A Genetic Algorithm Approach to the Container Loading Problem

The problem considered in this work is the Container Loading Problem. In this problem a set of rectangular boxes has to be packed in one rectangular container so that the available container space usage is maximized. The orientation constraints and the distinction between homogeneous and heterogeneous types of cargo are considered. We present the results obtained with a Genetic Algorithm approach. The good performance of this algorithm is shown by comparing them with well-known algorithms and results from the literature

Convective boundary layer flow in generalized Newtonian nanofluid under various boundary conditions

The four mathematical models of boundary layer flow solved under different boundary conditions. The first problem considered the unsteady squeezing flow of the Carreau nanofluid over the sensor surface, where three different nanoparticles were suspended in the base fluid. A comparison of the results of suspended materials in liquids proved that increased surface permeability leads to increased heat transfer. The second problem described the magnetohydrodynamics (MHD) Darcy-Forchheimer model, which considers Maxwell nanofluids' flow. It was observed that an increase in the Biot number coefficient increased heat transfer. The third problem evaluated activation energy and binary reaction effect on the MHD Carreau nanofluid model. Buongiorno nanofluid model was applied to shear-thinning or pseudoplastic fluid over the pereamble surface. The relationship between the activation energy and chemical reaction is influential and controls heat transfer processes. The fourth problem analyzed the radiative Sutterby model over a stretching/shrinking sheet towards stagnation point flow. Dual solutions were found using the scaling group transformation, which was examined by a stability approach. Such a problem found an increment in the suction parameter, the Deborah number, and the nanoparticle volume fraction delayed the flow separation. The influence of various pertinent parameters on the velocity and temperature distributions has been presented. The most relevant results by the forceful impacts of thermo-physical properties on fluids were analyzed through this work. Modeled equations are based on the conservation laws under the boundary layer approximation. The similarity transformation method is used to convert the governing partial differential equations into ordinary differential equations. They are then solved using a numerical technique, known as the Runge�Kutta-Fehlberg method with shooting technique in the MAPLE 17 or bvp4c method in the MATLAB 2019a

A Hybrid Meta-heuristic for the Container Loading Problem

It is very common in an enterprise daily operation to solve Container Loading Problem (CLP). Especially, it is an important issue in the logistic management. The problem aims to determine the arrangement of objects with the best utilization ratio in a container. It belongs to the combinatorial optimization problem. In this paper, a two-phased method focusing on the improvement of the efficiency and on the reducing of the problem size is proposed. In the first phase, a constructive method incorporated with a decision rule borrowing from ant colony optimization is used to construct tower set. The pheromone updating mechanism is useful in choosing proper object while constructing tower using decision rule. In the second phase, an improvement method based on genetic algorithm is used. First, the method sorts the towers by the utilization ratio and then assigns a number to each tower accordingly. The chromosome is a sequence of tower numbers which represents the arrangement of towers in the container’s bottom plane. The fitness function is defined as the utilization ratio. A new structure to store the pheromone is proposed which can help the ant in choosing the appropriate object while constructing tower. In this way, the efficiency of the method and the utilization of the container are improved

Menu Planning Model for Malaysian Boarding School Using Self-Adaptive Hybrid Genetic Algorithms

Malnutrition problem is the gravest single threat to the world's public health today. Statistics have showed that the number of under-nourished and over-nourished children and adolescents is increasing day by day. Thus, proper menu planning process among menu planners or caterers is important to avoid some diet-related diseases in the hture. Manual calculation of menu planning is unable to consider macronutrients and micronutrients simultaneously due to complexities of data and length of time. In this study, self-adaptive hybrid genetic algorithm (SHGA) approach has been proposed to solve the menu planning problem for Malaysian boarding school students aged 13 to 18 years old. The objectives of our menu planning model are to optimize the budget allocation for each student, to take into consideration the caterer's ability, to llfill the standard recommended nutrient intake (RNI) and maximize the variety of daily meals. New local search was adopted in this study, the insertion search with delete-and-create (ISDC) method, which combined the insertion search (IS) and delete-and-create (DC) local search method. The implementation of IS itself could not guarantee the production of feasible solutions as it only explores a small neighborhood area. Thus, the ISDC was utilized to enhance the search towards a large neighborhood area and the results indicated that the proposed algorithm is able to produce 100% feasible solutions with the best fitness value. Besides that, implementation of self-adaptive probability for mutation has significantly minimized computational time taken to generate the good solutions in just few minutes. Hybridization technique of local search method and self-adaptive strategy have improved the performance of traditional genetic algorithm through balanced exploitation and exploration scheme. Finally, the present study has developed a menu planning prototype for caterers to provide healthy and nutritious daily meals using simple and fhendly user interface

A Multi-Objective Genetic Algorithm for the Vehicle Routing with Time Windows and Loading Problem

This work presents the Vehicle Routing with Time Windows and Loading Problem (VRTWLP) as a multi-objective optimization problem, implemented within a Genetic Algorithm. Specifically, the three dimensions of the problem to be optimized – the number of vehicles, the total travel distance and volume utilization – are considered to be separated dimensions of a multi-objective space. The quality of the solution obtained using this approach is evaluated and compared with results of other heuristic approaches previously developed by the author. The most significant contribution of this work is our interpretation of VRTWLP as a Multi-objective Optimization Problem

A Hybrid Simulated Annealing Algorithm for Container Loading Problem

This paper presents a hybrid simulated annealing algorithm for container loading problem with boxes of different sizes and single container for loading. A basic heuristic algorithm is introduced to generate feasible solution from a special structure called packing sequence. The hybrid algorithm uses basic heuristic to encode feasible packing solution as packing sequence, and searches in the encoding space to find an approximated optimal solution. The computational experiments on 700 weakly heterogeneous benchmark show that our algorithm outperforms all previous methods in average

A two-stage packing procedure for a Portuguese trading company

This case study deals with a two-stage packing problem that has to be solved in the daily distribution process of a Portuguese trading company. At the first stage boxes including goods are to be packed on pallets while at the second stage these pallets are loaded into one or more trucks. The boxes have to be transported to different customers and the actual goal is to guarantee a sufficient utilization of the truck loading spaces. A two-stage packing procedure is proposed to cover both problem stages. First boxes are loaded onto pallets using a well-known container loading algorithm. Then trucks are filled with loaded pallets by means of a new tree search algorithm. The applicability and performance of the two-stage approach was evaluated with a set of instances that are based on actual company data

A heuristic for the container loading problem: A tertiary-tree-based dynamic space decomposition approach

Increasing fuel costs, post-911 security concerns, and economic globalization provide a strong incentive for container carriers to use available container space more efficiently, thereby minimizing the number of container trips and reducing socio-economic vulnerability. A heuristic algorithm based on a tertiary tree model is proposed to handle the container loading problem (CLP) with weakly heterogeneous boxes. A dynamic space decomposition method based on the tertiary tree structure is developed to partition the remaining container space after a block of homogeneous rectangular boxes is loaded into a container. This decomposition approach, together with an optimal-fitting sequencing and an inner-right-corner-occupying placement rule, permits a holistic loading strategy to pack a container. Comparative studies with existing algorithms and an illustrative example demonstrate the efficiency of this algorithm