Meta-Heuristics Approach to Knapsack Problem in Memory Management

Abstract

The Knapsack Problems are among the simplest integer programs which are NP-hard. Problems in this class are typically concerned with selecting from a set of given items, each with a specified weight and value, a subset of items whose weight sum does not exceed a prescribed capacity and whose value is maximum. The classical 0-1 Knapsack Problem arises when there is one knapsack and one item of each type. This paper considers the application of classical 0-1 knapsack problem with a single constraint to computer memory management. The goal is to achieve higher efficiency with memory management in computer systems. This study focuses on using simulated annealing and genetic algorithm for the solution of knapsack problems in optimizing computer memory. It is shown that Simulated Annealing performs better than the Genetic Algorithm for large number of processes.

Data Collection in Times of Pandemic: A Self-Study and Revisit of Research Practices During a Crisis

“…This means that non-probability sampling including convenience, quota, purposive, and snowball methods are often accepted in qualitative studies ( Creswell, 2014 ; Kumar, 2019 ) despite their greater likelihood to incur bias ( Skowronek & Duerr, 2009 ). Instead, Greene and McClintock (1985) , Tuckett (2004) , as well as Oppong (2013) and Hassmain (2020) all suggest the inclusion of different data collection techniques or employing a mixed-method approach to allow further interrogation of similarities or differences in data to ensure data and research quality.…”

A Hybrid Harmony Search Algorithm with Distribution Estimation for Solving the 0-1 Knapsack Problem

“…Wang et al proposed an improved adaptive binary harmony search algorithm (ABHS) in order to solve the degradation (1) for j � 1: N (2) Calculate the probability of each dimension of the population being selected (3) if rand < HMCR% Consideration of harmony memory bank (4) Operate on a harmonic vector randomly selected from the harmony memory library (5) if rand < PAR% Determine whether to make pitch adjustment (6) If rand < probability % e probability generated by the distribution estimation algorithm is used for judgment (7) B (j) � 1; (8) Else ( 9) B (j) � 0; (10) end if (11) end if (12) else (13) x new (j) � round(rand); %Random variation produces a harmony (14) End if (15) End for ALGORITHM 4: A novel form of directed improvisation.…”

“…(3) Calculate the fitness value after initialization. (4) for i � 1 to J1 do (5) Find the worst and best harmony in the harmony memory database as p (6) Calculate fitness values and sort them (7) For i � 1: K% select the dominant population (8) e number of K populations with the highest fitness value was selected ( 9) end (10) For j � 1: N%% Generates new harmonies based on Guided Improvisation (11) Count the number of bags selected in each column (12) if rand < HMCR (13) r � ceil (HMS * rand) Randomly select the harmonic vector (14) if rand < PAR (15) If rand < probability (16) Update the corresponding harmonies (17) end (18) end (19) else Random mutation produces new harmonies (20) end (21) end for (22) e total capacity of the newly produced harmony is calculated (23) If the knapsack capacity requirement is met, the greedy selection is made under the constraint (24) If the knapsack capacity requirement is not met, the harmony is repaired (25) if fit (B) > fit (p) (26) Update the global lowest harmony ( 27) end (28) end for ALGORITHM 7: e HHSEDA algorithm for the 0-1 knapsack problem. worst value can indicate the advantages and disadvantages of each algorithm.…”

“…e 0-1 knapsack problem proposed by Fayard in 1975, is a typical combinatorial optimization problem [5] and a NP problem. It is widely applied in many areas such as investment decision making problems [6], cutting stock problem [7], the housing problem [8], cryptography [9], adaptive multimedia system [10], the portfolio choice [11,12], the computer memory [13], the allocation of resources [14], energy minimization [15,16], cargo load problem [17][18][19], real estate property maintenance optimization [20], the main budget [21] and blanking problem [7]. Many real-world optimization problems are similar to 0-1 knapsack problem, therefore, exploring approaches to e ectively solve 0-1 knapsack problem is important and it can o er new methods for some complex engineering optimization problems.…”

Fitness-Based Acceleration Coefficients Binary Particle Swarm Optimization (FACBPSO) to Solve the Discounted Knapsack Problem

“…For classical optimization problems, KP is modeled in such a way that total profit among selected items should be maximized within a given capacity. Additionally, KPs became popular from their emergence in many realworld applications [2] including investment decisions, cargo loading problems [3], energy minimization [4,5], resource allocation [6,7], computer memory [8], project portfolio selection [8][9][10], adaptive multimedia systems [11], housing problems [12], cutting-stock problems [13] and many others [7,10,14,15]. There are many variants of KPs such as the bounded knapsack problem (BKP), the unbounded knapsack problem (UKP), the multidimensional knapsack problem (MDKP), the multiple knapsack problem (MKP), the quadratic knapsack problem (QKP), the set-union knapsack problem (SUKP), the randomized time-varying knapsack problem (RTVKP), the quadratic multiple knapsack problem (QMKP), the multiple-choice multidimensional knapsack problem (MMKP) and the discounted knapsack problem (DKP) [16][17][18][19][20][21].…”