Solving a tri-objective supply chain problem with modified NSGA-II algorithm

One of the important aspects of supply chain management is inventory management because the cost of inventories in a supply chain accounts for about 30% of the value of the product. The main focus of this work is to study the performance of a single-product serial supply chain operating with a base-stock policy and to optimize the inventory (i.e. base stock) levels in the supply chain so as to minimize the total supply chain cost (TSCC), comprising holding and shortage costs at all the installations in the supply chain. A genetic algorithm (GA) is proposed to optimize the base-stock levels with the objective of minimizing the sum of holding and shortage costs in the entire supply chain. Simulation is used to evaluate the base-stock levels generated by the GA. The proposed GA is evaluated with the consideration of a variety of supply chain settings in order to test for its robustness of performance across different supply chain scenarios. The effectiveness of the proposed GA (in terms of generating base-stock levels with minimum TSCC) is compared with that of a random search procedure. In addition, optimal base-stock levels are obtained through complete enumeration of the solution space and compared with those yielded by the GA. It is found that the solutions generated by the proposed GA do not significantly differ from the optimal solution obtained through complete enumeration for different supply chain settings, thereby showing the effectiveness of the proposed GA.

Non-orthogonal multiple access (NOMA) deployment in future wireless networks has been recently considered a promising radio access technology to enhance spectral efficiency (SE). However, gain in SE comes always with the cost of energy efficiency (EE). In this paper, we investigate the SE and EE tradeoff in downlink NOMA with the consideration of quality of service (QoS) requirements based on three population-based multi-objective evolutionary algorithms (MOEAs): multi-objective particle swarm optimization (MOPSO), non-dominated sorting genetic algorithm-II (NSGA-II) and strength Pareto evolutionary algorithm-2 (SPEA2). The tradeoff is optimized and Pareto optimal solutions are obtained through MOEAs. The effectiveness of the algorithms is evaluated based on the hypervolume metric and the capability of solving multi-objective optimization problems. Simulation results reveal that SPEA2 outperforms NSGA-II and MOPSO. Furthermore, NSGA-II is the loser among all algorithms in terms of finding Pareto optimal results.

Supply-chain scheduling in modern production systems faces significant challenges due to the complexity of balancing cost efficiency, delivery lead times, and order variability—especially under stochastic demand and uncertain transportation conditions. Conventional metaheuristic approaches, such as the standard Non-dominated Sorting Genetic Algorithm II (NSGA-II), often struggle with premature convergence, limited population diversity, and rigid parameter settings that hinder adaptability in dynamic environments. To address these limitations, this study proposes a novel Hybrid Adaptive NSGA-II (HA-NSGA-II) framework, enhanced by two key innovations: (1) a Global-Intensity Mutation Operator (GIMO) that strengthens population diversity by dynamically adjusting mutation intensity across the entire solution space; and (2) an Adaptive Parameter Self-Tuning (APST) module based on reinforcement learning, which intelligently regulates crossover and mutation rates in response to evolutionary progress and environmental changes. A tri-objective optimization model is formulated to simultaneously minimize total supply chain cost, order quantity variance (mitigating the bullwhip effect), and customer delivery delays. The proposed HA-NSGA-II demonstrates superior convergence and diversity performance compared to traditional NSGA-II, offering a more robust and adaptive solution for complex, real-world supply chain scheduling under uncertainty. The model is tested on a simulated supply chain with 5 factories, 15 warehouses, and 50 customers facing random demand and Gaussian-distributed lead times. The new HA-NSGA-II is compared with traditional NSGA-II, SPEA2, and MOEA/D based on Hypervolume (HV), Inverted Generational Distance (IGD), Spread (Δ), Total Inventory Cost, Bullwhip Index (BI), and Robustness Index (RI). Results of 50 simulation runs demonstrate that HA-NSGA-II surpasses all the baseline algorithms with 12.9% enhancement in HV, 41.1% improvement in IGD, and 13.7% reduction in convergence time. In addition, it delivers a 14.6% supply chain cost reduction, a 20.4% bullwhip effect suppression, and 25% accelerated times of fulfillment. The research concludes that the HA-NSGA-II provides a scalable and effective scheduling approach applicable for real-time Industry 4.0 supply chains. Work in the future involves expanding the framework towards multi-period dynamic environments using IoT and blockchain-based visibility.

This study compared the performances of three state-of-theart evolutionary multi-objective optimization algorithms: the Non-Dominated Sorted Genetic Algorithm II (NSGA-II), the Epsilon-Dominance Non-Dominated Sorted Genetic Algorithm II (e -NSGA-II) and the Epsilon-Dominance Multi-Objective Evolutionary Algorithm ( e MOEA), on a constrained biobjective crop-mix planning problem (BCP). The BCP test case objectives were to: (i) maximize crop production and (ii) minimize planting area. The BCP problem was enumerated to provide the true Pareto-optimal solution set to facilitate rigorous testing of the evolutionary multi-objective optimization algorithms. The performances of the three algorithms were assessed and compared using three performance metrics (additive epsilon indicator, inverted generational distance and spacing). For the comparative study, a graphical comparison with respect to true Pareto front of optimal crop planning problem was provided. Results of the analyses indicated that the e MOEA greatly outperforms the NSGAII and the e -NSGA-II.

Network reconfiguration is an alternative to reduce power losses and optimize the operation of power distribution systems. In this paper, an encoding scheme for evolutionary algorithms is proposed in order to search efficiently for the Pareto-optimal solutions during the reconfiguration of power distribution systems considering multiobjective optimization. The encoding scheme is based on the edge window decoder (EWD) technique, which was embedded in the Strength Pareto Evolutionary Algorithm 2 (SPEA2) and the Nondominated Sorting Genetic Algorithm II (NSGA-II). The effectiveness of the encoding scheme was proved by solving a test problem for which the true Pareto-optimal solutions are known in advance. In order to prove the practicability of the encoding scheme, a real distribution system was used to find the near Pareto-optimal solutions for different objective functions to optimize.

This paper proposed a multiobjective genetic algorithm approach for solving process planning and scheduling (PPS) problems in a distributed manufacturing system (DMS) environment. In this environment, factories processing various machines and tools at different geographical locations are often combined to produce various parts with different resource constraints. This paper proposed a fast multiobjective genetic algorithm with archive (fmoGA‐A) mechanism to deal with PPS problem with considering the minimization of the maximum total processing time and minimization of the maximum variation of workload of machine in DMS. The proposed algorithm has been compared with other approaches to testify and benchmark the optimization reliability on several PPS problems. These comparisons demonstrate the importance of PPS in DMS and indicate fmoGA‐A is better than adaptive weight approach genetic algorithm (awaGA) did on efficacy and efficient; the efficacy is not less than non‐dominated sorting genetic algorithm II (NSGA‐II) and strength Pareto evolutionary algorithm 2 (SPEA2) and the efficient is better than NSGA‐II and SPEA2. Copyright © 2010 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

Multi-criteria algorithms for portfolio optimization under practical constraints

Using Pareto-based multi-objective Evolution algorithms in decision structure to transfer the hazardous materials to safety storage centre

This article deals with the comparative performance of some established multi-objective evolutionary algorithms (MOEAs) for structural topology optimization. Four multi-objective problems, having design objectives like structural compliance, natural frequency and mass, and subjected to constraints on stress, etc., are posed for performance testing. The MOEAs include Pareto archive evolution strategy (PAES), population-based incremental learning (PBIL), non-dominated sorting genetic algorithm (NSGA), strength Pareto evolutionary algorithm (SPEA), and multi-objective particle swarm optimization (MPSO). The various MOEAs are implemented to solve the problems. The ground element filtering (GEF) technique is used to suppress checkerboard patterns on topologies. The results obtained from the various optimizers are illustrated and compared. It is shown that PBIL is far superior to the others. The optimal topologies from using PBIL can be compared with those obtained by employing the classical gradient-based approach. It can be considered as a powerful tool for structural topological design.

The potential and effectiveness of the newly developed Pareto-based multiobjective evolutionary algorithms (MOEA) for solving a real-world power system multiobjective nonlinear optimization problem are comprehensively discussed and evaluated in this paper. Specifically, nondominated sorting genetic algorithm, niched Pareto genetic algorithm, and strength Pareto evolutionary algorithm (SPEA) have been developed and successfully applied to an environmental/economic electric power dispatch problem. A new procedure for quality measure is proposed in this paper in order to evaluate different techniques. A feasibility check procedure has been developed and superimposed on MOEA to restrict the search to the feasible region of the problem space. A hierarchical clustering algorithm is also imposed to provide the power system operator with a representative and manageable Pareto-optimal set. Moreover, an approach based on fuzzy set theory is developed to extract one of the Pareto-optimal solutions as the best compromise one. These multiobjective evolutionary algorithms have been individually examined and applied to the standard IEEE 30-bus six-generator test system. Several optimization runs have been carried out on different cases of problem complexity. The results of MOEA have been compared to those reported in the literature. The results confirm the potential and effectiveness of MOEA compared to the traditional multiobjective optimization techniques. In addition, the results demonstrate the superiority of the SPEA as a promising multiobjective evolutionary algorithm to solve different power system multiobjective optimization problems.

Almost all real-world and engineering problems involve multi-objective optimization of some sort that is often constrained. To solve these constrained multi-objective optimization problems, constrained multi-objective optimization evolutionary algorithms (CMOEAs) are enlisted. These CMOEAs require specific constraint handling techniques. This study aims to address and test the most successful constraint handling techniques, seven different penalty constraint techniques, as applied to the Non-dominated Sorting Genetic Algorithm II (NSGA-II). In this paper, NSGA-II is chosen because of its high popularity amongst evolutionary algorithms. Inverted Generational Distance and Hypervolume are the main metrics that are discussed to compare the constraint handling techniques. NSGA-II is applied on 13 constrained multi-objective problems known as CF1-CF10, C1-DTLZ1, C2-DTLZ2, and C3-DTLZ4. The result of IGD and HV values are compared and the feasibility proportions of each combination on each problem are shown. The results of simulation present interesting findings that have been presented at the end of paper as discussion and conclusion.

Considering uncertainties in engineering optimum design is often a requirement. Here, the use of the deterministic optimum design as the reference point in g-dominance is proposed. The multiobjective optimum robust design in a structural engineering test case where uncertainties in the external loads are taken into account is proposed as application, where the simultaneous minimization of the constrained weight average and the standard deviation of the constraints violation are the objective functions. Results include a comparison between both non-dominated sorting genetic algorithm II (NSGA-II) and strength Pareto evolutionary algorithm (SPEA2), including S-metric (hypervolume) statistical comparisons with and without the g-dominance approach. The methodology is capable to provide robust optimum structural frame designs successfully.

Mathematical runtime analysis for the non-dominated sorting genetic algorithm II (NSGA-II)

The non-dominated sorting genetic algorithm II (NSGA-II) is the most intensively used multi-objective evolutionary algorithm (MOEA) in real-world applications. However, in contrast to several simple MOEAs analyzed also via mathematical means, no such study exists for the NSGA-II so far. In this work, we show that mathematical runtime analyses are feasible also for the NSGA-II. As particular results, we prove that with a population size larger than the Pareto front size by a constant factor, the NSGA-II with two classic mutation operators and three different ways to select the parents satisfies the same asymptotic runtime guarantees as the SEMO and GSEMO algorithms on the basic OneMinMax and LOTZ benchmark functions. However, if the population size is only equal to the size of the Pareto front, then the NSGA-II cannot efficiently compute the full Pareto front (for an exponential number of iterations, the population will always miss a constant fraction of the Pareto front). Our experiments confirm the above findings.

Water distribution networks (WDN) model optimization is an important part of smart water systems to achieve optimal strategies. WDN optimization focuses on the nonlinearity of the discharge head loss equation, the availability of discrete properties of pipe sizes, and the conservation of constraints. Multi-objective evolutionary algorithms (MOEAs) have been proposed and successfully applied in the field of WDN design optimization. Previous studies have focused on comparing the optimization effects of algorithms in water distribution networks, ignoring the problems of unbalanced pressure distribution and water hammer at the nodes of the pipe network caused by the complex terrain in mountainous areas. In this paper, a multi-objective water supply optimization model that integrated cost, reliability, and water quality was established for a mountainous WDN in real engineering. The method of traversing the nodes to solve the water age was introduced to find a more scientific and practical water age solution model, with setting the weight function to evaluate the water age of the water supply model comprehensively. Strength Pareto Evolutionary Algorithm II (SPEA-II) and Non-dominated Sorting Genetic Algorithm II (NSGA-II) were adopted to optimize the WDN design model in the mountainous complex terrain. The significance levels of the number of Pareto solutions (NOPS) and running time are 0.029 and 0.001, respectively, indicating that the two algorithms have significant differences. Compared to NSGA-II, SPEA-II has a better convergence rate and running time in multi-objective water supply optimization design. The solution set distribution of SPEA-II is more concentrated than that of NSGA-II, also the numerical value is better. The number of SPEA-II optimization schemes is larger and the scheme is more effective. Among them, the Pareto solution set of SPEA-II can obtain more desirable optimization results on cost, reliability index (RI) and water age. In summary, the study provides valuable information for decision makers in WDN with complex terrain.