Multi-objective Problem Research Articles

The multi-objective data-driven approach: A route to drive performance optimization in the food industry

Although standardized, food processing is subject to many sources of variability resulting from compositional and structural variabilities of raw materials and/or ingredients, human perception and intervention in the process, capabilities of processing tools and their wear and tear, etc. Altogether, they affect the reproducibility of final product characteristics representing deviations to standard, the production yield impacting the economic performance of the food manufacturing process, and many other performance indicators. They are grossly classified as economic, quality and environmental indicators and their simultaneous consideration can be used to define the overall performance of a manufacturing process. Optimizing the overall performance of food processing requires the use of multi-objective optimization methods. Multi-objective optimization methods include five steps: defining the objectives, modelling performance indicators, formulating the problem and constraints, solving the multi-objective problem, and finally identifying an ideal solution. The integration of data-driven approach, particularly machine learning, into the multi-objective optimization offers new perspectives for optimizing and controlling food processes. The potential of this approach is still underestimated by the food industry sector.

Multi-objective group learning algorithm with a multi-objective real-world engineering problem

The concern of multi-objective optimization is to deal with optimization problems with more than one objective that should be optimized at the same time. In this paper, a new multi-objective optimization algorithm called multi-objective group learning algorithm is examined. The algorithm is based on the effect of group leaders on the group members and the effect that the group members have on each other. The algorithm is evaluated against the five Zitzler, Deb and Thiele (ZDT) benchmark functions, two standard functions of the DTLZ benchmarks, and a real-world engineering problem. To quantitatively examine the ability of the algorithm four metrics are utilized. Additionally, to statistically confirm the results, standard deviation and the average metrics are used. Moreover, the Wilcoxon rank sum test is used to examine the importance of the results statistically. Finally, the results of the algorithm are evaluated against multi-objective ant lion optimizer, multi-objective evolutionary algorithm based on decomposition, Pareto envelop-based selection algorithm-II, and multi-object moth swarm algorithm. The results of the benchmark functions showed that the proposed work produced better results in most of the metrics for three out of five ZDT benchmarks, and for the rest of the benchmarks it produced better results in at least one of the metrics compared to the participated algorithms. Moreover, the result of the real world engineering problem proved the ability of the proposed algorithm in producing acceptable and better Pareto front in almost all the metrics. For the proposed algorithm, the result of the generational distance for the speed reducer design problem is 0.8002, whereas it is 7.9375710, and 61.98134 for the multi-objective evolutionary algorithm based on decomposition, multi-objective ant lion optimizer, respectively. Additionally, the produced result for the spacing metric by the proposed algorithm was smaller than the result of the other algorithms for the same metric by at least 100 points. The result of the aforementioned metric proves the good distribution of the non-dominated solutions by the proposed algorithm.

Striking the perfect balance: Multi-objective optimization for minimizing deployment cost and maximizing coverage with Harmony Search

In the Internet of Things (IoT) era, wireless sensor networks play a critical role in communication systems. One of the most crucial problems in wireless sensor networks is the sensor deployment problem, which attempts to provide a strategy to place the sensors within the surveillance area so that two fundamental criteria of wireless sensor networks, coverage and connectivity, are guaranteed. In this paper, we look to solve the multi-objective deployment problem so that area coverage is maximized and the number of nodes used is minimized. Since Harmony Search is a simple yet suitable algorithm for our work, we propose Harmony Search algorithm along with various enhancement proposals, including heuristic initialization, random sampling of sensor types, weighted fitness evaluation, and using different components in the fitness function, to provide a solution to the problem of sensor deployment in a heterogeneous wireless sensor network where sensors have different sensing ranges. On top of that, the probabilistic sensing model is used to reflect how the sensors work realistically. We also provide the extension of our solution to 3D areas and propose a realistic 3D dataset to evaluate it. The simulation results show that the proposed algorithms solve the area coverage problem more efficiently than previous algorithms. Our best proposal demonstrates significant improvements in coverage ratio by 10.20% and cost saving by 27.65% compared to the best baseline in a large-scale evaluation.

Multi-population genetic algorithm with crowding-based local search for fuzzy multi-objective supply chain configuration

Supply chain configuration is often fuzzy and involves multiple objectives in real-world scenarios, but existing researches lack the exploration in the fuzzy aspect. Therefore, this paper establishes a fuzzy multi-objective supply chain configuration problem model to minimize the lead time and product cost oriented towards real supply chain environments. To solve the fuzzy problem, the theories of membership and closeness degree in fuzzy mathematics are adopted, and a multi-population genetic algorithm (MPGA) with crowding-based local search method is proposed. The MPGA algorithm uses two populations for optimizing the two objectives separately and effectively, and is characterized by three main innovative aspects. Firstly, a radical-and-radial selection operator is designed to balance the convergence speed and diversity of population. In the early stage of the algorithm, two populations are both optimized towards the ideal knee point, and then are separately optimized towards the two ends of the Pareto front (PF). Secondly, an elitist crossover operator is devised to promote information exchange within two populations. Thirdly, a crowding-based local search is proposed to speed up convergence by improving the crowded solutions, and to enhance diversity by obtaining new solutions around the uncrowded ones. Comprehensive experiments are tested on a fuzzy dataset with different sizes, and the integral of the hypervolume of PF is used for the evaluation of the fuzzy PF. The results show that MPGA achieves the best performance over other comparative algorithms, especially on maximum spread metric, outperforming all others by an average of 39 % across all test instances.

A fuzzy multi-objective programming model for the delivery and distribution of humanitarian relief materials

Disaster relief presents many unique logistics challenges, including damaged transportation infrastructure, multiple conflicting goals, and secondary disasters caused by spontaneous disaster relief. The delivery and distribution of humanitarian relief materials faced by nonprofit organizations (NPOs) poses a critical challenge due to the highly unpredictable nature of disasters, conflicting missions, and the need to navigate government regulations in disaster management. In this paper, we propose a novel multi-objective disaster relief modeling system for NPOs, considering (1) prioritization (providing medical services to seriously injured victims), (2) effectiveness (degree of satisfaction), (3) efficiency (operational costs), and (4) equity (cost of maintaining order). To incorporate the practical constraints of disaster relief operations, we include factors such as road damage, transportation capacity limitations, and route flow saturation as part of the model formulation. We then utilize fuzzy multi-objective programming to optimize the proposed disaster relief model, considering two relief distribution schemes: a common NPOs' spontaneous relief scheme and a newly designed traffic control scheme with government regulation. Based on the real-world scenario of the 2008 Wenchuan earthquake, we demonstrate that the designed traffic control scheme exhibited remarkable improvement among the NPOs' four objectives compared to the spontaneous relief scheme. Moreover, in the process of solving fuzzy multi-objective programming problems, artificial intelligence technology is employed to handle the fuzziness in multi-objective and automatically adjust parameters, making the solution results better and in line with practical situations. And we also validate the proposed model can be solved in polynomial time, meeting the engineering practice requirements, and can be easily extend to most disaster relief distribution scenarios.

A Self-Learning Hyper-Heuristic Algorithm Based on a Genetic Algorithm: A Case Study on Prefabricated Modular Cabin Unit Logistics Scheduling in a Cruise Ship Manufacturer.

Hyper-heuristic algorithms are known for their flexibility and efficiency, making them suitable for solving engineering optimization problems with complex constraints. This paper introduces a self-learning hyper-heuristic algorithm based on a genetic algorithm (GA-SLHH) designed to tackle the logistics scheduling problem of prefabricated modular cabin units (PMCUs) in cruise ships. This problem can be regarded as a multi-objective fuzzy logistics collaborative scheduling problem. Hyper-heuristic algorithms effectively avoid the extensive evaluation and repair of infeasible solutions during the iterative process, which is a common issue in meta-heuristic algorithms. The GA-SLHH employs a genetic algorithm combined with a self-learning strategy as its high-level strategy (HLS), optimizing low-level heuristics (LLHs) while uncovering potential relationships between adjacent decision-making stages. LLHs utilize classic scheduling rules as solution support. Multiple sets of numerical experiments demonstrate that the GA-SLHH exhibits a stronger comprehensive optimization ability and stability when solving this problem. Finally, the validity of the GA-SLHH in addressing real-world decision-making issues in cruise ship manufacturing companies is validated through practical enterprise cases. The results of a practical enterprise case show that the scheme solved using the proposed GA-SLHH can reduce the transportation time by up to 37%.

Co-design of an unmanned cable shovel for structural and control integrated optimization: A highly heterogeneous constrained multi-objective optimization algorithm

Unmanned cable shovel is an intelligence-based large machine used for excavating in open-pit coal mines, with significant implications for the security and development of energy resources. The co-design of unmanned cable shovels, considering elements from both structural and control systems, has demonstrated superior performance in obtaining optimal solutions compared to the traditional approaches that focus on individual systems. However, the inherent complexities of diverse systems often lead to heterogeneous function evaluations, posing challenges for the existing optimization algorithms. To address highly heterogeneous multi-objective optimization problems characterized by surrogate-approximated expensive functions and explicit inexpensive functions, this study proposes a highly heterogeneous constrained multi-objective optimization (HHCMO) algorithm. Leveraging NSGA-III as an evolutionary optimizer and the Kriging model for approximating expensive functions, HHCMO strategically addresses the challenges posed by highly heterogeneous objective evaluations. A Monte Carlo sampling-based expected hypervolume improvement (EHVI) criterion, employing a new nearest point approximation method in a unified sampling space, effectively handles the impact of heterogeneous objective evaluations on the sequential infill of the Kriging model. Thorough evaluations on both unconstrained and constrained multi-objective benchmark problems validate the correctness of HHCMO and its superiority relative to state-of-the-art algorithms. Finally, the effectiveness of the proposed method is successfully demonstrated in an engineering scenario of an unmanned cable shovel, where it adeptly handles expensive functions from the structural system and inexpensive functions from the control system.

Lagrange Duality and Saddle-Point Optimality Conditions for Nonsmooth Interval-Valued Multiobjective Semi-Infinite Programming Problems with Vanishing Constraints

This article deals with a class of nonsmooth interval-valued multiobjective semi-infinite programming problems with vanishing constraints (NIMSIPVC). We introduce the VC-Abadie constraint qualification (VC-ACQ) for NIMSIPVC and employ it to establish Karush–Kuhn–Tucker (KKT)-type necessary optimality conditions for the considered problem. Regarding NIMSIPVC, we formulate interval-valued weak vector, as well as interval-valued vector Lagrange-type dual and scalarized Lagrange-type dual problems. Subsequently, we establish the weak, strong, and converse duality results relating to the primal problem, NIMSIPVC, and the corresponding dual problems. Moreover, we introduce the notion of saddle points for the interval-valued vector Lagrangian and scalarized Lagrangian of NIMSIPVC. Furthermore, we derive the saddle-point optimality criteria for NIMSIPVC by establishing the relationships between the solutions of NIMSIPVC and the saddle points of the corresponding Lagrangians of NIMSIPVC, under convexity assumptions. Non-trivial illustrative examples are provided to demonstrate the validity of the established results. The results presented in this paper extend the corresponding results derived in the existing literature from smooth to nonsmooth optimization problems, and we further generalize them for interval-valued multiobjective semi-infinite programming problems with vanishing constraints.

The Multi-Objective Shortest Path Problem with Multimodal Transportation for Emergency Logistics

The optimization of emergency logistical transportation is crucial for the timely dispatch of aid and support to affected areas. By incorporating practical constraints into emergency logistics, this study establishes a multi-objective shortest path mixed-integer programming model based on a multimodal transportation network. To solve multi-objective shortest path problems with multimodal transportation, we design an ideal point method and propose a procedure for constructing the complete Pareto frontier based on the k-shortest path multi-objective algorithm. We use modified Dijkstra and Floyd multimodal transportation shortest path algorithms to build a k-shortest path multi-objective algorithm. The effectiveness of the proposed multimodal transportation shortest path algorithm is verified using empirical experiments carried out on test sets of different scales and a comparison of the runtime using a commercial solver. The results show that the modified Dijkstra algorithm has a runtime that is 100 times faster on average than the modified Floyd algorithm, which highlights its greater applicability in large-scale multimodal transportation networks, demonstrating that the proposed method both has practical significance and can generate satisfactory solutions to the multi-objective shortest path problem with multimodal transportation in the context of emergency logistics.

Novel machine learning-driven multi-objective optimization method for EDM trajectory planning of distorted closed surfaces

Highly distorted closed surfaces pose significant challenges for machining trajectory planning due to their intricate surface constraints and closed structures. Despite these challenges, components with such features are prevalent in industries like aerospace. This paper presents a machine learning-driven multi-objective optimization method for electrical discharge machining (EDM) trajectory planning of highly distorted closed surfaces. The method transforms the structural design of forming electrodes and trajectory planning into a multi-objective decision problem. And a discrete point trajectory planning method, guided by surface average curvature, is employed to determine the optimal position and orientation of the electrode. Additionally, an elite dataset, generated using the Monte Carlo method and Arena's Principle, is utilized to train an artificial neural network (ANN). This network predicts hyperparameters for the nonlinear optimization problem. Based on the proposed method, a multi-objective optimization model is formulated for an integral shrouded blisk, considering minimization of iteration count, axial motion, and maximization of machining surface quality. The Pareto front is utilized to obtain the optimal EDM trajectory. Experimental results demonstrate a 17.38 % reduction in the overall machining cycle duration using this trajectory, and the surface roughness and profile accuracy satisfy the design specifications, which proves the effectiveness of this method.

A two-stage accelerated search strategy for large-scale multi-objective evolutionary algorithm

Since large-scale multi-objective problems (LSMOPs) have huge decision variables, the traditional evolutionary algorithms are facing difficulties of low exploitation efficiency and high exploration costs in solving LSMOPs. Therefore, this paper proposes an evolutionary strategy based on two-stage accelerated search optimizers (ATAES). Specifically, a convergence optimizer is devised in the first stage, while a three-layer lightweight convolutional neural network model is built, and the population is homogenized into two subsets, the diversity subset, and the convergence subset, which serve as input nodes and the expected output nodes of the neural network, respectively. Then, by constantly backpropagating the gradient, a satisfactory individual will be produced. Once exploitation stagnation is discovered in the first phase, the second phase will be run, where a diversity optimizer using a differential optimization algorithm with opposite learning is suggested to increase the exploration range of candidate solutions and thereby increase the population's diversity. Finally, to validate the algorithm's performance, on multi-objective LSMOP and DTLZ benchmark suits with decision variable quantities of 100, 300, 500, and 1000, the ATAES demonstrated its superiority with other advanced multi-objective evolutionary algorithms.

Hierarchical optimization by spatial-temporal indictor in multi-scale decision pyramid for constrained large-scale multi-objective problems

Most existing constrained multi-objective evolutionary algorithms (CMOEAs) are not so efficient when handling constrained large-scale multi-objective problems (CLSMOPs). To overcome CLSMOPs, a hierarchical optimization, based on the spatial–temporal indictor in the decision pyramid (HOSTI-DP), is proposed to determine the dynamic trade-off between feasible and infeasible solutions in the effectively shrunken searching area. The decision pyramid consists of multiple decision spaces with a set of descending numbers of variables; it is initially constructed to speed up the solution convergence by the layer-by-layer dimensionality reduction and increase the population diversity based on the accumulation of these layers. The spatial–temporal indictor considers both the optimization stage (time) and the hierarchy structure of the decision pyramid (space) and it is designed to restrain the prematurely feasible solutions and find the promising infeasible solutions. Finally, the hierarchical optimization strategy, which applies the spatial–temporal indicator to the evolutionary algorithms in every layer of the decision pyramid and dynamically arranging the proportion among them, is designed for comprehensive balance of objectives, constraints, and computational complexity. Nine representative and state-of-the-art CMOEAs have been compared with the HOSTI-DP to demonstrate its effectiveness through comparative experiments on CLSMOPs with equality and inequality constraints and 1000 decision variables. Experimental results show that HOSTI-DP can significantly improve the performance of these CMOEAs.

Optimized scheduling of integrated community energy stations based on improved NSGA-III algorithm

To cope with the problem of building and using a large number of fast electric vehicle stations (FEVS), adding FEVS to the integrated community energy system (ICES) provides new ideas for solving the problems of interaction with the grid, overall system stability, revenue benefits, and environmental pollution. To this end, this paper designs an ICES model with FEVS (ICES-FEVS). This model considers economy, stability, and sustainability to achieve all-around consideration. To further solve the complex multi-objective problem, the multi-objective improvement strategy NSGA-III algorithm (IS-NSGA-III), combined with fuzzy comprehensive evaluation (FCE), is used to solve the model. In the solution phase, the advantages of the IS-NSGA-III algorithm are first verified by the benchmark function, and the validity of the ICES-FEVS model is verified by comparing different models. In the optimization results, daily revenue was increased by 6.3 %, daily battery life loss was increased by 26.03 %, and pollution emissions were reduced by 46.9 %. The analysis of the results shows that introducing Electric Vehicle (EV) fast charging stations in an integrated community energy system ensures economic improvement, sustainable development, and more favorable regulation of the energy storage system. The simulation results show that compared with other algorithms, the HV metrics of IS-NSGA-III are lower by about 6.8 %, Spread metrics are better by about 1.35 %, and the proposed IS-NSGA-III is better in terms of convergence and distributivity.

Single-objective and multi-objective mixed-variable grey wolf optimizer for joint feature selection and classifier parameter tuning

Feature selection plays an essential role in data preprocessing, which can extract valuable information from extensive data, thereby enhancing the performance of machine learning classification. However, existing feature selection methods primarily focus on selecting feature subsets without considering the impact of classifier parameters on the optimal subset. Different from these works, this paper considers jointly optimizing the feature subset and classifier parameters to minimize the number of features and achieve a low classification error rate. Since feature selection is an optimization problem with binary solution space while classifier parameters involve both continuous and discrete variables, our formulated problem becomes a complex multi-objective mixed-variable problem. To address this challenge, we consider a single-objective optimization method and a multi-objective optimization approach. Specifically, in the single-objective optimization method, we adopt the linear weight method to convert our multiple objectives into a fitness function and then propose a mixed-variable grey wolf optimizer (MGWO) to optimize the function. The proposed MGWO introduces Chaos-Faure initialization, Log convergence factor adjustment, and optimal solution adaptive update operators to enhance its adaptability and balance the global and local search of the algorithm. Subsequently, an improved multi-objective grey wolf optimizer (IMOGWO) is introduced to directly address the problem. The proposed IMOGWO introduces improved initialization, local search, and binary variable mutation operators to balance its exploration and exploitation abilities, making it more suitable for our mixed-variable problem. Extensive simulation results show that our MGWO and IMOGWO outperform recent and classic baselines. Moreover, we also find that jointly optimizing classifier parameters can significantly improve classification accuracy.

A bi-evolutionary cooperative multi-objective algorithm for blocking group flow shop with outsourcing option

In this study, a multi-objective blocking group flow shop scheduling problem with outsourcing option (BGFSP_OO) is addressed, where three objectives, including makespan, total energy consumption (TEC) and outsourcing cost, are considered simultaneously. To solve the BGFSP_OO, a bi-evolutionary cooperative multi-objective algorithm (BECMOA) is proposed. First, a machine switching strategy based on machine idle and blocking time is used in the decoding part to optimize the objective value TEC. Then, an effective heuristic for classifying outsourcing groups is proposed. To balance convergence and diversity abilities, a bi-evolutionary mechanism is proposed. The particle swarm optimization algorithm based on the gravity factor (IPSO) is employed, which exploiting individual performance, can enhance the convergence ability. Cross evolutionary search (CES) strategy is developed which can improve search ability, aiming to ensure diversity of solutions and access to more non-dominated solutions. Finally, the experimental results show that BECMOA is effective in solving BGFSP_OO compared to the state-of-the-art methods.

An Improved Ant Colony Algorithm with Deep Reinforcement Learning for the Robust Multiobjective AGV Routing Problem in Assembly Workshops

Vehicle routing problems (VRPs) are challenging problems. Many variants of the VRP have been proposed. However, few studies on VRP have combined robustness and just-in-time (JIT) requirements with uncertainty. To solve the problem, this paper proposes the just-in-time-based robust multiobjective vehicle routing problem with time windows (JIT-RMOVRPTW) for the assembly workshop. Based on the conflict between uncertain time and JIT requirements, a JIT strategy was proposed. To measure the robustness of the solution, a metric was designed as the objective. Afterwards, a two-stage nondominated sorting ant colony algorithm with deep reinforcement learning (NSACOWDRL) was proposed. In stage I, ACO combines with NSGA-III to obtain the Pareto frontier. Based on the model, a pheromone update strategy and a transfer probability formula were designed. DDQN was introduced as a local search algorithm which trains networks through Pareto solutions to participate in probabilistic selection and nondominated sorting. In stage II, the Pareto frontier was quantified in feasibility by Monte Carlo simulation, and tested by diversity-robust selection based on uniformly distributed weights in the solution space to select robust Pareto solutions that take diversity into account. The effectiveness of NSACOWDRL was demonstrated through comparative experiments with other algorithms on instances. The impact of JIT strategy is analyzed and the effect of networks on the NSACOWDRL is further discussed.

Recommending for a Multi-Sided Marketplace: A Multi-Objective Hierarchical Approach

We propose a multi-objective hierarchical recommender that solves the multi-objective recommendation problem in a hierarchical setting and was deployed on Uber Eats.

Multi-Objective Unsupervised Feature Selection and Cluster Based on Symbiotic Organism Search

Unsupervised learning is a type of machine learning that learns from data without human supervision. Unsupervised feature selection (UFS) is crucial in data analytics, which plays a vital role in enhancing the quality of results and reducing computational complexity in huge feature spaces. The UFS problem has been addressed in several research efforts. Recent studies have witnessed a surge in innovative techniques like nature-inspired algorithms for clustering and UFS problems. However, very few studies consider the UFS problem as a multi-objective problem to find the optimal trade-off between the number of selected features and model accuracy. This paper proposes a multi-objective symbiotic organism search algorithm for unsupervised feature selection (SOSUFS) and a symbiotic organism search-based clustering (SOSC) algorithm to generate the optimal feature subset for more accurate clustering. The efficiency and robustness of the proposed algorithm are investigated on benchmark datasets. The SOSUFS method, combined with SOSC, demonstrated the highest f-measure, whereas the KHCluster method resulted in the lowest f-measure. SOSFS effectively reduced the number of features by more than half. The proposed symbiotic organisms search-based optimal unsupervised feature-selection (SOSUFS) method, along with search-based optimal clustering (SOSC), was identified as the top-performing clustering approach. Following this, the SOSUFS method demonstrated strong performance. In summary, this empirical study indicates that the proposed algorithm significantly surpasses state-of-the-art algorithms in both efficiency and effectiveness. Unsupervised learning in artificial intelligence involves machine-learning techniques that learn from data without human supervision. Unlike supervised learning, unsupervised machine-learning models work with unlabeled data to uncover patterns and insights independently, without explicit guidance or instruction.

Bi-level programming for joint order acceptance and production planning in industrial robot manufacturing enterprise

Effectively addressing the Order Acceptance and Production Planning (OAP) problem is crucial for industrial robot manufacturers, particularly considering the rapid expansion of the industrial robot market. A bi-level programming model is structured to enhance synergies in response to department reformation within an industrial robot manufacturer. The upper-level model focuses on order acceptance, considering rejection and delay penalty costs, aiming to maximize enterprise profit. The lower-level model concentrates on product production, aiming to minimize the total sum of production costs and Work-In-Progress (WIP) holding costs. Detailed constraints related to material readiness, including inventory levels and procurement lead times, are comprehensively examined. Given the NP-hard complexity of this multi-objective problem, a meta-heuristic algorithm Whale Optimization Algorithm (WOA) is implemented. To enhance WOA’s optimization capabilities, two heuristic algorithms, Solution Improvement policy (I-algorithm) and Heuristic-based acceleration strategy (H-algorithm), are introduced, resulting in the development of WOA-IH. The experimental evidence suggests that the proposed model facilitates decision coordination for manufacturers, particularly in order management, production planning, and material procurement. Furthermore, this study contributes to applying bi-level programming theory in managing supply chains for industrial robotics.

A branch and cut algorithm to optimize a weighted sum-of-ratios in multiobjective mixed-integer fractional programming

AbstractMultiobjective linear fractional programming is useful to model multiobjective problems where all or some of the objective functions are a ratio or proportion of one linear/affine function to another linear/affine function. In practice, many of such problems include integer variables. If the weighted-sum scalarization is used to compute efficient solutions to the multiobjective problem, then the scalar problem to be solved for each weight vector turns out to be a weighted sum-of-ratios. There are several algorithms reported in the literature to optimize weighted sum-of-ratios, but almost all of them cannot deal with integer variables. In this paper we propose a Branch & Cut algorithm to optimize weighted-sums of the objective functions in multiobjective mixed integer fractional programming (MOMIFP). Several theoretical properties that support the algorithm are presented and proved. Computational experiments with randomly generated general problems are presented and discussed, which show that the algorithm is able to deal with practical MOMIFP problems.