Time and multiple objectives in scheduling and routing problems

While the classical knapsack problem has been the object to be solved by optimization algorithm proposals for many years, another version of this problem, discounted {0-1} knapsack problem, is gaining a lot of attention recently. The original knapsack problem requires selecting specific items from an item set to maximize the total benefit while ensuring that the total weight does not exceed the knapsack capacity. Meanwhile, discounted {0-1} knapsack problem has more stringent requirements in which items are divided into groups, and only up to one item from a particular group can be selected. This constraint, which does not exist in the original knapsack problem, makes discounted {0-1} knapsack problem even more challenging. In this paper, we propose a new algorithm based on salp swarm algorithm in the form of four different variants to resolve the discounted {0-1} knapsack problem. In addition, we also make use of an effective data modeling mechanism and a greedy repair operator that helps overcome local optima when finding the global optimal solution. Experimental and statistical results show that our algorithm is superior to currently available algorithms in terms of solution quality, convergence, and other statistical criteria.

Some achievements have been made in the study on mechanical properties of antler, but they have not been applied in engineering practice, especially in the study of thin-walled tubes similar to antler crashworthiness. In order to improve the crashworthiness and energy absorption of the thin-walled tube structures, a bionic thin-walled tube with the same inner diameter and equal gradient of outer diameter was designed based on the structural characteristics of antler bone and the principle of structural bionics. The finite element method was used to simulate the energy absorption characteristics of 75 kinds of bionic thin-walled tube structures under the oblique impacts with the impact angles of 10°, 20° and 30°. The polynomial regression element model and multi-objective particle swarm optimization algorithm were used to optimize, and the Pareto front optimization principle was used to obtain the optimal allocation scheme of each target. The minimum distance selection method was used in optimization analysis to obtain the optimal structural design parameters of each scheme. The optimization method used in this study can provide reference for the follow-up research on the crashworthiness of thin-walled tubes, and the optimal structure of bionic thin-walled tubes can provide reference for practical engineering application. The results show that when only considering a single impact angle, the optimal number of biomimetic layers n is 6, and the parameter combination of maximum wall thickness and thickness gradient tmax-a is 2.84 mm-0.38 mm, 2.89 mm-0.29 mm, 2.91 mm-0.34 mm, respectively under 10°, 20° and 30° impact angles. Considering various impact angle weight factors and different configuration schemes, the optimal number of biomimetic layers n is 6, and the parameter combination of maximum wall thickness and thickness gradient tmax-a is 2.95 mm-0.28 mm, 2.92 mm-0.30 mm and 2.85 mm-0.33 mm, respectively.

We analyze the competitive ratio and the advice complexity of the online unbounded knapsack problem. An instance is given as a sequence of n items with a size and a value each, and an algorithm has to decide whether or not and how often to pack each item into a knapsack of bounded capacity. The items are given online and the total size of the packed items must not exceed the knapsack’s capacity, while the objective is to maximize the total value of the packed items. While each item can only be packed once in the classical knapsack problem (also called the 0-1 knapsack problem), the unbounded version allows for items to be packed multiple times. We show that the simple unbounded knapsack problem, where the size of each item is equal to its value, allows for a competitive ratio of 2. We also analyze randomized algorithms and show that, in contrast to the 0-1 knapsack problem, one uniformly random bit cannot improve an algorithm’s performance. More randomness lowers the competitive ratio to less than 1.736, but it can never be below 1.693. In the advice complexity setting, we measure how many bits of information (so-called advice bits) the algorithm has to know to achieve some desired solution quality. For the simple unbounded knapsack problem, one advice bit lowers the competitive ratio to 3/2. While this cannot be improved with fewer than log2n advice bits for instances of length n, a competitive ratio of 1+ε can be achieved with O(ε-1·log(nε-1)) advice bits for any ε>0}\\varvec{0}$$\\end{document}]]>. We further show that no amount of advice bounded by a function f(n) allows an algorithm to be optimal. We also study the online general unbounded knapsack problem and show that it does not allow for any bounded competitive ratio for both deterministic and randomized algorithms, as well as for algorithms using fewer than log2n advice bits. We also provide a surprisingly simple algorithm that uses O(ε-1·log(nε-1)) advice bits to achieve a competitive ratio of 1+ε for any ε>0}\\varvec{0}$$\\end{document}]]>.

Multi-band RF front-ends with adaptive image rejection : a DECT/Bluetooth study case

The pu IDR ose of this research is to solve the 0/1 integer knapsack problem, which is a problem of selecting items from a number of available items where each item has different weights and profits. The delivery of items at J&T Cargo Purwokerto is one of many item selection problems. The delivery of items at J&T Cargo Purwokerto is carried out progressively with higher profit values ​​first, due to the delivery capacity being able to accommodate only 700 kg. In order for J&T Cargo Purwokerto to obtain maximum profit, item selection for delivery must be carried out first. The item selection at J&T Cargo Purwokerto can be solved using the 0/1 integer knapsack problem method with a forward recursive dynamic programming algorithm with the help of Matlab R2021A software. The results of the research indicate that on July 1, 2025, a maximum profit of IDR 3,038,850 was achieved with a weight of 700 kg. On 2nd July 2025, a maximum profit of IDR 4,884,985 was achieved with a weight of 700 kg. On 3rd July 2025, a maximum profit of IDR 7,732,155 was achieved with a weight of 699 kg.

This paper addresses a multi-objective approach for simultaneous dynamic expansion planning of conventional sub-transmission grid and Regional Virtual Power Plant (RVPP). In such a feed-in tariff electricity market, it will assist RVVP’s stakeholders in deciding whether or not they should invest in new equipment’s installation. A Multi-Objective Particle Swarm Optimization (MOPSO) algorithm as a heuristic optimization method is proposed to eliminate the conventional centralized planning, which has led to competition between Regional Electric Company (REC) and RVPP for power delivery in sub-transmission system. Two objective functions are considered for simultaneous expansion planning of these two systems. The first one takes the minimum cost of the REC, as the sub-transmission grid operator, into account while the other one considers profit maximization for RVPP. To achieve the goals, MOPSO algorithm is employed to find the best expansion of REC and best location and capacity of RVPP’s resources. Having solved the proposed multi-objective optimization problem, a Pareto front is determined to show the trade-off between REC and RVPPs' contributions in joint optimal expansion planning of conventional sub-transmission grid and the RVPP. To demonstrate the applicability and effectiveness of the proposed approach, a realistic sub-transmission system in Guilan Province, Iran is used as a test system, and the results are evaluated accordingly.

The knapsack problem is a classical optimization problem in computer science that can be efficiently solved using an algorithm based on dynamic programming. This study investigates the impact of technical factors such as the number of elements, the size of the knapsack, or the sorting of elements on the performance of the algorithm. Performance refers to the speed of the algorithm implementation in solving the problem. The analysis focuses on so-called Performance Impact Factors, which are the selected influences that can affect the speed of the algorithm. While the size of the considered knapsack represents a parameterization/configuration, the number of items is directly related to the problem itself; therefore, the term Performance Impact Factors is generally used. The investigation is based on a simulation experiment. The analysis of the simulation experiment data shows that as the total number of elements and the knapsack capacity increase, the algorithm’s runtime also increases. In this context, an increase in knapsack capacity has a more pronounced negative effect on the algorithm’s runtime. An examination of sorting strategies further reveals that a prior sorting of elements by value in descending order can lead to significant deteriorations in runtime.

The 0/1 knapsack problem is one of the most exhaustively studied NP-hard combinatorial optimization problems. Many different approaches have been taken to obtain an approximate solution to the problem in polynomial time. Here we consider the biobjective 0/1 knapsack problem. The contribution of this paper is to show that a genetic programming system can evolve a set of heuristics that can give solutions on the Pareto front for multiobjective combinatorial problems. The genetic programming (GP) system outlined here evolves a heuristic which decides whether or not to add an item to the knapsack in such a way that the final solution is one of the Pareto optimal solutions. Moreover, the Pareto front obtained from the GP system is comparable to the front obtained from other human-designed heuristics. We discuss the issue of the diversity of the obtained Pareto front and the application of strongly-typed GP as a means of obtaining better diversity.

A classical knapsack problem with two objectives is considered in which concepts of supported and non supported efficient solutions are pointed out.

In this paper we propose a multi-objective optimization approach to solve nonlinear fuzzy optimization problems. Solutions in the Pareto front correspond with the fuzzy solution of the former fuzzy...

The knapsack problem is problem that is still often found in everyday life, one of which is the problem of selecting goods to be transported into containers for delivery of goods. This knapsack problem can be solved by using various optimization algorithms, one of which is the genetic algorithm. This study aims to design a genetic algorithm model to solve the 2-dimensional knapsack problem. 2-dimensional knapsack problem is a knapsack problem that has 2 constraints and in this study, the constraints used were weight and volume.. The evaluation results of the genetic algorithm will be compared with dynamic programming. From the evaluation results that have been carried out, it can be concluded that genetic algorithms can produce near-optimal results with faster computational times than dynamic programming.

Handling of many-objective problems is a hot issue in the evolutionary multiobjective optimization (EMO) community. It is well-known that frequently-used EMO algorithms such as NSGA-II and SPEA do not work well on many-objective problems whereas they have been successfully applied to a large number of test problems and real-world application tasks with two or three objectives. The main difficulty in the handling of many-objective problems is that almost all solutions in the current population of an EMO algorithm are non-dominated with each other. This means that Pareto dominance relation cannot generate enough selection pressure toward the Pareto front. As a result, Pareto dominance-based EMO algorithms such as NSGA-II and SPEA cannot drive the current population toward the Pareto front efficiently in a high-dimensional objective space of a many-objective problem. A simple idea for introducing additional selection pressure toward the Pareto front is the use of scalarizing fitness functions. In this paper, we examine the effect of using weighted sum fitness functions for parent selection and generation update on the performance of NSGA-II for many-objective 0/1 knapsack problems.

Shift-and-merge technique for the DP solution of the time-constrained backpacker problem

Previous chapter Next chapter Full AccessProceedings Proceedings of the 2011 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)Improved Approximation Results for Stochastic Knapsack ProblemsAnand Bhalgat, Ashish Goel, and Sanjeev KhannaAnand Bhalgat, Ashish Goel, and Sanjeev Khannapp.1647 - 1665Chapter DOI:https://doi.org/10.1137/1.9781611973082.127PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstract In the stochastic knapsack problem, we are given a set of items each associated with a probability distribution on sizes and a profit, and a knapsack of unit capacity. The size of an item is revealed as soon as it is inserted into the knapsack, and the goal is to design a policy that maximizes the expected profit of items that are successfully inserted into the knapsack. The stochastic knapsack problem is a natural generalization of the classical knapsack problem, and arises in many applications, including bandwidth allocation, budgeted learning, and scheduling. An adaptive policy for stochastic knapsack specifies the next item to be inserted based on observed sizes of the items inserted thus far. The adaptive policy can have an exponentially large explicit description and is known to be PSPACE-hard to compute. The best known approximation for this problem is a (3 + ∊)-approximation for any ∊ > 0. Our first main result is a relaxed PTAS (Polynomial Time Approximation Scheme) for the adaptive policy, that is, for any ∊ > 0, we present a poly-time computable (1 + ∊)-approximate adaptive policy when knapsack capacity is relaxed to 1+e. At a high-level, the proof is based on transforming an arbitrary collection of item size distributions to canonical item size distributions that admit a compact description. We then establish a coupling that shows a (1 + ∊)-approximation can be achieved for the original problem by a canonical policy that makes decisions at each step by observing events drawn from the sample space of canonical size distributions. Finally, we give a mechanism for approximating the optimal canonical policy. Our second main result is an (8/3 + ∊)-approximate adaptive policy for any ∊ > 0 without relaxing the knapsack capacity, improving the earlier (3 + ∊)-approximation result. Interestingly, we obtain this result by using the PTAS described above. We establish an existential result that the optimal policy for the knapsack with capacity 1 can be folded to get a policy with expected profit 3OPT/8 for a knapsack with capacity (1 − ∊), with capacity relaxed to 1 only for the first item inserted. We then use our PTAS result to compute the (1 + ∊)-approximation to such policy. Our techniques also yield a relaxed PTAS for non-adaptive policies. Finally, we also show that our ideas can be extended to yield improved approximation guarantees for multi-dimensional and fixed set variants of the stochastic knapsack problem. Previous chapter Next chapter RelatedDetails Published:2011ISBN:978-0-89871-993-2eISBN:978-1-61197-308-2 https://doi.org/10.1137/1.9781611973082Book Series Name:ProceedingsBook Code:PR138Book Pages:xviii-1788

An application of adaptive normalization evolutionary optimization ANMOGA for missile fin design based on trajectory parameters