Applying Gene Expression Programming for Solving One-Dimensional Bin-Packing Problems

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.

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.

The study on one-dimensional bin packing problem may bring about many important applications such as multiprocessor scheduling, resource allocating, real-world planning and packing. Harmonic algorithms (including H K, RH, etc.) for bin packing have been famous for their linear-time and on-line properties for a long time. This paper profoundly analyzes the average-case performance of harmonic algorithms for pieces of i.i.d. sizes, provides the average-case performance ratio of H K under (0,d] (d ≤ 1) uniform distribution and the average-case performance ratio of RH under (0,1] uniform distribution. We also finished the discussion of the worst-case performance ratio of RH. Moreover, we propose a new improved version of RH that obtains better worst- and average-case performance ratios.

In this paper we consider a one-dimensional bin packing problem where the bins do not have identical sizes, or a variable-sized bin packing problem, to minimize the bin consumption, i.e., the total size of the opened bins. The identical size problem has been extensively studied in the literature both for static and dynamic settings. The worst-case or average-case performance has been analyzed. Our problem setting particularly arises in metal cutting industries. Therefore, it presents a great practical relevance. Four greedy approximation algorithms based on a construction approach called largest object first with least absolute waste (LFLAW), largest object first with least relative waste (LFLRW), least absolute waste (LAW), and least relative waste (LRW) are examined. Their absolute worst-case performances are analyzed. The worst case bounds are 2 for LFLAW and LFLRW, 3 for LAW, and 2+ln 2 for LRW. We also show that these worst-case bounds are tight.

In this chapter it is shown how Automatically Defined Functions are encoded in the genotype/phenotype system of Gene Expression Programming. As an introduction, the fundamental differences between Gene Expression Programming and its predecessors, Genetic Algorithms and Genetic Programming, are briefly summarized so that the evolutionary advantages of Gene Expression Programming are better understood. The introduction proceeds with a detailed description of the architecture of the main players of Gene Expression Programming (chromosomes and expression trees), focusing mainly on the interactions between them and how the simple, yet revolutionary, structure of the chromosomes allows the efficient, unconstrained exploration of the search space. The work proceeds with an introduction to Automatically Defined Functions and how they are implemented in Gene Expression Programming. Furthermore, the importance of Automatically Defined Functions in Evolutionary Computation is thoroughly analyzed by comparing the performance of sophisticated learning systems with Automatically Defined Functions with much simpler ones on the sextic polynomial problem. 1. Genetic Algorithms: Historical Background The way nature solves problems and creates complexity has inspired scientists to create artificial systems that learn how to solve a particular problem without human intervention. The first attempts were done in the 1950s by Friedberg (Friedberg 1958; Friedberg et al. 1959), but ever since highly sophisticated systems have been developed that apply Darwin’s ideas of natural evolution to the artificial world of computers and modeling. Of particular interest to this work are the Genetic Algorithms (GAs) and the Genetic Programming (GP) technique as they are the predecessors of Gene Expression Programming (GEP), an extremely versatile genotype/phenotype system. The way Automatically Defined Functions (ADFs) are implemented in GEP is another example of the great versatility of this algorithm and the versatility of GEP ADFs opens up new grounds for the creation of even more sophisticated artificial learning systems. So let’s start by introducing briefly these three techniques in order to appreciate the versatility of the genotype/phenotype system of Gene Expression Programming with and without ADFs.

Soft computing approach to fault diagnosis of centrifugal pump

We describe a new heuristic algorithm to solve the one-dimensional bin-packing problem. The proposed algorithm is optimal if the sum of requirements of items is less than or equal to twice the bin capacity. Our computational results show that effectiveness of the proposed algorithm in finding optimal or near-optimal solutions is superior to that of the FFD and BFD algorithms, specifically for those so called 'difficult' problems that require an optimal solution to fill most of the bins, if not all, exactly to capacity.

Motivated by urban freight transportation practices in China, we study an optimal truck loading problem in which a fixed cost and an additional cost that depends on the number of unloading points are associated with each truck used. The truck loading problem is modeled as a one-dimensional bin packing problem, where the cost of each bin is a convex fixed-plus-linear function of the number of items in the bin. The objective is to minimize the total cost of bins used. We develop an asymptotic polynomial time approximation scheme and an efficient approximation algorithm with an asymptotic worst-case performance ratio of 1.5 to tackle the problem. Our computational experiments indicate that the approximation algorithm performs well for certain order patterns, and also reveal several important insights on using the freight charge scheme.

Multi-capacity bin-packing is a generalization of the classical one-dimensional bin-packing problem in which the bin capacity and the item sizes are represented by d-dimensional vectors. Previous work in d-capacity bin-packing algorithms analyzed variants of single capacity bin-packing, extended to deal with the d capacities. These extended algorithms are oblivious to the additional capacity information, however, and do not scale well with increasing d. We provide new packing algorithms which use the additional capacity information to provide better packing and show how these algorithms might lead to better multi-resource allocation and scheduling solutions.

We present several polynomial-time approximation algorithms for the one-dimensional bin-packing problem. using a subroutine to solve a certain linear programming relaxation of the problem. Our main results are as follows: There is a polynomial-time algorithm A such that A(I) ≤ OPT(I) + O(log2 OPT(I)). There is a polynomial-time algorithm A such that, if m(I) denotes the number of distinct sizes of pieces occurring in instance I, then A(I) ≤ OPT(I) + O(log2 m(I)). There is an approximation scheme which accepts as input an instance I and a positive real number ε, and produces as output a packing using as most (1 + ε) OPT(I) + O(ε-2) bins. Its execution time is O(ε-c n log n), where c is a constant. These are the best asymptotic performance bounds that have been achieved to date for polynomial-time bin-packing. Each of our algorithms makes at most O(log n) calls on the LP relaxation subroutine and takes at most O(n log n) time for other operations. The LP relaxation of bin packing was solved efficiently in practice by Gilmore and Gomory. We prove its membership in P, despite the fact that it has an astronomically large number of variables.

Dispatching rules are most commonly used to solve scheduling problems under dynamic conditions. Since designing new dispatching rules is a time-consuming process, it can be automated by using various machine learning and evolutionary computation methods. In previous research, genetic programming has been the most commonly used method for automatically designing new dispatching rules. However, there are many other evolutionary methods that use representations other than genetic programming that can be used to create dispatching rules. Some, such as gene expression programming, have already been used successfully, while others, such as Cartesian genetic programming or grammatical evolution, have not yet been used to generate dispatching rules. In this paper, six different methods (genetic programming, gene expression programming, Cartesian genetic programming, grammatical evolution, stack representation, and analytic programming) for generating dispatching rules for the unrelated machines environment are tested and the results for various scheduling criteria are analysed. It is also analysed how different individual sizes in the tested methods affect the performance and average size of the generated dispatching rules. The results show that, with the exception of grammatical evolution and analytic programming, all tested methods perform quite similarly, with results depending on the selected scheduling criterion. The results also show that Cartesian genetic programming is the most resistant to the occurrence of bloat and evolves dispatching rules with the smallest average size.

This study aims to develop a data-driven approach for predicting and formulating the pull-out force of steel fibers in cementitious composites using a genetic programming variant, gene expression programming (GEP). A comprehensive dataset of 437 experimental data was collected from previous studies, including key variables such as embedment length, fiber inclination angle, tensile strength of fibers, aspect ratio, loading rate, water-to-cement ratio, compressive strength of matrix, and fiber geometry. The GEP model developed in this study demonstrated notable accuracy in predicting pull-out force, with an R2 of 0.93. Model performance was evaluated using multiple statistical criteria, confirming its satisfactory predictive ability. Furthermore, a k-fold cross-validation was performed, and the results confirmed the model’s robustness and capability for generalizing to new data. Sensitivity analysis using SHAP interpretation revealed that the fibers’ tensile strength and the embedment length are the most influential factors affecting the pull-out force. The GEP method was adopted for its ability to generate accurate and interpretable mathematical formulas. Accordingly, a mathematical formula for the pull-out force is proposed, providing an efficient and interpretable tool for future studies. Overall, the GEP approach can significantly reduce reliance on costly and time-consuming experimental procedures while ensuring reliable performance predictions and practical formulations.Supplementary InformationThe online version contains supplementary material available at 10.1038/s41598-025-22595-x.

Gene expression programming (GEP), improved genetic programming (GP), has become a popular tool for data mining. However, like other evolutionary algorithms, it tends to suffer from premature convergence and slow convergence rate when solving complex problems. In this paper, we propose an enhanced GEP algorithm, called CTSGEP, which is inspired by the principle of minimal free energy in thermodynamics. In CTSGEP, it employs a component thermodynamical selection (CTS) operator to quantitatively keep a balance between the selective pressure and the population diversity during the evolution process. Experiments are conducted on several benchmark datasets from the UCI machine learning repository. The results show that the performance of CTSGEP is better than the conventional GEP and some GEP variations.

Chapter 13 - Gene expression models

18 - Expression Programming Techniques for Formulation of Structural Engineering Systems