Genetic Algorithm With Random Crossover and Dynamic Mutation on Bin Packing Problem

Approximation and online algorithms for multidimensional bin packing: A survey

The light propagation in tissues has been simulated successfully by Monte Carlo method. Since the result of Monte Carlo simulation is discrete and statistic, the traditional optimizations and search algorithms encounter irresolvable difficulty in an inverse problem, but it can be overcome effectively by Genetic Algorithms due to their global search, robustness and self-adapting. In the present paper, we consider a tissue volume in which there is a spherical tumor with different optical parameters. A thin collimated NIR laser beam incidents normally on the surface. Monte Carlo method is used as a solution to the direct problem after some improvements, and in the inverse problem a genetic algorithm is applied to reconstruct the tumor. An appropriate evaluation function related to forward light distribution is designed to improve the stability and the speed of convergence. The selection based on fitness expectation is adopted as well as the random crossover and random mutation. Four parameters which determine the location and size of the tumor are to be reconstructed. The reconstructed tumor has a good agreement with the true tumor.

The bin packing problem is one of the most fundamental optimization problems. Owing to its hardness as a combinatorial optimization problem class and its wide range of applications in different domains, different variations of the problem are emerged and many heuristics have been proposed for obtaining approximate solutions. In this paper, we solve a Multi-Level Bin Packing (MLBP) problem in the real make-to-order industry scenario. Existing solutions are not applicable to the problem due to: 1. the final packing may consist multiple levels of sub-packings; 2. the geometry shapes of objects as well as the packing constraints may be unknown. We design an automatic packing framework which extracts the packing knowledge from historical records to support packing without geometry shape and constraint information. Furthermore, we propose a dynamic programming approach to find the optimal solution for normal size problems; and a heuristic multi-level fuzzy-matching algorithm for large size problems. An inverted index is used to accelerate strategy search. The proposed auto packing framework has been deployed in Huawei Process & Engineering System to assist the packing engineers. It achieves a performance of accelerating the execution time of processing 5,000 packing orders to about $8$ minutes with an average successful packing rate as $80.54%$, which releases at least $30%$ workloads of packing workers.

The bin packing problem is a classical problem widely existing in practical applications, such as shipping, warehousing and manufacturing industries. Whereas current research mainly focuses on reducing packing costs by optimizing the packing scheme, this study explores a novel approach by redesigning the bin sizes to fit the items ready to be packed. Specifically, this study considers a general three-dimensional open dimension problem (3D-ODP) where all dimensions, i.e. length, width and height, of a number of heterogeneous bin types are unknown and need to be decided. Based on the designed bin types, the corresponding packing scheme with minimal total costs is optimized, which is referred to as a three-dimensional multiple-bin-size bin packing problem (3D-MBSBPP). The combination of 3D-ODP and 3D-MBSBPP is redefined as a three-dimensional bin design and packing problem (3D-BDPP), for which a two-layer heuristic is developed. It consists of an outer heuristic framework (i.e. genetic algorithm or differential evolution algorithm) to design bin types, and an inner deterministic constructive heuristic (i.e. placement algorithm) to generate an effective solution for the 3D-MBSBPP. Extensive simulation tests on the classical benchmark and a case study derived from an e-commerce company are conducted to verify the algorithms and deduce managerial insights.

Bin packing problems consist of allocating a set of small parts to a set of large bins by minimizing the number of used bins. Although several boundary conditions have been stated in the past, for example conflicts or restrictions on cutting and rotations, we introduce a set of constraints, which lead to a new problem structure. These constraints are motivated by the precast-concrete-part industry and represent requirements on the ordering of parts and their positions, machinery restrictions and due dates. Furthermore, we solve the problem using several heuristic approaches that are based on algorithms for the standard bin packing problem. Therefore, existing concepts are classified and adapted to fit the new problem, including Simulated Annealing, Genetic Algorithms, Tabu Search methods and SubSetSum based search routines. Finally, all proposed algorithms are tested and obtained results are discussed.

The solution of bi-objective bin packing problems with many constraints is of fundamental importance for a wide range of engineering applications such as wireless communication, logistics, or automobile sheet metal forming processes. When the bi-objective bin packing problem is single-constrained, state-of-the-art multi-objective genetic algorithms such as NSGA-II combined with standard constraint handling techniques can be used. In the case of many-constraint bin packing problems, problems with thousand of additional constraints, it is not easy to solve this kind of problem accurately and fast with classical methods. Our approach relies on two key ingredients, NSGA-II and a clustering algorithm in order to generate always feasible solutions independent of the number of constraints. The method allows to tackle bi-objective many-constraint bin packing problems. We will present results for challenging artificial bin packing problems which model typical bi-objective bin packing problems with many constraints arising in the automobile industry.

In this paper, the NP-complete problem of 1D bin packing is considered. In the 'bin packing problem', a set of numbers or elements that need to be loaded in the bins is considered. The total load of the elements in any bin must not exceed the bin size or bin capacity. These elements must be packed or loaded in the bins in such a way that there is minimum amount of space left in each bin and the number of bins to be used is minimised. A new algorithm, which helps in tackling the bin packing problem, by giving optimal solutions in minimum time, is presented. The algorithms currently in use, requires the elements to be sorted before the loading. The algorithm discussed in this paper avoids the sorting operation before the loading while giving the same best fit results.

A two-dimensional bin packing model was established to solve the problem of goods placement in the material box, which was optimized to improve space utilization. By discretization of the model, a bin packing algorithm with left-bottom priority is designed. By adopting the improved genetic algorithm with the optimal individual retention strategy, the optimal sequence of various kinds of goods in the material box is obtained. Two types of experiments of multi-algorithm comparison simulation and multi-solution simulation are designed. The first type of experimental results show that the algorithm has some advantages in fitness and convergence speed, and the second type of experimental results show that it can provide multiple optimal solutions for solving small-scale bin packing problems.

Previous researches have shown the success of using Reinforcement Learning in solving combinatorial optimization problems. The main idea of these methods is to learn (near) optimal evaluation functions to improve local searches and find (near) optimal solutions. STAGE algorithm, introduced by Boyan & Moore, is one of the most important algorithms in this area. In this paper, we focus on Bin-Packing problem, an important NP-Complete problem. We analyze cost surface structure of this problem and investigate big valley structure for the set of its local minima. The result gives reasons for STAGE's success in solving this problem. Then by comparing the results of experiments on Bin-Packing problem, we analyze the effectiveness of steepest-descent hill climbing, stochastic hill climbing and first-improvement hill climbing as the local search algorithms in STAGE.

The objective is to minimize the production cost of the thermal units. An elegant approach is presented in order to obtain the equivalent cost function of the participating nonfuel restricted units [N. Ramaraj (1993)]. The hybrid genetic algorithm (GA) technique is used for real power optimization. Here real coded GA is used for global search and the fine tunings are done by tabu search (TS) to direct the search towards the optimal region and local optimization. The GA operator's selection, arithmetic crossover and dynamic mutation are used to generate successive sets of possible operating policies. This technique improves the quality of the solution and reduces the computation time. The optimal solution is obtained neglecting losses. The fast decoupled load flow (FDLF) analysis is conducted to find the losses by substituting the generation values. Then the loss is participated among all generating units using participation factor method. Applying the results again to the load flow, checks the voltage limit violation. The Algorithm is tested on IEEE 6-bus system and a practical 66-bus system. The proposed method is compared with the classical method. It is observed that the proposed algorithm is superior, reliable and fast.

Bin Packing (BP) is an NP-hard combinatorial optimization problem. Sophisticated algorithms are needed for solving large instances of the problem. A hybrid framework that includes a Ruin and Recreate (RR) procedure and an acceptance criterion similar to the Metropolis Criterion, is proposed for the problem in this study. Ruin and Recreate is used to create new individuals in the search process and the acceptance mechanism is used for balancing the exploration and exploitation of the search space. Also hill climbers are integrated into the framework for fine-tuning. Furthermore, the algorithm is run on a population of individuals and a certain amount of crossover operation is utilized on the population in order to benefit from the reproduction process that takes place in Genetic Algorithms (GAs). The constructed algorithm is applied on frequently used data sets in the literature and the results are compared with other state of the art algorithms.

Advances in digitalized image optics has increased the importance of chromatic aberration. The axial and lateral chromatic aberrations of an optical lens depends on the choice of optical glass. Based on statistics from glass companies worldwide, more than 300 optical glasses have been developed for commercial purposes. However, the complexity of optical systems makes it extremely difficult to obtain the right solution to eliminate small chromatic aberration. Even the damped least-squares technique, which is a ray-tracing-based method, is limited owing to its inability to identify an enhanced optical system configuration. Alternatively, this study instead attempts to eliminate even negligible axial and lateral colour aberration by using algorithms involving the theories of geometric optics in triplet lens, binary and real encoding, multiple dynamic crossover and random gene mutation techniques.

In this paper, our objective is to develop a mathematical formulation of solving the Bin Packing Problem (BPP) with different sizes of box. It has become one of the most important mathematical applications throughout the time. In our study, Modified Branch and Bound Algorithm (MBBA) is developed to generate all the feasible packing patterns of given boxes to required containers for One-Dimensional BPP. Further development of algorithms was made to ascertain the locations of each box within the containers by using Cartesian coordinate system. Developed algorithms are coded and programmed in the Python programming environment to generate feasible packing patterns.

Improved random selection strategy, self-adaptive crossover and mutation operators, population co-evolution algorithm are adopted in this paper to set up a new genetic algorithm(GA), guaranteeing the universality of population, the thoroughness of solution and the execution efficiency of algorithm in solving multi-process, process crossover, work-piece flow and other condition based scheduling problem of flexible manufacturing system(FMS). The problem of GA in solving FMS scheduling is summarized in this paper, reasons and countermeasures for GA's pre-maturing are studied, longitudinal and transverse comprehensive state-based correlative self-adaptive crossover and mutation operators are raised according to the analysis on GA to avoid local optimization and pre-maturity, the co-evolutionary GA is designed to solve the scheduling model for FMS, and the algorithm is validated for the scheduling of box-type parts for precise machine tools.

Background: Logistics and transport, core of many business processes, are continuously optimized to improve efficiency and market competitiveness. The paper describes a modular coordination of vehicle routing and bin packing problems that enables independent instances of the problems to be joined together, with the aim that the vehicle routing solution satisfies all the constraints from real-world applications. Methods: The vehicle routing algorithm is based on an adaptive memory procedure that also incorporates a simple, one-dimensional bin packing problem. This preliminary packing solution is refined by a complex, three dimensional bin packing for each vehicle to identify the infeasible packages. The method iteratively adjusts virtual volumes until reaching near-optimal routes that respect bin-packing constraints. Results: The coordination enables independent applications of an adaptive memory procedure to vehicle routing and a genetic algorithm approach to bin packing while joining them in a computationally tractable way. Such a coordinated approach is applied to a frequently used public benchmark and proven to provide commensurate costs while significantly lowering algorithm complexity. Conclusions: The proposed method is further validated on a real industrial case study and provided additional savings of 14.48% in average daily distance traveled compared to the current industrial standard.