the complexity of real-world inventory control problems, which involves conflicting objectives such as minimizing cost and maximizing service level, the need arises to employ more precise optimizers that can generate better and more diverse non-dominated solutions of reorder point and order size system. In this paper multi-criteria decision-making framework that combines MOPSO algorithm and TOPSIS method to generate a Pareto front of non-dominated solutions and rank them based on decision makers' preferences. Initially, the original MOPSO is applied to the multi-objective inventory control problem, and then the mutation operator is integrated into the MOPSO to maintain diversity in the swarm and explore the entire search space. Next, the leader selection strategy called the geographically-based system (Grids) is replaced by the crowding distance factor to choose the global optimal particle as a leader. Additionally, the ε-dominance concept is employed to limit the archive size and maintain more diversity and convergence in the MOPSO for optimizing the inventory control problem. In conclusion, this work not only pioneers a cutting-edge approach to multi objective inventory control but also underscores its practical value. By facilitating the generation of superior solutions that cater to diverse decision-maker preferences, our methodology resonates deeply with real-world challenges and sets a new benchmark for effective inventory planning.

MaOEA/D with adaptive external population guided weight vector adjustment

In order to make multiobjective evolutionary algorithm based on decomposition (MOEA/D) have better performance in dealing with many-objective optimization problems (MaOPs) with different Pareto fronts (PFs), this paper proposes a MOEA/D with adaptive external population guided weight vector adjustment (MaOEA/D-AEW). The algorithm modifies the MOEA/D method of constructing mating pools by calculating the utility function value of individuals in the population to produce high-quality offspring. For the maintenance of non-dominated solutions in the external population (EP), solutions exceeding the capacity of the EP are removed by the method of minimum Euclidean distance combined with the aggregation function value to ensure the convergence and diversity of non-dominated solutions in the EP. For the addition of weight vectors, a new sparsity evaluating method (SL+) is proposed to determine the sparsity of weight vectors by multiplying parallel distances between individuals. For the deletion of the weight vector, the minimum Euclidean distance combined with the aggregation function value is used to delete the weight vector corresponding to invalid or crowded individuals in the population. Comparing MaOEA/D-AEW with six state-of-the-art algorithms on regular PF and irregular PF test problems respectively, simulation results show that the proposed algorithm can adapt well to MaOPs with different PFs and significantly outperforms other comparative algorithms in terms of convergence and diversity of solution sets.

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 self-exploratory competitive swarm optimization algorithm for large-scale multiobjective optimization

With the popularity of “flipped classrooms,” teachers pay more attention to cultivating students’ autonomous learning ability while imparting knowledge. Inspired by this, this paper proposes a Self-exploratory Competitive Swarm Optimization algorithm for Large-scale Multiobjective Optimization (SECSO). Its idea is very simple and there are no parameters that need to be adjusted. Particles evolve by exploring their neighboring space and learning from other particles in the swarm, thereby simultaneously enhancing the diversity and convergence performance of the algorithm. Compared with eight state-of-the-art large-scale multiobjective evolutionary algorithms, the proposed method exhibited outstanding performance on LSMOP problems with up to 10,000 decision variables. Unlike most existing large-scale evolutionary algorithms that usually require a large number of objective evaluations, SECSO shows the ability to find a set of well converged and diverse non-dominated solutions.

A multi-resolution grid-based bacterial foraging optimization algorithm for multi-objective optimization problems

In recent years, bacterial foraging optimization (BFO) has been used to solve multiobjective optimization problems (MOPs). However, BFO has not fully developed its potentials on MOPs for the reason of lacking of in-depth research on the optimization mechanisms and the diversity maintenance strategies. To solve it, this paper develops a multi-resolution grid-based BFO algorithm (called as MRBFO). MRBFO redesigns four tailored optimization mechanisms for MOPs including chemotaxis, conjugation, reproduction, and elimination and dispersal to search optimal nondominated solutions. Moreover, MRBFO defines a multi-resolution grid strategy to produce well-distributed diverse nondominated solutions. The performance of MRBFO is comprehensively evaluated by comparing it with several state-of-the-art algorithms on many benchmark test problems. The empirical results have sufficiently verified the advantages of MRBFO.

Level-based multi-objective particle swarm optimizer for integrated production scheduling and vehicle routing decision with inventory holding, delivery, and tardiness costs

Integrated optimisation of production scheduling and distribution decision is necessary for reducing the whole cost of the supply chain in the make-to-order business environment. This paper studies a new integrated production scheduling and vehicle routing problem (IPSVRP) with inventory holding, delivery, and tardiness costs. The considered IPSVRP is modelled as a triple-objective optimisation problem, where the first objective aims to obtain the minimal total holding cost in the inventory, the second one attempts to achieve the minimal total travelling cost, and the third one tries to acquire the minimal total tardiness cost. To obtain a set of diverse non-dominated solutions in the Pareto-optimal front of the problem, we first derive several key structural properties used to provide necessary conditions for any solution to be Pareto-optimal through theoretical investigation. Based on the derived structural properties, a level-based multi-objective particle swarm optimizer (LMPSO) is subsequently designed. The performance of LMPSO is analysed by conducting a set of experiments, and its superiority is verified through comparing with other optimisation algorithms. Moreover, the convergence behaviour of LMPSO is also investigated, and the experimental results prove that it has the ability to achieve a set of non-dominated solutions proximity to the true Pareto front.

Uncertainty-wise Requirements Prioritization with Search

Requirements review is an effective technique to ensure the quality of requirements in practice, especially in safety-critical domains (e.g., avionics systems, automotive systems). In such contexts, a typical requirements review process often prioritizes requirements, due to limited time and monetary budget, by, for instance, prioritizing requirements with higher implementation cost earlier in the review process. However, such a requirement implementation cost is typically estimated by stakeholders who often lack knowledge about (future) requirements implementation scenarios, which leads to uncertainty in cost overrun. In this article, we explicitly consider such uncertainty (quantified as cost overrun probability) when prioritizing requirements based on the assumption that a requirement with higher importance, a higher number of dependencies to other requirements, and higher implementation cost will be reviewed with the higher priority. Motivated by this, we formulate four objectives for uncertainty-wise requirements prioritization: maximizing the importance of requirements, requirements dependencies, the implementation cost of requirements, and cost overrun probability. These four objectives are integrated as part of our search-based uncertainty-wise requirements prioritization approach with tool support, named as URP. We evaluated six Multi-Objective Search Algorithms (MOSAs) (i.e., NSGA-II, NSGA-III, MOCell, SPEA2, IBEA, and PAES ) together with Random Search ( RS ) using three real-world datasets (i.e., the RALIC, Word, and ReleasePlanner datasets) and 19 synthetic optimization problems. Results show that all the selected MOSAs can solve the requirements prioritization problem with significantly better performance than RS . Among them, IBEA was over 40% better than RS in terms of permutation effectiveness for the first 10% of prioritized requirements in the prioritization sequence of all three datasets. In addition, IBEA achieved the best performance in terms of the convergence of solutions, and NSGA-III performed the best when considering both the convergence and diversity of nondominated solutions.

Bi-Objective Re-Entrant Hybrid Flow Shop Scheduling considering Energy Consumption Cost under Time-of-Use Electricity Tariffs

Re-entrant hybrid flow shop scheduling problem (RHFSP) is widely used in industries. However, little attention is paid to energy consumption cost with the raise of green manufacturing concept. This paper proposes an improved multiobjective ant lion optimization (IMOALO) algorithm to solve the RHFSP with the objectives of minimizing the makespan and energy consumption cost under Time-of-Use (TOU) electricity tariffs. A right-shift operation is then used to adjust the starting time of operations by avoiding the period of high electricity price to reduce the energy consumption cost as far as possible. The experimental results show that IMOALO algorithm is superior to multiobjective ant lion optimization (MOALO) algorithm, NSGA-II, and MOPSO in terms of the convergence, dominance, and diversity of nondominated solutions. The proposed model can make enterprises avoid high price period reasonably, transfer power load, and reduce the energy consumption cost effectively. Meanwhile, parameter analysis indicates that the period of TOU electricity tariffs and energy efficiency of machines have great impact on the scheduling results.

Tri-objective optimal scheduling of smart energy hub system with schedulable loads

Many researches have investigated the optimal energy scheduling to meet the demand regarding the sustainable development issues and the economic and environmental indices. The energy hub system (EHS) is introduced as an appropriate framework in which the demands are supplied by multi carrier energy (MCE) such as electricity, natural gas, and thermal energy. In this paper, the optimal scheduling problem of an EHS is modeled as a tri-objective optimization problem in which the operation cost, the emission pollution, and the deviation of the electrical load profile from its desired value is minimized. In the proposed model, the third objective function as a Demand-side Management (DSM) strategy is considered for the optimal shifting of the electrical deferrable loads (EDLs) based on the day-ahead electrical energy prices. Moreover, the reserve scheduling is proposed by the interruptible loads (ILs) of the thermal and the electrical demand. The proposed model is solved using the augmented ε-constraint method in the General Algebraic Modeling System (GAMS) optimization software environment. The generated solutions by the augmented ε-constraint method have diverse non-dominated solutions in which the best solution is selected by the fuzzy approach. In order to validate the proposed approach, three Case studies are investigated and their results are compared with each other. The operation cost and the emission pollution of the EHS in the first case is 402130.12 $ and 36162.26 kg. With the participation of EDLs in the second case, the operation cost and the emission reduces 0.4% and 3.02%, respectively. Finally, with the simultaneous participation of EDLs and ILs in the third case, the operation cost and the emission pollution reduces 0.38% and 2.53% in comparison with the second case. • Proposing tri-objective functions in smart EHS with optimal shifting of EDLs. • Implementation of optimal shifting and strategic conversion of DSM strategies. • Proposing ILs as reserve in smart EHS. • Utilization of augmented ɛ-constraint method to solve objective functions. • Finding best solution by fuzzy approach.

Multi-Objective Reentrant Hybrid Flowshop Scheduling with Machines Turning on and off Control Strategy Using Improved Multi-Verse Optimizer Algorithm

This paper focuses on the multi-objective optimization of the reentrant hybrid flowshop scheduling problem (RHFSP) with machines turning on and off control strategy. RHFSP exhibits significance in many industrial applications, but scheduling with both energy consumption consideration and reentrant concept is relatively unexplored at present. In this study, an improved Multi-Objective Multi-Verse Optimizer (IMOMVO) algorithm is proposed to optimize the RHFSP with objectives of makespan, maximum tardiness, and idle energy consumption. To solve the proposed model more effectively, a series of improved operations are carried out, including population initialization based on Latin hypercube sampling (LHS), individual position updating based on Lévy flight, and chaotic local search based on logical self-mapping. In addition, a right-shift procedure is used to adjust the start time of operations aiming to minimize the idle energy consumption without changing the makespan. Then, Taguchi method is utilized to study the influence of different parameter settings on the scheduling results of the IMOMVO algorithm. Finally, the performance of the proposed IMOMVO algorithm is evaluated by comparing it with MOMVO, MOPSO, MOALO, and NSGA-II on the same benchmark set. The results show that IMOMVO algorithm can solve the RHFSP with machines turning on and off control strategy effectively, and in terms of convergence and diversity of non-dominated solutions, IMOMVO is obviously superior to other algorithms. However, the distribution level of the five algorithms has little difference. Meanwhile, by turning on and off the machine properly, the useless energy consumption in the production process can be reduced effectively.

Dispatching strategies for coordinating environmental awareness and risk perception in wind power integrated system

Wind power plays a significant role in economic and environmental operation of electric power system. Meanwhile, the variability and uncertainty characteristics of wind power generation bring technical and economical challenges for power system operation. In order to harmonize the relationship between environmental protection and risk management in power dispatching, this paper presents a stochastic dynamic economic emission dispatch model combining risk perception with environmental awareness of decision-makers by following the principle of chance-constrained programming. In this power dispatching model, the description of wind power uncertainty is derived from the probability statistic character of wind speed. Constraints-handling techniques as a heuristic strategy are embedded into non-dominated sorting genetic algorithm-II. In addition, more information is digested from the Pareto optimum solution set by cluster analysis and fuzzy set theory. The simulation results eventually demonstrate that the increase of the share of wind power output will bring higher risk, though it is beneficial for economic cost and environmental protection. Since different risk perception and environmental awareness can possibly lead to diverse non-dominated solutions, decision-makers may choose an appropriate dispatching strategy according to their specific risk perception and environmental awareness.

Modified differential evolution algorithm using a new diversity maintenance strategy for multi-objective optimization problems

In this paper, we propose a modified differential evolution (DE) based algorithm for solving multi-objective optimization problems (MOPs). The proposed algorithm, called multi-objective DE with dynamic selection mechanism (DSM), i.e., MODE-DSM, modifies the general DE mutation operation to produce a population at each generation. To determine and evaluate a better spread of the non-dominated solution, a DSM with a new cluster degree measure is developed. The DSM is also used to select diverse non-dominated solutions. The performance of the proposed algorithm is evaluated against seventeen bi-objective and two tri-objective benchmark test problems. The experimental results show that the proposed algorithm achieves better convergence to the Pareto-optimal front as well as better diversity on the final non-dominated solutions than the other five multi-objective evolutionary algorithms (MOEAs). It suggests that the proposed algorithm is promising in dealing with MOPs. The ability of MODE-DSM with small population and the sensitivity of MODE-DSM have also been experimentally investigated in this paper.

Resource allocation model and double-sphere crowding distance for evolutionary multi-objective optimization

Convergence speed and diversity of nondominated solutions are two important performance indicators for Multi-Objective Evolutionary Algorithms (MOEAs). In this paper, we propose a Resource Allocation (RA) model based on Game Theory to accelerate the convergence speed of MOEAs, and a novel Double-Sphere Crowding Distance (DSCD) measure to improve the diversity of nondominated solutions. The mechanism of RA model is that the individuals in each group cooperate with each other to get maximum benefits for their group, and then individuals in the same group compete for private interests. The DSCD measure uses hyper-spheres consisting of nearest neighbors to estimate the crowding degree. Experimental results on convergence speed and diversity of nondominated solutions for benchmark problems and a real-world problem show the efficiency of these two proposed techniques.

MOEA/D-SQA: a multi-objective memetic algorithm based on decomposition

A multi-objective memetic algorithm based on decomposition is proposed in this article, in which a simplified quadratic approximation (SQA) is employed as a local search operator for enhancing the performance of a multi-objective evolutionary algorithm based on decomposition (MOEA/D). The SQA is used for a fast local search and the MOEA/D is used as the global optimizer. The multi-objective memetic algorithm based on decomposition, i.e. a hybrid of the MOEA/D with the SQA (MOEA/D-SQA), is designed to balance local versus global search strategies so as to obtain a set of diverse non-dominated solutions as quickly as possible. The emphasis of this article is placed on demonstrating how this local search scheme can improve the performance of MOEA/D for multi-objective optimization. MOEA/D-SQA has been tested on a wide set of benchmark problems with complicated Pareto set shapes. Experimental results indicate that the proposed approach performs better than MOEA/D. In addition, the results obtained are very competitive when comparing MOEA/D-SQA with other state-of-the-art techniques.

A hybrid multiobjective evolutionary algorithm: Striking a balance with local search

This paper presents a hybrid multiobjective evolutionary algorithm (HMEA) that efficiently deals with multiobjective optimization problems (MOPs). The aim is to discover new nondominated solutions in the neighborhood of the most promising individuals in order to effectively push individuals toward the global Pareto front. It can be achieved by bringing the strength of an adaptive local search (ALS) to bear upon the evolutionary multiobjective optimization. The ALS is devised by combining a weighted fitness strategy and a knowledge-based local search which does not incur any significant computational cost. To be more exact, the highly converged and less crowded solutions selected in accordance with the weighted fitness values are improved by the local search, thereby helping multiobjective evolutionary algorithms (MEAs) to economize on the search time and traverse the search space. Thus, the proposed HMEA that transplants the ALS to the framework of MEAs can achieve higher proximity and better diversity of nondominated solutions. To show the utility of HMEA, the ALS for multiobjective knapsack problems (MKPs) is developed by exploiting the problem’s knowledge. Experimental results on the MKPs have provided evidence for its effectiveness as regards the proximity and the diversity performances.

An improved Non-dominated Sorting Genetic Algorithm-II (ANSGA-II) with adaptable parameters

Multi-Objective Evolutionary Algorithms (MOEAs) are not easy to use because they require parameter tunings to achieve good solutions and performance for an arbitrary complex problem. This paper introduces a MOEA with adaptive population size, self-adaptive crossover and self-adaptive mutation for automating the process of adjusting parameter values to make the MOEA simple to use. The new MOEA is built on the Non-dominated Sorting Genetic Algorithm-II (NSGA-II) and named as Adaptable NSGA-II (ANSGA-II). Simulation results on 13 multi-objective problems demonstrate that the ANSGA-II out-performs the NSGA-II in terms of finding diverse non-dominated solutions and converging to the true Pareto-optimal front.

A genetic algorithm for multiple objective sequencing problems in mixed model assembly lines

Presented in this paper is a new genetic algorithm to solve multiple objective sequencing problems in mixed model assembly lines. Mixed model assembly lines are a type of production line where a variety of product models similar in product characteristics are assembled. Such an assembly line is increasingly accepted in industry to cope with the recently observed trend of diversification of customer demands. While several objectives have been investigated for an efficient use of the production line, they are usually dealt with independently in existing researches. Relatively little attention has been paid to multiple objective problems. A new genetic algorithm is developed and is applied to the multiple objective problems addressed in this paper. The problem simultaneously considers three objectives found often in literature and meaningful in reality. The proposed genetic algorithm places emphasis on seeking for a set of diverse non-dominated solutions. Extensive computational experiments are carried out to demonstrate the superiority of the algorithm.Sequencing problems are important for an efficient use of mixed model assembly lines. There is a rich set of criteria on which to judge sequences of product models in terms of line utilization. We consider three practically important objectives: minimizing total utility work, keeping a constant rate of part usage and minimizing total setup cost. A considerate line manager would like to take into account all these factors. The multiple objective sequencing problem is described and its mathematical formulation is provided. A genetic algorithm is designed for finding near-Pareto or Pareto optimal solutions for the problem. A new genetic evaluation and selection mechanism, called Pareto stratum–niche cubicle, is proposed. The performance comparison of the proposed genetic algorithm with three existing genetic algorithms is made for various test-bed problems in terms of solution quality and diversity. The results reveal that the proposed genetic algorithm outperforms the existing genetic algorithms, especially for problems that are large and involve great variation in setup cost.