Goal Programming Algorithm Research Articles

Fuzzy Goal Programming Algorithm for Multi-Objective Trajectory Optimal Parking of Autonomous Vehicles

Fuzzy Goal Programming Algorithm for Multi-Objective Trajectory Optimal Parking of Autonomous Vehicles

Reliable scheduling and routing in robust multiple cross-docking networks design

This study introduces a novel framework called Reliable Pollution Scheduling and Routing with Multi-Cross-Docking. The core idea behind this framework is to optimize the processing and transportation of products through each vehicle, ensuring that each vehicle serves its specified destinations only once before returning to the cross-dock. The objective of this research is to develop a multi-objective mixed integer programming model that efficiently manages scheduling and routing complexities in a multi-cross-docking system, taking into account uncertainties in demand. The primary goals of the model are to minimize the overall costs associated with pollution, loading/unloading, and transportation, while simultaneously reducing distribution and shipping durations. Additionally, the model aims to maximize the reliability of the supply chain for perishable products, contributing to sustainable development in the supply chain domain. To address the inherent complexity of the model, especially in dealing with demand uncertainties, we employ a robust optimization method. The multi-objective challenge is tackled using an innovative hybrid approach that combines goal programming and genetic algorithms. The effectiveness of our proposed solution strategies is rigorously assessed using a variety of metrics and subjected to comprehensive statistical testing. Furthermore, we validate the competence of our methodology by conducting a real-world case study, which includes sensitivity analysis of demand parameters and robustness analysis. Our findings confirm that our solution technique produces high-quality solutions. Notably, our approach optimizes route planning for delivery and pick-up phases, resulting in a significant 36.5% reduction in transportation time and a noteworthy 17.27% decrease in the overall system costs compared to existing conditions. Additionally, we observe a substantial 23.15% reduction in vehicle arrival times at cross-docks, contributing significantly to reduced product expenses.

A goal programming strategy for bi-level decentralised multi-objective linear programming problem with neutrosophic numbers

This paper develops a goal programming (GP) algorithm to evaluate bi-level decentralised multi-objective linear programming problem (BLDMOLPP) in neutrosophic number (NN) environment. In a BLDMOLPP, a single decision maker (DM) is present at the upper level and multiple decision makers at the lower level. Here the parameters of the problem are considered to be NNs in the form of [P+QI], where P and Q are real numbers and indeterminacy is represented through the symbol I. I is expressed in the form of a real interval as agreed upon by the DMs. The BLDMOLPP with NNs then gets converted into an interval BLDMOLPP. Using interval programming, the target intervals for the objective functions are identified and subsequently, the goal achievement functions are constructed. The upper level DM provides some possible relaxation on the decision variables under his/her control to cooperate with the lower level DMs to attain a compromise optimal solution. Thereafter, goal programming (GP) models are formulated by minimising the deviational variables and thereby obtaining the most satisfactory solution for all DMs. Finally, a numerical example demonstrates the feasibility and simplicity of the proposed strategy.

Goal programming and genetic algorithm in multiple objective optimization model for project portfolio selection: a review

Many scientific fields, such as engineering, data analytics, and deep learning, focus on optimization. Optimization problems are classified into two types based on the number of optimized objective functions: single objective and multi objective optimization problems. In this paper, a comparative review since 2000 using one of the deterministic and stochastic modelling approaches called goal programming (GP) and genetic algorithm (GA) in multi-objective optimization problem is discussed. This study gives a prime review of the application of GP and GA in various criteria of project portfolio selection problem. GP is a method for solving large-scale multi-objective optimization problems to assist decision makers in finding solutions that satisfy several competing goals. GA on the other hand are global meta-heuristic search algorithms that are used to provide approximation or optimal solutions to large-scale optimization problems. Of the 23 articles considered in this review showed that, from more than 100 projects, GA proved near optimal, feasible solution and efficient frontier in projects ranking, projects interaction and a preferred decision support tool of project portfolio selection. In addition, the two models select projects on risk-based approach, but GA proved to be more effective in terms of number of projects proposed, central processing unit (CPU) time and accuracy. The review concludes that, in multi-objective optimization model for project portfolio selection problems on a large-scale, very large or complex problems and less CPU time, GA is more effective than GP in multi-objective optimization problems. The review also showed gaps in previous studies of GP and GA application on project portfolio selection problem (PPSP). This review will aid scholars and demanding practitioners in gaining a broader understanding of goal programming and genetic algorithms in the context of project portfolio selection problems.

A hybrid optimization method to design a sustainable resilient supply chain in a perishable food industry.

To integrate the location, inventory, and routing (LIR) problems arising in designing a resilient sustainable perishable food supply network (RSPFSN), a bi-objective optimization model is developed. To improve the resiliency and sustainability of the RSPFSN, a dynamic pricing strategy is used to cope with the disrupting events, along with minimizing the total cost and CO2 emission of the whole network. One of the important features of the proposed model is taking into account the effects of route disruptions and traffic conditions on the deterioration of products. To solve the mixed-integer nonlinear bi-objective optimization model, a novel hybrid method is developed using the Heuristic Multi-Choice Goal Programming and Utility Function Genetics Algorithm (HMCGP-UFGA). To improve resiliency, the dynamic pricing strategy, considering the traffic condition, can lead to around a 20% improvement in both cost and CO2 emission, based on the results of our case study in a dairy supply chain. Besides, the results of sensitivity analysis display the high flexibility of the proposed approach for various problems.

Solving Multi-Objective Multilevel Programming problems using two-phase Intuitionistic Fuzzy Goal Programming method

This paper presents a two-phase intuitionistic fuzzy goal programming (two-phase IFGP) algorithm to solve Multi-Objective Multilevel Programming (MO-MLP) problems. The coefficient of each objective and constraint function is assumed to be triangular intuitionistic fuzzy parameters and the crisp MO-MLP problems are obtained using the accuracy function method. To avoid decision lock, the top levels set tolerance limits for decision variables to control the lower levels. The problem is modeled in the intuitionistic fuzzy environment using membership and non-membership functions for each objective function at all levels and decision variables controlled by the top levels. Then, we proposed an IFGP algorithm to achieve the highest degree of each membership and non-membership goal by minimizing unwanted deviational variables and generating compensatory solutions for all decision-makers at all levels. Moreover, in the proposed approach, two-phase IFGP is modeled to yield a compromise solution that satisfies both the MN-Pareto optimal solution and the Pareto optimal solution at each level. Also, verification of the proposed method is discussed with numerical examples.

Multi-Criteria Inventory Optimisation of University of Ibadan, Ibadan, Nigeria’s Bakery Using Goal Programming Approach and Flour as the Major Raw-Material

Asides inventory cost, which is being used as the only inventory performance measure at the University of Ibadan bakery, a number of other criteria, such as inventory cost, service level, inventory turnover and delivery lead time which influence the performance of an inventory system have surfaced over the years. Hence, there is the need to examine all these criteria-objectives altogether. Therefore, this research was centred towards optimising the inventory system of University of Ibadan bakery, putting multiple criteria into consideration.
 Data on 17 raw materials: their costs, suppliers, usage rate, lead time, storage space and available capital were collected by means of interviews, past records and observations. The weighted goal program algorithm was adopted to find the best compromise between fulfilling the four objectives by minimising the sum of the deviation from the target values of the goals. Subsequently, Lingo 17.0 and Tora 1.0 optimisation software packages were used to solve and compare the model generated, while putting into consideration storage space constraint and budgeted capital.
 The developed model from the goal programming algorithm exhibited four goals (combined into one objective function). Same solutions were obtained from Lingo 17.0 and Tora 1.0. While Lingo 17.0 gave a uniform service level of 100% , a turnover ratio greater than 1(>1) for all the materials at a negligible increase (of < 0.0001%) in total inventory cost of the raw materials and available lead time duration of zero days (< 24 hours) for each material, Tora 1.0 gave a uniform service level of 100% , a turnover ratio greater than 1 (> 1) for all the materials at a negligible increase (of < 0.0001%) in total inventory cost of the raw materials and available lead time duration of zero days (< 24 hours) for each material.
 Implementation of the developed model will eliminate unnecessary waiting time between production, thereby ensuring effective and efficient utilisation of raw materials in production which will lead to reduced cost of holding inventory, elimination of unnecessary overall cost and wastages, and also improvement of the productivity and profit on the long run.

GA-FGP based Intelligent Systems incorporating on-board Music Systems for stress relief for Solar Power Driven and Wirelessly charged Electric Car

This paper elucidates Intelligent System for stress relief through music in a complex structure of wirelessly driven Fuzzy Goal Programming (FGP) and Genetic Algorithm (GA) based performance optimized wirelessly charged electric car. It further presents under uncertainty, how the GA can be used in the process of solving a fuzzy goal programming (FGP) formulation of a wirelessly charged Solar powered Electric Car with an inbuilt state of the art entertainment system incorporating Automatic Speech Recognition (ASR) and Natural Language Understanding (NLU) technologies. The extension idea behind incorporation of Music System for stress relief is driven. In an effort through Artificial Intelligence guided System to make use of music in extension to relaxation, recreation for the therapeutic cause of individual to make them get rid of stress and tension, the present work is an attempt to develop a production system to extend further the pattern identification of regional music in this part of the globe from the erstwhile published work on measurement of recorded effect of sound wave on human brain inquest of improved attentiveness and concentration [1]. Initially, the model of the Car with all its components is presented. It is followed by a brief description of the entertainment system and it’s features. In the model formulation of the problem, the various types of goals are fuzzily described. Then, a pre-emptive priority based FGP model is developed with optimal usability. In the optimization model solution process, GA is employed in the formulated performance model of the car on the basis of the assigned priorities. In the decision process, both the GA and Fuzzy are employed so as to optimize the charging capacity with overall performance taking into consideration the issue of self-discharge. The design and constructional framework of this optimized Electric Car model is pictorially represented.

Solving multi-level multiobjective fractional programming problem with rough interval parameter in neutrosophic environment

In this study, a novel algorithm is developed to solve the multi-level multiobjective fractional programming problems, using the idea of a neutrosophic fuzzy set. The co-efficients in each objective functions is assumed to be rough intervals. Furthermore, the objective functions are transformed into two sub-problems based on lower and upper approximation intervals. The marginal evaluation of pre-determined neutrosophic fuzzy goals for all objective functions at each level is achieved by different membership functions, such as truth, indeterminacy/neutral, and falsity degrees in neutrosophic uncertainty. In addition, the neutrosophic fuzzy goal programming algorithm is proposed to attain the highest degrees of each marginal evaluation goals by reducing their deviational variables and consequently obtain the optimal solution for all the decision-makers at all levels. To verify and validate the proposed neutrosophic fuzzy goal programming techniques, a numerical example is adressed in a hierarchical decision-making environment along with the conclusions.

Real-time dispatching of air taxis in metropolitan cities using a hybrid simulation goal programming algorithm

Expected to begin its operations in the coming years, air taxi aims to provide everyday transportation services to customers in metropolitan cities. These vehicles offer urban air mobility (UAM) services using the electric vertical takeoff and landing (eVTOL) technology. This research is the first to present a hybrid simulation goal programming (HSGP) approach to dispatch vehicles in a centralized air taxi network. After each customer drop-off, the model makes real-time decisions on (i) whether the air taxi must become idle or pick up customers, and (ii) the station to which the air taxi should be dispatched (if the air taxi is operational). The feasibility of the HSGP approach is tested using potential air taxi demands in New York City (NYC) provided by a prior study. The results of the experimentation suggest that the minimum number of air taxis required for efficient operation in NYC is 84, functioning with an average utilization rate of 66%. In addition, the impacts of commuter’s “willingness to fly” rate, percentage of demand fulfillment, on-road travel limit, maximum customer wait time, and arrival distribution on the optimal number of air taxis, utilization rate, number of customers served, and cost incurred per customer are examined. Analyses show that the “willingness to fly” rate appears to have a linear influence on the number of air taxis and the efficiency, while on-road travel distance has an exponential impact on the performance measures. The HSGP algorithm developed in this paper can be used by any company that is interested in venturing into the air taxi market.

Multi-Objective Assembly Line Balancing Problem with Setup Times Using Fuzzy Goal Programming and Genetic Algorithm

Assembly lines are often indispensable in factories, and in order to attain a certain level of assembly line productivity, multiple goals must be considered at the same time. However, these multiple goals may conflict with each other, and this is a multi-objective assembly line balancing problem. This study considers four objectives, namely minimizing the cycle time, minimizing the number of workstations, minimizing the workload variance, and minimizing the workstation idle time. Since the objectives conflict with each other, for example, minimizing the cycle time may increase the number of workstations, the fuzzy multi-objective linear programming model is used to maximize the satisfaction level. When the problem becomes too complicated, it may not be solved by the fuzzy multi-objective linear programming model using a mathematical software package. Therefore, a genetic algorithm model is proposed to solve the problem efficiently. By studying practical cases of an automobile manufacturer, the results show that the proposed fuzzy multi-objective linear programming model and the genetic algorithm model can solve small-scale multi-objective assembly line balancing problems efficiently, and the genetic algorithm model can obtain good solutions for large-scale problems in a short computational time. Datasets from previous works are adopted to examine the applicability of the proposed models. The results show that both the fuzzy multi-objective linear programming model and the genetic algorithm model can solve the smaller problem cases and that the genetic algorithm model can solve larger problems. The proposed models can be applied by practitioners in managing a multi-objective assembly line balancing problem.

Fuzzy Multi-Choice Goal Programming and Artificial Bee Colony Algorithm for Triangular and Trapezoidal Membership Functions

Multi-choice goal programming (MCGP) has been widely used to find satisfying solutions for multiple criteria/objective decision problems in which the target value of “the more, the better,” or “the less, the better” can easily be obtained. This paper proposes two new models for representing the triangular and trapezoidal membership functions, which improve the efficacy of fuzzy MCGP (FMCGP). Two real-world applications are provided in this study to demonstrate the usefulness of the proposed models. Furthermore, the same problems are resolved by using the proposed nature-inspired optimization method (NIOM) to find the differences between them. While the artificial bee colony (ABC) algorithm is a well-known NIOM technique, studies have shown that it has an excellent performance with high-quality solutions. Thus, this study initially uses the ABC algorithm to find the differences between MCGP and ABC. Finally, some insightful information is obtained from the comparison to contribute to the NIOM and MCGP fields and their respective applications.

A bi-level programming approach for improving relief logistics operations: A real case in Kermanshah earthquake

Due to its location on the world dry belt, Iran is known as a disaster-prone country. Regarding such a problem, planning for relief operations in disaster situations seems significant and undeniable. The literature on disaster management has mostly defined their problems in a single-level framework, ignoring the bi-level aspect of such problems in both preparedness and response phases. However, in the context of disaster in the real world, there is normally more than one decision-maker that each of them may have their own objective. In this study, a bi-level multi-objective programming approach is extended to design a pre-positioning and distribution network under disastrous conditions considering both preparedness and response phases. The extended framework takes into account simultaneous planning for the distribution of drug, blood and relief items among disaster victims, and transferring the injured to hospital in order to diminish the adverse effects of potential disasters in the response phase. Additionally, to determine suitable candidate places for locating relief centers in the preparedness phase, a modified version of data envelopment analysis model is utilized, something that is not frequently done for facility location planning in the disaster management field. On the other hand, to solve the bi-level multi-objective programming problem with decision-makers at the upper level (the affected country) and the lower level (the international organization), a fuzzy goal programming algorithm is proposed. Furthermore, a consolidated method with respect to a novel fuzzy measure is developed to keep the considered network safe against the inherent uncertainty. Finally, the extended framework is utilized to solve a case study in Kermanshah, the province of Iran.

Multi-Objective Inventory Model with Lead-Time and Defective Items

Inventory problem are generally classified under decision making problem where lead time plays an important role in performance and services to customers during supply and placement of order of an item orders can be placed in shorter lead time with higher price or in longer lead time with lower cost. In this paper we have formulated multi-objective inventory model with one objective of minimizing the total inventory cost and other objective of maintaining the quality of the product by discarding the defective items. The model involved the deterministic demand, lead time dependent lead time cost, holding cost, ordering cost and inspection cost for inspecting defective items. The techniques of priority goal programming and genetic algorithm are applied and the results are compared. The sensitivity analysis is explained due to restriction in cost parameter. The model is finally illustrated with a numerical example.

Optimal irrigation for sustainable development considering water rights transaction: A Stackelberg-Nash-Cournot equilibrium model

This paper focuses on water allocation in an irrigation district considering water rights transaction. The relationship between the reservoir authority and the sub-area managers is explored based on a novel Stackelberg-Nash-Cournot equilibrium model. In this framework, the reservoir authority has higher priority in allocating initial water rights to Sancha town, Danjing and Xinmin villages; after get the decisions from the reservoir authority, the sub-area managers decide water distribution to multi-crops planting areas and water rights transaction with the promise of Nash-Cournot equilibrium, then the reservoir authority can modify his decision by Stackelberg strategic interaction. To obtain the optimal irrigation strategy, fuzzy goal programming and genetic algorithm methods are applied. In this context, a Stackelberg-Nash-Cournot equilibrium solution can be obtained. The proposed model is applied to Sancha irrigation area, and the results show that more available water can be distributed in Sancha town while guaranteeing the equity among the sub-areas in this irrigation district; more water was utilized for wheat and oilseed rape than paddy and bean, which matched the fact that wheat and oilseed rape grow in quarters with relatively less rainfall inflows. A changeable and uncertain environment, regarding inflow levels, planting areas, and irrigation coefficient, take potential challenges to agricultural irrigation process. Hence, to cope with the challenges, cope with the future uncertainty and offer more information on the adjustment of agricultural irrigation patterns, scenario technique is applied by changing the three parameters – inflow levels, planting areas, and irrigation coefficient respectively. Finally, to highlight the superiority of the proposed model, a comparative analysis is conducted in a situation without considering the water market, which verifies the importance and effectiveness of water rights transaction.

Multi-Objective Vendor Selection Problem of Supply Chain Management Under Fuzzy Environment

Survival of a company in today’s competitive business environment depends mainly on its supply chain. An adequate supply chain gives a competitive edge to a company. Sourcing, which is the initial stage of a supply chain, can be made efficient by making an appropriate selection of vendors. Appropriate vendor selection results not only in reduced purchasing costs, decreased production lead time, increased customer satisfaction but also in improved corporate competitiveness. In general, the vendor selection problem is a multi-objective decision-making problem that involves some quantitative and qualitative factors. So, we have considered a multi-objective vendor selection problem (MOVSP) with three multiple objective goals: minimization of net ordering price, minimization of rejected units and minimization of late delivered units. In most of the cases, information about the price of a unit, percentage of rejected units, percentage of late delivered units, vendor rating value and vendor quota flexibility may not be known precisely due to some reasons. In this paper, imprecision in input information is handled by the concept of a simulation technique, where the parameter follows the uniform distribution. Deterministic, stochastic, $$ \alpha $$ -cut and ranking function approaches are used to get the crisp value of the simulated data sets. The four different algorithms, namely—fuzzy programming, goal programming, lexicographic goal programming and D1-distance algorithm, have been used for solving the MOVSP. In last, three different types of simulated data sets have been used to illustrate the work.

Interactive goal programming algorithm with Taylor series and interval type 2 fuzzy numbers

This paper presents an interactive fuzzy goal programming (FGP) approach for solving Multiobjective Nonlinear Programming Problems (MONLPP) with interval type 2 fuzzy numbers (IT2 FNs). The cost and time of the objective functions, and the requirements of each kind of resources are taken to be trapezoidal IT2 FNs. Here, the considered fuzzy problem is first transformed into an equivalent crisp MONLPP, and then the MONLPP is converted into an equivalent multiobjective linear programming problem (MOLPP). By using an algorithm based on Taylor series, this problem is also reduced into a single objective linear programming problem (LPP) which can be easily solved by Maple 2017 optimization toolbox. Finally, the proposed solution procedure is illustrated by a numerical example.

Solving a multi-objective location routing problem for infectious waste disposal using hybrid goal programming and hybrid genetic algorithm

Solving a multi-objective location routing problem for infectious waste disposal using hybrid goal programming and hybrid genetic algorithm

Stochastic Multi-Objectives Supply Chain Optimization with Forecasting Partial Backordering Rate: A Novel Hybrid Method of Meta Goal Programming and Evolutionary Algorithms

This study proposes a model for a multi-objective, multi-buyer, multi-vendor, multi-product and multi-constraint supply chain. The buyers’ demand rates are stochastic variables with known probability distribution functions. The classical ([Formula: see text]) inventory control system is used to manage the inventories of all buyers where the lead times are production rate dependent. Shortage is permitted and is partially backordered where the partial back ordering rate is forecasted. The model is considered as a multi-objective integer nonlinear programming problem including cost, service level and lead time objectives and using a novel hybrid method, a hybrid of Meta Goal Programming (MGP) and Firefly Algorithm (FA) are solved. Numerical examples are given to illustrate the proposed method in the study. The results of the study are compared to other hybrid methods of Meta Goal Programming with other evolutionary algorithms such as Bees Algorithms (BA), Particle Swarm Optimization (PSO), Genetic Algorithm (GA) and Simulated Annealing (SA).

Conceptualization of Community-Based Integrated Farming System Model Design with Multi-Objective Optimization Management

Effective utilization of land and water resources is attempted in the present study through an integrated farming system and multi-objective optimization management framework model using goal programming algorithm in a coastal waterlogged paddy area in Odisha, India. A methodology is developed to identify the water harvesting structure locations in the study area using spatial science tool. Due to the uncertainty of parameters and control variables, development of management framework was considered with 85% and 75% probability of rainfall occurrence and runoff generation. To incorporate the uncertainties, a multi-objective linear goal programming optimization model is developed considering the objective of maximizing the net annual return and production subject to optimal allocation of land. While evaluating the model for different water resources scenarios, the net annual return is found to be Rs 4,343,474 and maximum production is 10,424 q from scenario I, whereas maximum production of 10,980 q is obtained in scenario II. Tomato and rice cultivation area increased from 11.47 to 21.43 ha and 8.82 to 10.48 ha respectively in scenario II. The developed methodology shows the potential applicability in similar farming situations in other areas.