A Boolean Local Improvement Method for General Discrete Optimization Problems

1993 ◽  
Vol 115 (4) ◽  
pp. 776-783 ◽  
Author(s):  
Peng Lu ◽  
J. N. Siddall
Keyword(s):  
Optimization Problem ◽  
Optimization Problems ◽  
Continuous Variable ◽  
Local Region ◽  
Boolean Logic ◽  
Discrete Variable ◽  
New Approach ◽  
Local Improvement ◽  
Improvement Method ◽  
Discrete Optimization Problems

The paper proposes a new approach to solving the discrete design optimization problem by combining Boolean logic methods with conventional nonlinear optimization. A continuous variable optimum is first found, and then the Boolean method searches the local region for the discrete variable optimum.

A Boolean Local Improvement Method for General Discrete Optimization Problems

1991 ◽  
Author(s):  
Peng Lu ◽  
James N. Siddall
Keyword(s):  
Optimization Problem ◽  
Optimization Problems ◽  
Continuous Variable ◽  
Local Region ◽  
Boolean Logic ◽  
Discrete Variable ◽  
New Approach ◽  
Local Improvement ◽  
Improvement Method ◽  
Discrete Optimization Problems

Abstract The paper proposes a new approach to solving the discrete design optimization problem by combining Boolean logic methods with conventional nonlinear optimization. A continuous variable optimum is first found, and then the Boolean method searches the local region for the discrete variable optimum.

scholarly journals A new approach to optimality in a class of nonconvex smooth optimization problems

2018 ◽  
Vol 34 (1) ◽  
pp. 01-07
Author(s):  
TADEUSZ ANTCZAK ◽  
Keyword(s):  
Approximation Method ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Extremum Problem ◽  
Optimal Solutions ◽  
New Approach ◽  
Smooth Optimization

In this paper, a new approximation method for a characterization of optimal solutions in a class of nonconvex differentiable optimization problems is introduced. In this method, an auxiliary optimization problem is constructed for the considered nonconvex extremum problem. The equivalence between optimal solutions in the considered differentiable extremum problem and its approximated optimization problem is established under (Φ, ρ)-invexity hypotheses.

scholarly journals Application Analysis on PSO Algorithm in the Discrete Optimization Problems

2021 ◽  
Vol 2078 (1) ◽  
pp. 012018
Author(s):  
Qinglong Chen ◽  
Yong Peng ◽  
Miao Zhang ◽  
Quanjun Yin
Keyword(s):  
Discrete Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Pso Algorithm ◽  
Discrete Optimization Problem ◽  
Spatial Search ◽  
Continuous Problems ◽  
Application Analysis ◽  
Discrete Pso ◽  
Discrete Optimization Problems

Abstract Particle Swarm Optimization (PSO) is kind of algorithm that can be used to solve optimization problems. In practice, many optimization problems are discrete but PSO algorithm was initially designed to meet the requirements of continuous problems. A lot of researches had made efforts to handle this case and varieties of discrete PSO algorithms were proposed. However, these algorithms just focus on the specific problem, and the performance of it significantly degrades when extending the algorithm to other problems. For now, there is no reasonable unified principle or method for analyzing the application of PSO algorithm in discrete optimization problem, which limits the development of discrete PSO algorithm. To address the challenge, we first give an investigation of PSO algorithm from the perspective of spatial search, then, try to give a novel analysis of the key feature changes when PSO algorithm is applied to discrete optimization, and propose a classification method to summary existing discrete PSO algorithms.

Finance-based scheduling using meta-heuristics: discrete versus continuous optimization problems

2015 ◽  
Vol 20 (1) ◽  
pp. 85-104 ◽  
Author(s):  
Ashraf Elazouni ◽  
Anas Alghazi ◽  
Shokri Z. Selim
Keyword(s):  
Time Management ◽  
Optimization Problems ◽  
Continuous Variable ◽  
Discrete Variable ◽  
Content Type ◽  
Project Duration ◽  
Project Completion ◽  
Management Aspect ◽  
Discrete Variable Optimization ◽  
Cost Components

Purpose – The purpose of this paper is to compare the performance of the genetic algorithm (GA), simulate annealing (SA) and shuffled frog-leaping algorithm (SFLA) in solving discrete versus continuous-variable optimization problems of the finance-based scheduling. This involves the minimization of the project duration and consequently the time-related cost components of construction contractors including overheads, finance costs and delay penalties. Design/methodology/approach – The meta-heuristics of the GA, SA and SFLA have been implemented to solve non-deterministic polynomial-time hard (NP-hard) finance-based scheduling problem employing the objective of minimizing the project duration. The traditional problem of generating unfeasible solutions in scheduling problems is adequately tackled in the implementations of the meta-heuristics in this paper. Findings – The obtained results indicated that the SA outperformed the SFLA and GA in terms of the quality of solutions as well as the computational cost based on the small-size networks of 30 activities, whereas it exhibited the least total duration based on the large-size networks of 120 and 210 activities after prolonged processing time. Research limitations/implications – From researchers’ perspective, finance-based scheduling is one of the few domain problems which can be formulated as discrete and continuous-variable optimization problems and, thus, can be used by researchers as a test bed to give more insight into the performance of new developments of meta-heuristics in solving discrete and continuous-variable optimization problems. Practical implications – Finance-based scheduling discrete-variable optimization problem is of high relevance to the practitioners, as it allows schedulers to devise finance-feasible schedules of minimum duration. The minimization of project duration is focal for the minimization of time-related cost components of construction contractors including overheads, finance costs and delay penalties. Moreover, planning for the expedient project completion is a major time-management aspect of construction contractors towards the achievement of the objective of client satisfaction through the expedient delivery of the completed project for clients to start reaping the anticipated benefits. Social implications – Planning for the expedient project completion is a major time-management aspect of construction contractors towards the achievement of the objective of client satisfaction. Originality/value – SFLA represents a relatively recent meta-heuristic that proved to be promising, based on its limited number of applications in the literature. This paper is to implement SFLA to solve the discrete-variable optimization problem of the finance-based scheduling and assess its performance by comparing its results against those of the GA and SA.

scholarly journals An Interactive Regret-Based Genetic Algorithm for Solving Multi-Objective Combinatorial Optimization Problems

2020 ◽  
Vol 34 (03) ◽  
pp. 2335-2342
Author(s):  
Nawal Benabbou ◽  
Cassandre Leroy ◽  
Thibaut Lust
Keyword(s):  
Combinatorial Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Computation Time ◽  
Preference Elicitation ◽  
Combinatorial Optimization Problem ◽  
New Approach ◽  
Multi Objective ◽  
Combinatorial Optimization Problems

We propose a new approach consisting in combining genetic algorithms and regret-based incremental preference elicitation for solving multi-objective combinatorial optimization problems with unknown preferences. For the purpose of elicitation, we assume that the decision maker's preferences can be represented by a parameterized scalarizing function but the parameters are initially not known. Instead, the parameter imprecision is progressively reduced by asking preference queries to the decision maker during the search to help identify the best solutions within a population. Our algorithm, called RIGA, can be applied to any multi-objective combinatorial optimization problem provided that the scalarizing function is linear in its parameters and that a (near-)optimal solution can be efficiently determined when preferences are known. Moreover, RIGA runs in polynomial time while asking no more than a polynomial number of queries. For the multi-objective traveling salesman problem, we provide numerical results showing its practical efficiency in terms of number of queries, computation time and gap to optimality.

A Novel Binary Differential Evolution for Discrete Optimization

2010 ◽  
Vol 439-440 ◽  
pp. 1493-1498 ◽  
Author(s):  
Guo Ping Hou ◽  
Xuan Ma
Keyword(s):  
Differential Evolution ◽  
Discrete Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Discrete Optimization Problem ◽  
Sigmoid Function ◽  
Mutation Operator ◽  
Binary Differential Evolution ◽  
The Individual ◽  
Discrete Optimization Problems

Differential evolution （DE） is an evolutionary algorithm that is based on the individual differential reconstruction idea. It is proposed by Stom and Price in 1997, and is very suitable to solve optimization problem over continuous spaces. First of all, with the introduction of concepts of differential operator （DO）, etc., the concise description of DE is given and the analysis of its main features is advanced. For solving discrete optimization problem using DE, a new operator, mapping operator, in the new algorithm was used to ensure the original mutation operator still effective. Then a new S operator, with sigmoid function, was used to keep the result of the mutation operator falls in the interval [0, 1]. The algorithm not only has the advantages of DE, but also is very suitable to solve discrete optimization problems. Calculations of 0/1 knapsack problem show that algorithm has better convergence capability and stability.

Optimal Layout of Shell Stiffeners With Frequency Design Considerations

1995 ◽  
Author(s):  
Yong Fu ◽  
Hae Chang Gea
Keyword(s):  
Topology Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Optimal Layout ◽  
Two Phase ◽  
New Approach ◽  
Topology Optimization Problem ◽  
Design Considerations ◽  
Programming Tools ◽  
Effective Material Properties

Abstract In this paper, a new method to design the layout of shell stiffeners is introduced. This new approach has been derived from a two-phase spherical micro-inclusions model and resulted in very simple closed-form expressions for the effective material properties. The “relaxed” topology optimization problem can then be solved by general mathematical programming tools. It is very common to experience the eigenvalue switchover when solving topology optimization problems with frequency design considerations. An incremental objective function formulation with two strategies were studied to reduce the oscillation of optimization solutions. Design Examples are presented and compared.

Mode Pursuing Sampling Method for Discrete Variable Optimization on Expensive Black-Box Functions

2008 ◽  
Vol 130 (2) ◽  
Author(s):  
Behnam Sharif ◽  
G. Gary Wang ◽  
Tarek Y. ElMekkawy
Keyword(s):  
Global Optimization ◽  
Optimization Problems ◽  
Continuous Variable ◽  
Black Box ◽  
Test Problems ◽  
Continuous Variables ◽  
Optimization Strategy ◽  
Discrete Variable ◽  
Mps Method ◽  
Search Control

Based on previously developed Mode Pursuing Sampling (MPS) approach for continuous variables, a variation of MPS for discrete variable global optimization problems on expensive black-box functions is developed in this paper. The proposed method, namely, the discrete variable MPS (D-MPS) method, differs from its continuous variable version not only on sampling in a discrete space, but moreover, on a novel double-sphere strategy. The double-sphere strategy features two hyperspheres whose radii are dynamically enlarged or shrunk in control of, respectively, the degree of “exploration” and “exploitation” in the search of the optimum. Through testing and application to design problems, the proposed D-MPS method demonstrates excellent efficiency and accuracy as compared to the best results in literature on the test problems. The proposed method is believed a promising global optimization strategy for expensive black-box functions with discrete variables. The double-sphere strategy provides an original search control mechanism and has potential to be used in other search algorithms.

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